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what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | $ \large \blued2^\greene4=\goldd { 16 } \quad\iff\quad\log_\blued2 ( \goldd { 16 } ) =\greene4 $ both equations describe the same relationship between the numbers $ \blued2 $ , $ \greene4 $ , and $ \goldd { 16 } $ , where $ \blued2 $ is the base and $ \greene4 $ is the exponent . the difference is that while the expone... | is n't power and exponent same ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | $ \large \blued2^\greene4=\goldd { 16 } \quad\iff\quad\log_\blued2 ( \goldd { 16 } ) =\greene4 $ both equations describe the same relationship between the numbers $ \blued2 $ , $ \greene4 $ , and $ \goldd { 16 } $ , where $ \blued2 $ is the base and $ \greene4 $ is the exponent . the difference is that while the expone... | is n't power and exponent same ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | now , suppose someone asked us , `` $ \blued2 $ raised to which power equals $ \goldd { 16 } $ ? '' the answer would be $ \greene4 $ . this is expressed by the logarithmic equation $ \log_\blued2 ( \goldd { 16 } ) =\greene4 $ , read as `` log base two of sixteen is four '' . | how would you calculate logs with a calculator ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | these restrictions are a result of the connection between logarithms and exponents . restriction | reasoning : - | : - $ b & gt ; 0 $ | in an exponential function , the base $ b $ is always defined to be positive . $ a & gt ; 0 $ | $ \log_b ( a ) =c $ means that $ b^c=a $ . | why a and b must be bigger than 0 ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | let 's check them out . the common logarithm the common logarithm is a logarithm whose base is $ 10 $ ( `` base- $ 10 $ logarithm '' ) . when writing these logarithms mathematically , we omit the base . | what is the inverse of being a logarithm base ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | now consider the equation $ \log_1 ( 3 ) =x $ . the equivalent exponential form would be $ 1^x=3 $ . but this can never be true since $ 1 $ to any power is always $ 1 $ . so , it follows that $ b\neq1 $ . | log ( 1 ) =1 ( base 1 ) log ( 1 ) =0 ( base1 ) 1 could n't be equal to 0 ... can this be the reason why the base could n't be 0 ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . | so why do we use logs ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | it is understood to be $ 10 $ . $ \log_ { 10 } { ( x ) } =\log ( x ) $ the natural logarithm the natural logarithm is a logarithm whose base is the number $ e $ ( `` base- $ e $ logarithm '' ) . instead of writing the base as $ e $ , we indicate the logarithm with $ \ln $ . | does the ln stand for log natural ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | because a positive number raised to any power is positive , meaning $ b^c & gt ; 0 $ , it follows that $ a & gt ; 0 $ . $ b\neq1 $ | suppose , for a moment , that $ b $ could be $ 1 $ . now consider the equation $ \log_1 ( 3 ) =x $ . | would n't both restrictions together imply b has to be greater than 1 ( b > 0 ) ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | let 's check them out . the common logarithm the common logarithm is a logarithm whose base is $ 10 $ ( `` base- $ 10 $ logarithm '' ) . when writing these logarithms mathematically , we omit the base . | is n't log to the base 10 also written as lg ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | let 's check them out . the common logarithm the common logarithm is a logarithm whose base is $ 10 $ ( `` base- $ 10 $ logarithm '' ) . when writing these logarithms mathematically , we omit the base . | how does a logarithm table work ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | this is expressed by the exponential equation $ \blued2^\greene4=\goldd { 16 } $ . now , suppose someone asked us , `` $ \blued2 $ raised to which power equals $ \goldd { 16 } $ ? '' the answer would be $ \greene4 $ . | how would you simplify 4 raised to the power of log base 2 of 8x ? |
what you should be familiar with before taking this lesson you should be familiar with exponents , preferably including negative exponents . what you will learn in this lesson you will learn what logarithms are , and evaluate some basic logarithms . this will prepare you for future work with logarithm expressions and f... | $ \large\log_\blued b ( \goldd a ) =\greend c\quad \iff\quad \blued b^\greend c=\goldd a $ both equations describe the same relationship between $ \goldd a $ , $ \blued b $ , and $ \greene c $ : $ \blued b $ is the $ \blued { \text { base } } $ , $ \greene c $ is the $ \greene { \text { exponent } } $ , and $ \goldd a ... | or 4^log base 2 of 8x ? |
on the eve of the jewish holiday of passover , a child traditionally asks a critical question : “ why is this night different from all other nights ? ” this question sets up the ritual narration of the story of passover , when moses led the jews out of slavery in egypt with a series of miraculous events ( recounted in ... | the style of the manuscript may look familiar to you—it is very similar to christian gothic manuscripts such as the bible of saint louis ( below ) . look , for example , at the figure of moses and the pharaoh ( above ) . he doesn ’ t really look like an egyptian pharaoh at all but more like a french king . | in the picture of moses and aaron going before the pharaoh what is the pharaoh 's left hand holding ? |
on the eve of the jewish holiday of passover , a child traditionally asks a critical question : “ why is this night different from all other nights ? ” this question sets up the ritual narration of the story of passover , when moses led the jews out of slavery in egypt with a series of miraculous events ( recounted in ... | the reason it is called the `` golden '' haggadah is clear—each miniature is decorated with a brilliant gold-leaf background . as such , this manuscript would have been quite expensive to produce and was certainly owned by a wealthy jewish family . so although many haggadot show signs of use—splashes of wine , etc.—the... | i wonder if it would have been dangerous for a non-jewish artist to make images for a jewish patron such of this ( certainly the 14th century was not an era friendly to jews ) ? |
on the eve of the jewish holiday of passover , a child traditionally asks a critical question : “ why is this night different from all other nights ? ” this question sets up the ritual narration of the story of passover , when moses led the jews out of slavery in egypt with a series of miraculous events ( recounted in ... | 179-85 . julie harris , `` polemical images in the golden haggadah ( british library add . ms 27210 ) , '' medieval encounters , 8 ( 2002 ) , pp . | where is the golden haggadah ( the plagues of egypt , scenes of liberation , and preparation for passover ) located now ? |
on the eve of the jewish holiday of passover , a child traditionally asks a critical question : “ why is this night different from all other nights ? ” this question sets up the ritual narration of the story of passover , when moses led the jews out of slavery in egypt with a series of miraculous events ( recounted in ... | whether the artists of the golden haggadah themselves were jewish is open to debate , although it is certainly evident that regardless of their religious beliefs , the dominant style of christian art in europe clearly influenced the artists of this manuscript . cross-cultural styles so the golden haggadah is both styli... | since the creator of the piece is unknown , is n't it possible this could have originally been christian art ? |
