problem stringlengths 0 1.31k | answer stringclasses 340
values | images images listlengths 1 1 |
|---|---|---|
Consider the graph shown. A curve passes (0,1), (1,2), (2,4), (3,8). As x increases, y increases.
Which of the following relationships could be represented by the given graph?
Choices:
A:The number of handshakes, y, made by x people in a room if every person shakes hands with every other person.
B:The number of layer... | B | |
Consider the graph shown.
Which of the following relationships could be represented by the given graph?
Choices:
A:The number of handshakes, y, made by x people in a room if every person shakes hands with every other person.
B:The number of layers, y, resulting from a rectangular piece of paper being folded in half x... | B | |
Consider the graph shown.
Which of the following relationships could be represented by the given graph?
Choices:
A:The number of handshakes, y, made by x people in a room if every person shakes hands with every other person.
B:The number of layers, y, resulting from a rectangular piece of paper being folded in half x... | B | |
Consider the graph shown.
Which of the following relationships could be represented by the given graph?
Choices:
A:The number of handshakes, y, made by x people in a room if every person shakes hands with every other person.
B:The number of layers, y, resulting from a rectangular piece of paper being folded in half x... | B | |
B | ||
The logarithm function and a line are graphed. Logarithm function $f$ is graphed in blue and it goes through (30,4), (5,2), (55,5). Line $y=4$ is graphed in red and parallel to x-axis. A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how... | C | |
The logarithm function and a line are graphed. A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.
The amount of time (in hours) the active ingredient ... | C | |
A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.
The amount of time (in hours) the active ingredient remains in the bloodstream can be modeled by $f... | C | |
The logarithm function and a line are graphed. A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.
The amount of time (in hours) the active ingredient ... | C | |
C | ||
Two piecewirse function $g$ and $f$ are graphed, $g$ is graphed in purple and goes through (0,10000), (40,9000), (80,9000), (100,11000), (130,11000), $f$ is graphed in blue and goes through (10,11000), (50,11000), (60,10000), (100,10000), (120,0). t is the number of minutes that have passed since noon at a local airpor... | 90 | |
Piecewise functions f and g can model the heights (in meters) of two airplanes. Here are the graphs of f and g, where t is the number of minutes that have passed since noon at a local airport.
The airplanes have the same height about 9 minutes after noon.
What is the other time the airplanes have the same height?
Round... | 90 | |
Functions f and g can model the heights (in meters) of two airplanes. Here are the graphs of f and g, where t is the number of minutes that have passed since noon at a local airport.
The airplanes have the same height about 9 minutes after noon.
What is the other time the airplanes have the same height?
Round your answ... | 90 | |
Piecewise functions f and g can model the heights (in meters) of two airplanes. Here are the graphs of f and g, where t is the number of minutes that have passed since noon at a local airport.
The airplanes have the same height about 9 minutes after noon.
What is the other time the airplanes have the same height?
Round... | 90 | |
90 | ||
For the following exercises, use the graph in Figure 7, which shows the profit, y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980. The line chart is begin from (15,150) and goes to (25,130).
Find the linear function y, where y depends on t, the number ... | y=-2 t+180 | |
For the following exercises, which shows the profit, y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980.
Find the linear function y, where y depends on t, the number of years since 1980.
| y=-2 t+180 | |
For the following exercises, which shows the profit, y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980.
Find the linear function y, where y depends on t, the number of years since 1980.
| y=-2 t+180 | |
For the following exercises, which shows the profit, y, in thousands of dollars, of a company in a given year, t, where t represents the number of years since 1980.
Find the linear function y, where y depends on t, the number of years since 1980. | y=-2 t+180 | |
y=-2 t+180 | ||
A cake maker has rectangular boxes measuring $40 \mathrm{~cm}$ in length and 20 $\mathrm{cm}$ in width. The four vertices of the rectangle are (0,0), (0,20), (40,20), (40,0). She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside t... | Center $=(20,10)$ | |
A cake maker has rectangular boxes. She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.
State the coordinates of the center of the cake in the form $(a, b)$.
| Center $=(20,10)$ | |
A cake maker has rectangular boxes. She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.
State the coordinates of the center of the cake in the form $(a, b)$.
| Center $=(20,10)$ | |
A cake maker has rectangular boxes. She often receives orders for cakes in the shape of an ellipse, and wants to determine the largest possible cake that can be made to fit inside the rectangular box.
State the coordinates of the center of the cake in the form $(a, b)$. | Center $=(20,10)$ | |
Center $=(20,10)$ | ||
The linear function is graphed. The slope is less than 0. It passes through (0,4) and (4,0). Consider the graph of $y=4-x$.
State the coordinates of the $x$-intercept in the form $(a, b)$.
| $=(4,0)$ | |
The linear function is graphed. Consider the graph of $y=4-x$.
State the coordinates of the $x$-intercept in the form $(a, b)$.
| $=(4,0)$ | |
Consider the graph of $y=4-x$.