the human body is amazingly complex and yet , it functions because of a molecule that supports many of our essential life processes - called atp ( adenosine triphosphate ) . atp is the energy currency of the cell and provides energy for processes that build molecules and tissues , to transport molecules across the cell... | step 2 as the hydronium ion was made in step 1 , the electrons that make the bond between the stolen hydrogen and its original water molecule are donated as a third lone pair to the oxygen of the robbed molecule . the robbed molecule is a hydroxyl group that is unstable , meaning it is eager to form new bonds . step 3 ... | should n't the electrons hydroxyl group in figure 3 be attacking the phosphorus , not the oxygen of atp ? |
the human body is amazingly complex and yet , it functions because of a molecule that supports many of our essential life processes - called atp ( adenosine triphosphate ) . atp is the energy currency of the cell and provides energy for processes that build molecules and tissues , to transport molecules across the cell... | the human body is amazingly complex and yet , it functions because of a molecule that supports many of our essential life processes - called atp ( adenosine triphosphate ) . atp is the energy currency of the cell and provides energy for processes that build molecules and tissues , to transport molecules across the cell... | if so is the written/drawn material at least fixed ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | they can be attached to the ends of integral proteins , or not , and help with transport or communication . what makes the cell membrane fluid ? the fluid mosaic model of the cell membrane is how scientists describe what the cell membrane looks and functions like , because it is made up of a bunch of different molecule... | how exactly does the structure of a cell membrane supports its functions ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | the movement of the mosaic of molecules makes it impossible to form a completely impenetrable barrier . there are 3 main factors that influence cell membrane fluidity : temperature : the temperature will affect how the phospholipids move and how close together they are found . when it ’ s cold they are found closer tog... | how do lipid rafts affect membrane fluidity ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | nonpolar means the electrons are evenly distributed , so the molecule is evenly charged across the surface . the other class of protein is called peripheral proteins , which don ’ t extend across the membrane . they can be attached to the ends of integral proteins , or not , and help with transport or communication . | i 'd expect large protein aggregates in the membrane to decrease fluidity ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | integral proteins are nestled into the phospholipid bilayer and stick out on either end . integral proteins are helpful for transporting larger molecules , like glucose , across the cell membrane . they have regions , called “ polar ” and “ nonpolar ” regions , that correspond with the polarity of the phospholipid bila... | how does nonpolar molecules move across the membrane ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | they can be attached to the ends of integral proteins , or not , and help with transport or communication . what makes the cell membrane fluid ? the fluid mosaic model of the cell membrane is how scientists describe what the cell membrane looks and functions like , because it is made up of a bunch of different molecule... | what is the actual size of the smallest thing in the cell ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | when it ’ s cold they are found closer together and when it ’ s hot they move farther apart . cholesterol : the cholesterol molecules are randomly distributed across the phospholipid bilayer , helping the bilayer stay fluid in different environmental conditions . the cholesterol holds the phospholipids together so that... | how does phospholipid movement ( flipping , flopping , scrambling ) in the bilayer contribute to the survival of a cell ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | integral proteins are helpful for transporting larger molecules , like glucose , across the cell membrane . they have regions , called “ polar ” and “ nonpolar ” regions , that correspond with the polarity of the phospholipid bilayer . polar and nonpolar refer to the concentration of electrons on a molecule . polar mea... | but would n't the molecule want to stay in-between the two layers , in the nonpolar part of the bilayer ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | they can be attached to the ends of integral proteins , or not , and help with transport or communication . what makes the cell membrane fluid ? the fluid mosaic model of the cell membrane is how scientists describe what the cell membrane looks and functions like , because it is made up of a bunch of different molecule... | why cell surface membrane is described as fluid mosaic ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | one of these is alzheimer ’ s disease , characterized by brain shrinkage and memory loss . one idea explaining why alzheimer ’ s disease occurs is the forming of plaque sticking to the phospholipid bilayer of the brain neurons . these plaques block communication between the brain neurons , eventually leading to neuron ... | from the last article , from where did the plaque , sticking to the phospholipid bilayer of the brain neurons causing symptoms of alzheimer came from ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | they can be attached to the ends of integral proteins , or not , and help with transport or communication . what makes the cell membrane fluid ? the fluid mosaic model of the cell membrane is how scientists describe what the cell membrane looks and functions like , because it is made up of a bunch of different molecule... | what property of the cell membrane does this represent ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | without cholesterol , the phospholipids start to separate from each other , leaving large gaps . saturated and unsaturated fatty acids : fatty acids are what make up the phospholipid tails . saturated fatty acids are chains of carbon atoms that have single bonds between them . | can a unsaturated fatty acid become saturated , can the phospholipid become kinked and than straight in a repeating process , back and forth ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | they can be attached to the ends of integral proteins , or not , and help with transport or communication . what makes the cell membrane fluid ? the fluid mosaic model of the cell membrane is how scientists describe what the cell membrane looks and functions like , because it is made up of a bunch of different molecule... | also , how are dead phospholipid 's replaced in the cell membrane ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | recall that the interior of the phospholipid bilayer is made up of the hydrophobic tails . it won ’ t be easy for the water molecules to cross , but they can cross without the help of proteins . this is a somewhat slower process . large , nonpolar molecules ( ex : carbon rings ) : these rings can pass through but it is... | am i correct in thinking that water molecules can pass through the cell wall without protein channels but the process is slow due to the fact that the middle of the cell wall is hydrophobic ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | we ’ ll talk about this in more depth later , but for now remember it ’ s part of the cell membrane . 