State the coordinates of the $x$-intercept in the form $(a, b)$.
| $=(4,0)$ | |
The linear function is graphed. Consider the graph.
State the coordinates of the $x$-intercept in the form $(a, b)$. | $=(4,0)$ | |
$=(4,0)$ | ||
Two linear functions are graphed. The slope of function is greater than 0. It intersects the x-axis and the y-axis at (0,-4). Consider the graph of $y=x-4$.
State the coordinates of the $x$-intercept in the form $(a, b)$.
| $(4,0)$ | |
Two linear functions are graphed.Consider the graph of $y=x-4$.
State the coordinates of the $x$-intercept in the form $(a, b)$.
| $(4,0)$ | |
Consider the graph of $y=x-4$.
State the coordinates of the $x$-intercept in the form $(a, b)$.
| $(4,0)$ | |
Two linear functions are graphed.
State the coordinates of the $x$-intercept in the form $(a, b)$. | $(4,0)$ | |
$(4,0)$ | ||
Two linear functions are graphed. The slope of function is less than 0. It intersects the x-axis at (4,0) and the y-axis at (0,4). Consider the graph of $y=4-x$.
If the graph is translated 10 units up, what will be the coordinates of the new $y$-intercept?
State the coordinates in the form $(a, b)$.
| $(0,14)$ | |
Two linear functions are graphed. Consider the graph of $y=4-x$.
If the graph is translated 10 units up, what will be the coordinates of the new $y$-intercept?
State the coordinates in the form $(a, b)$.
| $(0,14)$ | |
Consider the graph of $y=4-x$.
If the graph is translated 10 units up, what will be the coordinates of the new $y$-intercept?
State the coordinates in the form $(a, b)$.
| $(0,14)$ | |
Two linear functions are graphed.
If the graph is translated 10 units up, what will be the coordinates of the new $y$-intercept?
State the coordinates in the form $(a, b)$. | $(0,14)$ | |
$(0,14)$ | ||
The linear function is graphed. The x-axis represents Time (minutes) and the y-axis represents Water (liters). The slope is less than 0. It intersects the x-axis at (5,0) and the y-axis at (0,360). Archimedes drained the water in his tub.
The amount of water left in the tub (in liters) as a function of time (in minutes... | Bugs Bunny | |
The linear function is graphed. Archimedes drained the water in his tub.
The amount of water left in the tub (in liters) as a function of time (in minutes) is graphed.
How much water was initially in the tub?
| Bugs Bunny | |
Archimedes drained the water in his tub.
The amount of water left in the tub (in liters) as a function of time (in minutes) is graphed.
How much water was initially in the tub?
| Bugs Bunny | |
The linear function is graphed. Archimedes drained the water in his tub.
The amount of water left in the tub (in liters) as a function of time (in minutes) is graphed.
How much water was initially in the tub? | Bugs Bunny | |
Bugs Bunny | ||
The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). Consider the graph of y=\sin x. Its first maximum point for x\ge 0 is at \left(90^\circ ,1\right).
By considering the transformation that ha... | y=\sin x=\left(90^\circ ,5\right) | |
The Sine function is graphed. Consider the graph of y=\sin x.
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=5\sin x
| y=\sin x=\left(90^\circ ,5\right) | |
Consider the graph of y=\sin x.
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=5\sin x
| y=\sin x=\left(90^\circ ,5\right) | |
The Sine function is graphed.
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=5\sin x. | y=\sin x=\left(90^\circ ,5\right) | |
y=\sin x=\left(90^\circ ,5\right) | ||
The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x... | \left(x,y\right)=\left(270^\circ ,5\right) | |
The Sine function is graphed.
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=-5\sin x
| \left(x,y\right)=\left(270^\circ ,5\right) | |
Consider the graph of y=\sin x.
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=-5\sin x
| \left(x,y\right)=\left(270^\circ ,5\right) | |
The Sine function is graphed.
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=-5\sin x | \left(x,y\right)=\left(270^\circ ,5\right) | |
\left(x,y\right)=\left(270^\circ ,5\right) | ||
The Cosine function is graphed. It passes through (0,1), (90,0), (180,-1), (270,0), and (360,1). It is symmetric about the y-axis. A black vertex labeled on the function at (0,1). Consider the graph of y=\cos x. Its first maximum point for x\ge 0 is at \left(0^\circ ,1\right).
By considering the transformation that ha... | \left(315^\circ ,1\right) | |
The Cosine function is graphed. Consider the graph of y=\cos x. By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=\cos \left(x+45^\circ \right)
| \left(315^\circ ,1\right) | |
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=\cos \left(x+45^\circ \right)
| \left(315^\circ ,1\right) | |
The Cosine function is graphed. By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for x\ge 0.
y=\cos \left(x+45^\circ \right). | \left(315^\circ ,1\right) | |
\left(315^\circ ,1\right) | ||
The Sine function is graphed. It passes through (0,0), (90,1), (180,0), (270,-1), and (360,0). It is symmetric about the origin. A black vertex labeled on the function at (90,1). Consider the graph of $y=\sin x$. Its first maximum point for $x \geq 0$ is at $\left(90^{\circ}, 1\right)$.