3 ) proteins the cell is made up of two different types , or “ classes ” , of proteins . integral proteins are nestled into the phospholipid bilayer and stick out on either end . | is it that an alzheimer 's patient may be lacking a certain type of protein , like the channel protein and carrier proteins that aid the passage of different things in the cell ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | nonpolar means the electrons are evenly distributed , so the molecule is evenly charged across the surface . the other class of protein is called peripheral proteins , which don ’ t extend across the membrane . they can be attached to the ends of integral proteins , or not , and help with transport or communication . | can we consider receptor protein as one kind of peripheral protein ? |
it may seem like the human body is made up of a chaotic mix of random parts , but that ’ s not the case . the liquid nutrients , cell machinery , and blueprint information that make up the human body are tucked away inside individual cells , surrounded by a double layer of lipids . the purpose of the cell membrane is t... | nonpolar means the electrons are evenly distributed , so the molecule is evenly charged across the surface . the other class of protein is called peripheral proteins , which don ’ t extend across the membrane . they can be attached to the ends of integral proteins , or not , and help with transport or communication . | if not , what is the main function of the peripheral protein ? |
key points if inventors received a greater share of the broader social benefits for their work , they would have a greater incentive to seek out new inventions . positive externalities are beneficial spillovers to a third party or parties . private benefits are the dollar value of all benefits of a new product or proce... | samsung ’ s r & amp ; d investment in digital devices has increased profits by 20 % . is this a private or social benefit ? the gizmo company is planning to develop new household gadgets . | regarding the junkbuyers company self-check question , how are we certain that the social benefit outweighs the private benefit ? |
the word “ icon ” refers to many different things today . for example , we use this word to refer to the small graphic symbols in our software and to powerful cultural figures . nevertheless , these different meanings retain a connection to the word 's original meaning . “ icon ” is greek for “ image ” or “ painting ” ... | the conflict pitted the emperor and certain high church officials ( patriarchs , bishops ) who supported iconoclasm , against other bishops , lower clergy , laity and monks , who defended the icons . the original theological basis for iconoclasm was fairly weak . arguments relied mostly on the old testament prohibition... | how does iconoclasm translate in the muslim world at that time ? |
the word “ icon ” refers to many different things today . for example , we use this word to refer to the small graphic symbols in our software and to powerful cultural figures . nevertheless , these different meanings retain a connection to the word 's original meaning . “ icon ” is greek for “ image ” or “ painting ” ... | the conflict pitted the emperor and certain high church officials ( patriarchs , bishops ) who supported iconoclasm , against other bishops , lower clergy , laity and monks , who defended the icons . the original theological basis for iconoclasm was fairly weak . arguments relied mostly on the old testament prohibition... | why would people do iconoclasm ? |
the word “ icon ” refers to many different things today . for example , we use this word to refer to the small graphic symbols in our software and to powerful cultural figures . nevertheless , these different meanings retain a connection to the word 's original meaning . “ icon ” is greek for “ image ” or “ painting ” ... | the word “ icon ” refers to many different things today . for example , we use this word to refer to the small graphic symbols in our software and to powerful cultural figures . | what are the differences between the theology of the west and that of the east regarding this issue ? |
the word “ icon ” refers to many different things today . for example , we use this word to refer to the small graphic symbols in our software and to powerful cultural figures . nevertheless , these different meanings retain a connection to the word 's original meaning . “ icon ” is greek for “ image ” or “ painting ” ... | they claimed that the iconoclast arguments were simply confused . images of christ do not depict natures , being either divine or human , but a concrete person—jesus christ , the incarnate son of god . they claimed that in christ the meaning of the old testament prohibition is revealed : god prohibited any representati... | since they made images of jesus christ in the west , would they have said that christ is purely human to avoid making a picture of god ? |
the word “ icon ” refers to many different things today . for example , we use this word to refer to the small graphic symbols in our software and to powerful cultural figures . nevertheless , these different meanings retain a connection to the word 's original meaning . “ icon ” is greek for “ image ” or “ painting ” ... | the iconophile ( pro-icon ) counter-argument was most convincingly articulated by st. john of damascus and st. theodore the studite . they claimed that the iconoclast arguments were simply confused . images of christ do not depict natures , being either divine or human , but a concrete person—jesus christ , the incarna... | is n't the opposite of an iconoclast an iconodule , not an iconophile ? |
the word “ icon ” refers to many different things today . for example , we use this word to refer to the small graphic symbols in our software and to powerful cultural figures . nevertheless , these different meanings retain a connection to the word 's original meaning . “ icon ” is greek for “ image ” or “ painting ” ... | they produced the icons and were a primary target of the violence of the iconoclastic controversy . other scholars offer a less political motive , suggesting that the prohibition was primarily religious , an attempt to correct the wayward practice of worshiping images . the trigger for leo iii ’ s prohibition may have ... | how does the smashing of religious images affect the world today ? |
the word “ icon ” refers to many different things today . for example , we use this word to refer to the small graphic symbols in our software and to powerful cultural figures . nevertheless , these different meanings retain a connection to the word 's original meaning . “ icon ” is greek for “ image ” or “ painting ” ... | both muslims and jews perceived christian images ( that existed from the earliest times of christianity ) as idols and in direct opposition to the old testament prohibition of visual representations . the first commandment states , you shall have no other gods before me . you shall not make for yourself a carved image ... | in the sixth paragraph you that the second commandment is you shall not make for your-self a carved image ... what about `` thou shalt not take the name of the lord your god in vain '' ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | note that we indicated the image by $ \maroond { a ' } $ —pronounced a prime . it is common , when working with transformations , to use the same letter for the image and the source ; simply add the prime suffix to the image . let 's try some practice problems problem 1 problem 2 problem 3 challenge problem 1 $ \maroon... | can you add more easy science for 7th grade and also social studies plz thx ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! | up at challenge problem 1 , point t is `` a rotation about p by -90 degrees '' , but could it also be a rotation about p by 270 ( positive ) degrees ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | clockwise and counterclockwise rotations conventionally , positive angle measures describe counterclockwise rotations . if we want to describe a clockwise rotation , we use negative angle measures . for example , here 's the result of rotating a point about $ p $ by –30 $ ^\circ $ . | how can i translate negative numbers across the origin ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | now that we 've got a basic understanding of what rotations are , let 's learn how to use them in a more exact manner . the angle of rotation every rotation is defined by two important parameters : the center of the rotation—we already went over that—and the angle of the rotation . the angle determines by how much we r... | where did it tell you the expression that represents the angle of rotation like in the last problem ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . | what color is red if purple is green ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | in order to define the measure of the rotation , we look at the angle that 's created between the segments $ \overline { pa } $ and $ \overline { pa ' } $ . this way , we can say that $ \maroond { a ' } $ is the result of rotating $ \blued { a } $ by 45 $ ^\circ $ about $ p $ . clockwise and counterclockwise rotations ... | so is there a way to calculate how calculate where the line segment will go , without using this online tool ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | it is common , when working with transformations , to use the same letter for the image and the source ; simply add the prime suffix to the image . let 's try some practice problems problem 1 problem 2 problem 3 challenge problem 1 $ \maroond { r } $ , $ \maroond { s } $ , and $ \maroond { t } $ are all images of $ \bl... | in the challenge problem # 2 , how is it that a and b represents the angle of the rotation ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . | how big is the moon ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | move the point across this slider to see how a square is rotated about one of its vertices . notice how the square 's sides change direction , but the general shape remains the same . rotations do n't distort shapes , they just whirl them around . furthermore , note that the vertex that is the center of the rotation do... | what are the rules for ( x , y ) when you rotate a shape around ( 0 , 0 ) ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | clockwise and counterclockwise rotations conventionally , positive angle measures describe counterclockwise rotations . if we want to describe a clockwise rotation , we use negative angle measures . for example , here 's the result of rotating a point about $ p $ by –30 $ ^\circ $ . | if the rotation if -90 degrees , does that mean that the object was rotated 90 degrees counter-clockwise ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | this way , we can say that $ \maroond { a ' } $ is the result of rotating $ \blued { a } $ by 45 $ ^\circ $ about $ p $ . clockwise and counterclockwise rotations conventionally , positive angle measures describe counterclockwise rotations . if we want to describe a clockwise rotation , we use negative angle measures . | how do i perform rotations without a tool ? |
to see what a rotation is , grab the point on the slider and move it from side to side . this will cause the other point to rotate about point $ p $ . nice ! you rotated a point . in geometry , rotations make things turn in a cycle around a definite center point . notice that the distance of the rotated point from the ... | notice how the square 's sides change direction , but the general shape remains the same . rotations do n't distort shapes , they just whirl them around . furthermore , note that the vertex that is the center of the rotation does not move at all . | are red lumps around my armpits healthy ? |
key points : apoptosis is a form of programmed cell death , or “ cellular suicide. ” it is different from necrosis , in which cells die due to injury . apoptosis is an orderly process in which the cell ’ s contents are packaged into small packets of membrane for “ garbage collection ” by immune cells . apoptosis remove... | phosphatidylserine is usually hidden on the inside of the membrane , and when it is on the outside , it lets the phagocytes bind and `` eat '' the cell fragments . why do cells undergo apoptosis ? many cells in the human body have the built-in ability to undergo apoptosis ( in the same way that they have the built-in a... | if cells undergo apoptosis to get rid of default or harmful cells why do we have diseases of the cell like sickle cell anemia or cancer ? |
key points : apoptosis is a form of programmed cell death , or “ cellular suicide. ” it is different from necrosis , in which cells die due to injury . apoptosis is an orderly process in which the cell ’ s contents are packaged into small packets of membrane for “ garbage collection ” by immune cells . apoptosis remove... | in this article , we ’ ll take a closer look at apoptosis , seeing when it happens and why it ’ s important . apoptosis vs. necrosis broadly speaking , there are two ways that cells die in a multicellular organism such as yourself : they are killed by things that harm them ( such as toxic chemicals or physical injury )... | for multicellular organism we have things like apoptosis and necrosis , what about organism with only one cell ? |
key points : apoptosis is a form of programmed cell death , or “ cellular suicide. ” it is different from necrosis , in which cells die due to injury . apoptosis is an orderly process in which the cell ’ s contents are packaged into small packets of membrane for “ garbage collection ” by immune cells . apoptosis remove... | phosphatidylserine is usually hidden on the inside of the membrane , and when it is on the outside , it lets the phagocytes bind and `` eat '' the cell fragments . why do cells undergo apoptosis ? many cells in the human body have the built-in ability to undergo apoptosis ( in the same way that they have the built-in a... | in this essay , '' eliminating bad cells '' function of apoptosis is mentioned.can we kill cancers and infections by expanding this function of apoptosis ? |
key points : apoptosis is a form of programmed cell death , or “ cellular suicide. ” it is different from necrosis , in which cells die due to injury . apoptosis is an orderly process in which the cell ’ s contents are packaged into small packets of membrane for “ garbage collection ” by immune cells . apoptosis remove... | this often causes inflammation in the tissue surrounding the dead cell . apoptosis ( the tidy way ) cells that undergo apoptosis go through a different and much more orderly process . they shrink and develop bubble-like protrusions ( technical name : “ blebs ” ) on their surface . | how could the process of apoptosis hurt a multi-cellular organism ? |
key points : apoptosis is a form of programmed cell death , or “ cellular suicide. ” it is different from necrosis , in which cells die due to injury . apoptosis is an orderly process in which the cell ’ s contents are packaged into small packets of membrane for “ garbage collection ” by immune cells . apoptosis remove... | other examples of apoptosis during normal development include the loss of a tadpole ’ s tail as it turns into a frog , and the removal of unneeded neurons in as neural circuits in the brain are “ wired. ” apoptosis can eliminate infected or cancerous cells in some cases , a cell can pose a threat to the rest of the bod... | some viruses induce apoptoses in cells , but i do n't understand why they would want to do that , because then they will die aswell right ? |
key points : apoptosis is a form of programmed cell death , or “ cellular suicide. ” it is different from necrosis , in which cells die due to injury . apoptosis is an orderly process in which the cell ’ s contents are packaged into small packets of membrane for “ garbage collection ” by immune cells . apoptosis remove... | apoptosis vs. necrosis broadly speaking , there are two ways that cells die in a multicellular organism such as yourself : they are killed by things that harm them ( such as toxic chemicals or physical injury ) , a process called necrosis . they are triggered to undergo programmed cell death . the best-understood form ... | could you please clarify the role that calcium plays in programmed cell death ? |
key points : apoptosis is a form of programmed cell death , or “ cellular suicide. ” it is different from necrosis , in which cells die due to injury . apoptosis is an orderly process in which the cell ’ s contents are packaged into small packets of membrane for “ garbage collection ” by immune cells . apoptosis remove... | apoptosis is part of development in many organisms , programmed cell death is a normal part of development . in some cases , apoptosis during development occurs in a very predictable way : in the worm c. elegans , $ 131 $ cells will die by apoptosis as the worm develops from a single cell to an adult ( and we know exac... | i want to know apoptosis occurs in which phase , or cell can program to die in each phase ? |
on the road imagine you pack up your belongings in a sack , tie on your cloak , and start off on a months-long journey through treacherous mountains , unpredictable weather and unknown lands . for the medieval pilgrim , life was a spiritual journey . why did people in the middle ages take pilgrimages ? there are many r... | indeed , this portal was not only a warning for pilgrims , but for the clergy who lived in conques as well . the reliquary pilgrims arriving in conques had one thing on their mind : the reliquary of saint foy . this reliquary , or container holding the remains of a saint or holy person , was one of the most famous in a... | is the reliquary the physical container of the relic ( in this case , the gold figure around foy 's skull ) , or can we call the whole church itself a reliquary ? |
on the road imagine you pack up your belongings in a sack , tie on your cloak , and start off on a months-long journey through treacherous mountains , unpredictable weather and unknown lands . for the medieval pilgrim , life was a spiritual journey . why did people in the middle ages take pilgrimages ? there are many r... | and if you were closer to god in this life , you would also be closer to god in the next . a romanesque pilgrimage church : saint-foy , conques located in conques , the church of saint-foy ( saint faith ) is an important pilgrimage church on the route to santiago de compostela in northern spain . it is also an abbey , ... | what is the artists innovation for creating the church ? |
on the road imagine you pack up your belongings in a sack , tie on your cloak , and start off on a months-long journey through treacherous mountains , unpredictable weather and unknown lands . for the medieval pilgrim , life was a spiritual journey . why did people in the middle ages take pilgrimages ? there are many r... | at first , bernard was frightened that the statue was too beautiful stating , `` brother , what do you think of this idol ? would jupiter or mars consider himself unworthy of such a statue ? '' he was concerned about idolatry—that pilgrims would begin to worship the jewel-encrusted reliquary rather than what that reliq... | is there any sort of reconstruction , what it would have looked like freshly painted ? |
overview richard m. nixon served as president of the united states from 1969 to 1974 . nixon attempted to extricate the united states from the ongoing war in vietnam with limited success . although his administration negotiated a cease-fire in 1973 , in 1975 north vietnam overran the south and united the country under ... | tapes of nixon 's conversations in the oval office revealed that he had forbidden the fbi from investigating the incident , a clear obstruction of justice . facing impeachment , nixon resigned in 1974 . he was succeeded by vice president gerald ford , who immediately pardoned nixon on all charges. $ ^ { 11 } $ what do ... | why exactly did president ford pardon nixon ? |
overview richard m. nixon served as president of the united states from 1969 to 1974 . nixon attempted to extricate the united states from the ongoing war in vietnam with limited success . although his administration negotiated a cease-fire in 1973 , in 1975 north vietnam overran the south and united the country under ... | the burger court had a mixed record on racial issues , however , extending affirmative action protections but ruling against busing students to combat de facto segregation. $ ^9 $ economically , nixon tried and failed to cope with the growing issue of stagflation , an unprecedented combination of wage stagnation and pr... | what is the gold standard ? |
overview richard m. nixon served as president of the united states from 1969 to 1974 . nixon attempted to extricate the united states from the ongoing war in vietnam with limited success . although his administration negotiated a cease-fire in 1973 , in 1975 north vietnam overran the south and united the country under ... | in 1972 , allegations emerged that nixon loyalists had wiretapped the democratic national committee office in washington 's watergate building in order to spy on democratic nominee george mcgovern . tapes of nixon 's conversations in the oval office revealed that he had forbidden the fbi from investigating the incident... | is it mandatory for president 's to record conversations that occur in the oval office ? |
overview richard m. nixon served as president of the united states from 1969 to 1974 . nixon attempted to extricate the united states from the ongoing war in vietnam with limited success . although his administration negotiated a cease-fire in 1973 , in 1975 north vietnam overran the south and united the country under ... | facing impeachment , nixon resigned in 1974 . he was succeeded by vice president gerald ford , who immediately pardoned nixon on all charges. $ ^ { 11 } $ what do you think ? was vietnamization a good idea ? | was gerald ford a popular president ? |
the adena complex , in the middle and upper ohio valley , is the most significant evidence of an early woodlands society in the last millennium b.c.e . the economy was based on hunting and fishing , and from 100 b.c.e . apparently also on the growing of squash , pumpkin , sunflowers , goosefoot and marsh elder . buria... | the economy was based on hunting and fishing , and from 100 b.c.e . apparently also on the growing of squash , pumpkin , sunflowers , goosefoot and marsh elder . burial mounds were constructed in several stages , with log-lined pits containing burials with fine grave goods , including smoking pipes . | what is goosefoot and marsh elder ? |
the adena complex , in the middle and upper ohio valley , is the most significant evidence of an early woodlands society in the last millennium b.c.e . the economy was based on hunting and fishing , and from 100 b.c.e . apparently also on the growing of squash , pumpkin , sunflowers , goosefoot and marsh elder . buria... | if not , who built them ? the `` moundbuilder myth '' most american antiquarians thought that the scale and magnificence of the earthworks indicated that they had been erected by an unrelated people , the `` moundbuilders , '' whom the native indian replaced . to support their theory , they claimed that the otter pipes... | are there `` hopewell '' human remains , or coprolitefor dna samples to compare with native american groups today ? |
the adena complex , in the middle and upper ohio valley , is the most significant evidence of an early woodlands society in the last millennium b.c.e . the economy was based on hunting and fishing , and from 100 b.c.e . apparently also on the growing of squash , pumpkin , sunflowers , goosefoot and marsh elder . buria... | mounds were constructed within large earthworks that were probably built for ceremonial and economic purposes , rather than as defensive strongpoints . one or two double pots of this type have been recovered from mound sites . they are decorated with figures which represent aquatic and/or raptorial birds , suggesting t... | what is the mound builder myth ? |
the adena complex , in the middle and upper ohio valley , is the most significant evidence of an early woodlands society in the last millennium b.c.e . the economy was based on hunting and fishing , and from 100 b.c.e . apparently also on the growing of squash , pumpkin , sunflowers , goosefoot and marsh elder . buria... | the economy was based on hunting and fishing , and from 100 b.c.e . apparently also on the growing of squash , pumpkin , sunflowers , goosefoot and marsh elder . burial mounds were constructed in several stages , with log-lined pits containing burials with fine grave goods , including smoking pipes . | also did the moundbuilders have their homes underground ; if not did they have anything underground ? |
near misses in place of meaningful interactions , the four characters inside the diner of edward hopper ’ s nighthawks are involved in a series of near misses . the man and woman might be touching hands , but they aren ’ t . the waiter and smoking-man might be conversing , but they ’ re not . the couple might strike up... | this is a world shut down . because our characters are awake , they are alienated—not only from each other , but also from civilization itself . a timeless feel nighthawks is one of hopper ’ s new york city paintings , and the artist said that it was based on a real café . | what is about this particular time period that caused artists of all arts , to express this feelings of loneliness and epitomize it in mainly cynical and broken characters ? |
near misses in place of meaningful interactions , the four characters inside the diner of edward hopper ’ s nighthawks are involved in a series of near misses . the man and woman might be touching hands , but they aren ’ t . the waiter and smoking-man might be conversing , but they ’ re not . the couple might strike up... | the windows of the shops and apartments are empty and dark . the only remnants of human activity outside the diner are a cash register in a shop window and a cigar advertisement above the glass pane . there is no clock in the restaurant , but the empty coffee tureens on the back counter betray the indecent hour of nigh... | what do you think the purpose of the cash register is supposed to elude to ? |
near misses in place of meaningful interactions , the four characters inside the diner of edward hopper ’ s nighthawks are involved in a series of near misses . the man and woman might be touching hands , but they aren ’ t . the waiter and smoking-man might be conversing , but they ’ re not . the couple might strike up... | the angle also allows him to show the people in a mix of frontal and profile views , heightening the sense that no figure is really communicating with another . this feeling can be understood by comparing nighthawks to hopper ’ s earlier painting early sunday morning . both paintings are set in front of the red brick a... | why is certain parts of the painting oddly colored ? |
art for the sake of art the aesthetic movement , also known as “ art for art ’ s sake , ” permeated british culture during the latter part of the 19th century , as well as spreading to other countries such as the united states . based on the idea that beauty was the most important element in life , writers , artists an... | in the visual arts in the visual arts , the concept of art for arts sake was widely influential . many of the later paintings of dante gabriel rossetti , such as monna vanna ( above ) , are simply portraits of beautiful women that are pleasing to the eye , rather than related to some literary story as in earlier pre-ra... | what were the after-affects of the pre-raphaelite 's actions ? |
art for the sake of art the aesthetic movement , also known as “ art for art ’ s sake , ” permeated british culture during the latter part of the 19th century , as well as spreading to other countries such as the united states . based on the idea that beauty was the most important element in life , writers , artists an... | art for the sake of art the aesthetic movement , also known as “ art for art ’ s sake , ” permeated british culture during the latter part of the 19th century , as well as spreading to other countries such as the united states . based on the idea that beauty was the most important element in life , writers , artists an... | why was `` art for art 's sake '' and beauty without context such a controversial idea ? |
overview rome went from being one of many city-states in the italian peninsula to being the center of the most powerful empire in the world between the fifth century bce and the first century ce . during the republican period of rome , political offices and institutions were designed to prevent any one man from becomin... | although the office of consul probably did not exist in its final form until around 300 bce , the idea behind this change—to prevent any one man from becoming too powerful—was present early on in roman thought and shaped many of rome ’ s political institutions . roman political institutions reflected roman society , wh... | when did people start calling it that , and did they call it that at the same time as the roman empire was flourishing ? |
overview rome went from being one of many city-states in the italian peninsula to being the center of the most powerful empire in the world between the fifth century bce and the first century ce . during the republican period of rome , political offices and institutions were designed to prevent any one man from becomin... | some owners of large farms even switched from growing staple grains to high-value crops , such as olives and grapes , or raising animals—this wouldn ’ t have been an option for small family farms . review the map above . how might roman expansion have impacted trade patterns ? | are the units in that map of the aqueducts in kilometers or miles ? |
overview rome went from being one of many city-states in the italian peninsula to being the center of the most powerful empire in the world between the fifth century bce and the first century ce . during the republican period of rome , political offices and institutions were designed to prevent any one man from becomin... | each century—or voting group—had one vote , but the wealthy were split into smaller groups than the poor , giving the vote of a wealthy roman more influence . in what ways did the romans limit the political power of any one man ? how did roman political structures limit the influence of the poor ? | n what ways did the romans limit the political power of any one man ? |
overview rome went from being one of many city-states in the italian peninsula to being the center of the most powerful empire in the world between the fifth century bce and the first century ce . during the republican period of rome , political offices and institutions were designed to prevent any one man from becomin... | in what ways did the romans limit the political power of any one man ? how did roman political structures limit the influence of the poor ? military although the voting system might appear a deliberate strategy to empower the wealthy , it was actually a reflection of the roman military structure . | how did roman political structures limit the influence of the poor ? |
overview rome went from being one of many city-states in the italian peninsula to being the center of the most powerful empire in the world between the fifth century bce and the first century ce . during the republican period of rome , political offices and institutions were designed to prevent any one man from becomin... | as rome expanded its influence over more and more areas , its political institutions proved both resilient and adaptable , allowing it to incorporate diverse populations . according to roman tradition , the republic began in 509 bce when a group of noblemen overthrew the last king of rome . the romans replaced the king... | how long has roman republic been around ? |
overview rome went from being one of many city-states in the italian peninsula to being the center of the most powerful empire in the world between the fifth century bce and the first century ce . during the republican period of rome , political offices and institutions were designed to prevent any one man from becomin... | although the office of consul probably did not exist in its final form until around 300 bce , the idea behind this change—to prevent any one man from becoming too powerful—was present early on in roman thought and shaped many of rome ’ s political institutions . roman political institutions reflected roman society , wh... | and is roman empire and roman republic the same ? |
overview rome went from being one of many city-states in the italian peninsula to being the center of the most powerful empire in the world between the fifth century bce and the first century ce . during the republican period of rome , political offices and institutions were designed to prevent any one man from becomin... | the plebeian council had real power and influence in roman politics and some plebeians gained power and wealth under these new arrangements , but many remained poor . one reason that political rights did not lead to major changes was that the comitia centuriata—the main voting assembly that elected consuls and other im... | what is actually 'comitia centuriata ' ? |
systems of equations that have the same solution are called equivalent systems . given a system of two equations , we can produce an equivalent system by replacing one equation by the sum of the two equations , or by replacing an equation by a multiple of itself . in contrast , we can be sure that two systems of equati... | for example , $ x=1 $ , $ y=1 $ is a solution to the second equation in system a , but it 's not a solution to the second equation in system b . system a and system b are not equivalent . want to learn more about non-equivalent systems of equations ? check out this video practice want more practice ? | i do n't really understand the non-equivalent system of equations ; how do you work out which equations are equivalent and which are not ? |
systems of equations that have the same solution are called equivalent systems . given a system of two equations , we can produce an equivalent system by replacing one equation by the sum of the two equations , or by replacing an equation by a multiple of itself . in contrast , we can be sure that two systems of equati... | systems of equations that have the same solution are called equivalent systems . given a system of two equations , we can produce an equivalent system by replacing one equation by the sum of the two equations , or by replacing an equation by a multiple of itself . | why does it say that only the solution needs to be the same for two systems of equations to be equivalent ? |
key points : boveri and sutton 's chromosome theory of inheritance states that genes are found at specific locations on chromosomes , and that the behavior of chromosomes during meiosis can explain mendel ’ s laws of inheritance . thomas hunt morgan , who studied fruit flies , provided the first strong confirmation of ... | in the end , it was confirmed through the work of geneticist thomas hunt morgan and his students , who studied the genetics of fruit flies $ ^5 $ . t. h. morgan : fun with fruit flies morgan chose the fruit fly , drosophila melanogaster , for his genetic studies . what fruit flies may lack in charisma ( depending on yo... | with genotype xw+xw ) female fruit fly ? |
key points : boveri and sutton 's chromosome theory of inheritance states that genes are found at specific locations on chromosomes , and that the behavior of chromosomes during meiosis can explain mendel ’ s laws of inheritance . thomas hunt morgan , who studied fruit flies , provided the first strong confirmation of ... | confirming the model morgan did lots of other experiments to confirm an x chromosome location for the eye color gene . he was careful to rule out alternative possibilities ( for instance , that it was simply impossible to get a white-eyed female fruit fly ) $ ^6 $ . pulling together all of his observations , morgan con... | do n't we get a white eyed female fruit fly ? |
key points : boveri and sutton 's chromosome theory of inheritance states that genes are found at specific locations on chromosomes , and that the behavior of chromosomes during meiosis can explain mendel ’ s laws of inheritance . thomas hunt morgan , who studied fruit flies , provided the first strong confirmation of ... | in 1902 and 1903 , sutton and boveri published independent papers proposing what we now call the chromosome theory of inheritance . this theory states that individual genes are found at specific locations on particular chromosomes , and that the behavior of chromosomes during meiosis can explain why genes are inherited... | if mendelian characters are determined by genes located on the chromosomes and if the independent assortment of mendelian traits reflects the independent assortment if chromosomes in meiosis , why does the number of characters that assort independently in a given kind of organism often greatly exceed the number of chro... |
key points : boveri and sutton 's chromosome theory of inheritance states that genes are found at specific locations on chromosomes , and that the behavior of chromosomes during meiosis can explain mendel ’ s laws of inheritance . thomas hunt morgan , who studied fruit flies , provided the first strong confirmation of ... | this may have come as a surprise to morgan , who had been a critic of the chromosome theory $ ^ { 7 } $ ! a `` sex limited '' inheritance pattern $ ^6 $ what made morgan think that the eye color gene was on the x chromosome ? let 's look at some of his data . | why is the white eye mutant gene on the x chromosome and not the y chromosome ? |
factoring a polynomial involves writing it as a product of two or more polynomials . it reverses the process of polynomial multiplication . in this article , we 'll learn how to factor perfect square trinomials using special patterns . this reverses the process of squaring a binomial , so you 'll want to understand tha... | if we rewrite the equations in the reverse order , we will have patterns for factoring polynomials of the form $ a^2\pm2ab+b^2 $ . $ \blued a^2+2\blued a\greend b+\greend b^2~= ( \blued a+\greend b ) ^2 $ $ \blued a^2-2\blued a\greend b+\greend b^2~= ( \blued a-\greend b ) ^2 $ we can apply the first pattern to factor ... | what do the a and b stand for in the equation a^2+2ab+b^2 ? |
factoring a polynomial involves writing it as a product of two or more polynomials . it reverses the process of polynomial multiplication . in this article , we 'll learn how to factor perfect square trinomials using special patterns . this reverses the process of squaring a binomial , so you 'll want to understand tha... | if we rewrite the equations in the reverse order , we will have patterns for factoring polynomials of the form $ a^2\pm2ab+b^2 $ . $ \blued a^2+2\blued a\greend b+\greend b^2~= ( \blued a+\greend b ) ^2 $ $ \blued a^2-2\blued a\greend b+\greend b^2~= ( \blued a-\greend b ) ^2 $ we can apply the first pattern to factor ... | is there any more formulas like ( a+b ) ^2 ? |
factoring a polynomial involves writing it as a product of two or more polynomials . it reverses the process of polynomial multiplication . in this article , we 'll learn how to factor perfect square trinomials using special patterns . this reverses the process of squaring a binomial , so you 'll want to understand tha... | example 1 : factoring $ x^2+8x+16 $ notice that both the first and last terms are perfect squares : $ x^2= ( \blued x ) ^2 $ and $ 16= ( \greend4 ) ^2 $ . additionally , notice that the middle term is two times the product of the numbers that are squared : $ 2 ( \blued x ) ( \greend 4 ) =8x $ . this tells us that the p... | and how to factorize irrational numbers ? |
on august 21 , 2017 , the mainland united states will experience an event that hasn ’ t happened across the entire country in about a century - a total solar eclipse ! a solar eclipse is one of the most spectacular events you can ever see . the sky goes dark , and the stars come out just like it is nighttime . ancient ... | check for recommendations from nasa . with your solar eclipse glasses , you can see some pretty cool features . one is called “ bailey ’ s beads ” . | how do you know if it is safe to take off your glasses ? |
on august 21 , 2017 , the mainland united states will experience an event that hasn ’ t happened across the entire country in about a century - a total solar eclipse ! a solar eclipse is one of the most spectacular events you can ever see . the sky goes dark , and the stars come out just like it is nighttime . ancient ... | doing so will cause blindness . however , you may view the solar eclipse using special solar eclipse glasses or by making a solar eclipse viewer yourself at home . check for recommendations from nasa . | why will looking at the sun/moon during the total solar eclipse damage your eyes ? |
on august 21 , 2017 , the mainland united states will experience an event that hasn ’ t happened across the entire country in about a century - a total solar eclipse ! a solar eclipse is one of the most spectacular events you can ever see . the sky goes dark , and the stars come out just like it is nighttime . ancient ... | doing so will cause blindness . however , you may view the solar eclipse using special solar eclipse glasses or by making a solar eclipse viewer yourself at home . check for recommendations from nasa . | what time will the eclipse be occurring ? |
on august 21 , 2017 , the mainland united states will experience an event that hasn ’ t happened across the entire country in about a century - a total solar eclipse ! a solar eclipse is one of the most spectacular events you can ever see . the sky goes dark , and the stars come out just like it is nighttime . ancient ... | doing so will cause blindness . however , you may view the solar eclipse using special solar eclipse glasses or by making a solar eclipse viewer yourself at home . check for recommendations from nasa . | when will the next solar eclips ? |
on august 21 , 2017 , the mainland united states will experience an event that hasn ’ t happened across the entire country in about a century - a total solar eclipse ! a solar eclipse is one of the most spectacular events you can ever see . the sky goes dark , and the stars come out just like it is nighttime . ancient ... | doing so will cause blindness . however , you may view the solar eclipse using special solar eclipse glasses or by making a solar eclipse viewer yourself at home . check for recommendations from nasa . | when an eclipse goes into totality , how long will it take to go back to partiality ? |
on august 21 , 2017 , the mainland united states will experience an event that hasn ’ t happened across the entire country in about a century - a total solar eclipse ! a solar eclipse is one of the most spectacular events you can ever see . the sky goes dark , and the stars come out just like it is nighttime . ancient ... | doing so will cause blindness . however , you may view the solar eclipse using special solar eclipse glasses or by making a solar eclipse viewer yourself at home . check for recommendations from nasa . | is it safe to drive during an eclipse , or will the eclipse find a way to your eyes ? |
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