By considering the transformati... | $(x, y)=\left(90^{\circ}, 5\right)$ | |
The Sine function is graphed. By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \geq 0$.
$y=5 \sin x$
| $(x, y)=\left(90^{\circ}, 5\right)$ | |
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \geq 0$.
$y=5 \sin x$
| $(x, y)=\left(90^{\circ}, 5\right)$ | |
The Sine function is graphed. By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \geq 0$.
$y=5 \sin x$ | $(x, y)=\left(90^{\circ}, 5\right)$ | |
$(x, y)=\left(90^{\circ}, 5\right)$ | ||
The Cosine function is graphed. It passes through (0,1), (90,0), (180,-1), (270,0), and (360,1). It is symmetric about the y-axis. A black vertex labeled on the function at (0,1). Consider the graph of $y=\cos x$. Its first maximum point for $x \geq 0$ is at $\left(0^{\circ}, 1\right)$.
By considering the transformati... | $(x, y)=\left(315^{\circ}, 1\right)$ | |
The Cosine function is graphed. By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \geq 0$.
$y=\cos \left(x+45^{\circ}\right)$
| $(x, y)=\left(315^{\circ}, 1\right)$ | |
By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \geq 0$.
$y=\cos \left(x+45^{\circ}\right)$
| $(x, y)=\left(315^{\circ}, 1\right)$ | |
The Cosine function is graphed. By considering the transformation that has taken place, state the coordinates of the first maximum point of each of the given functions for $x \geq 0$.
$y=\cos \left(x+45^{\circ}\right)$ | $(x, y)=\left(315^{\circ}, 1\right)$ | |
$(x, y)=\left(315^{\circ}, 1\right)$ | ||
Consider a cone with slant height 13m and perpendicular height 12m.
Hence, find the length of the diameter of the cone's base. | diameter $=10 \mathrm{~m}$ | |
The perpendicular height of the cone is 12m.
Hence, find the length of the diameter of the cone's base. | diameter $=10 \mathrm{~m}$ | |
The perpendicular height of the solid figure is 12m.
Hence, find the length of the diameter of the solid figure's base. | diameter $=10 \mathrm{~m}$ | |
Find the length of the diameter of the cone's base. | diameter $=10 \mathrm{~m}$ | |
diameter $=10 \mathrm{~m}$ | ||
The diagram shows a cone with a slant height of 13 m and a perpendicular height of 12 m. The radius of the base of the cone is denoted by $r$.
Find the value of $r$. | $r=5$ | |
The diagram shows a cone with a slant height of 13 m. The radius of the base of the cone is denoted by $r$.
Find the value of $r$. | $r=5$ | |
The diagram shows a solid figure with a slant height of 13 m. The radius of the base of the solid figure is denoted by $r$.
Find the value of $r$. | $r=5$ | |
The radius of the base of the cone is denoted by $r$.
Find the value of $r$. | $r=5$ | |
$r=5$ | ||
A square prism has sides of length 11cm, 11cm and 15cm as shown.
Now, we want to find $y$, the length of the diagonal $DF$.
Calculate $y$ to two decimal places.
| $y=21.61$ | |
A square prism has a side $GF$ of length 15cm as shown.
Now, we want to find $y$, the length of the diagonal $DF$.
Calculate $y$ to two decimal places.
| $y=21.61$ | |
A solid figure has a side $GF$ of length 15cm as shown.
Now, we want to find $y$, the length of the diagonal $DF$.
Calculate $y$ to two decimal places.
| $y=21.61$ | |
We want to find $y$, the length of the diagonal $DF$.
Calculate $y$ to two decimal places.
| $y=21.61$ | |
$y=21.61$ | ||
A triangular divider has been placed into a box, as shown in the diagram. The box has sides of length 12cm, 12cm and 17cm.
Calculate the area of the triangular divider correct to two decimal places. | Area $=124.85 \mathrm{~cm}^{2}$ | |
The length of CD side is 12cm.
Calculate the area of the triangular divider correct to two decimal places. | Area $=124.85 \mathrm{~cm}^{2}$ | |
The length of CD side is 12cm.
Calculate the area of the triangular divider correct to two decimal places. | Area $=124.85 \mathrm{~cm}^{2}$ | |
Calculate the area of the triangular divider correct to two decimal places. | Area $=124.85 \mathrm{~cm}^{2}$ | |
Area $=124.85 \mathrm{~cm}^{2}$ | ||
Find the volume of a concrete pipe with outer radius 7 metres, inner radius 3 metres and length 13 metres. Write your answer correct to two decimal places. | Volume $=1633.63 \mathrm{~m}^{3}$ | |
Find the volume of a concrete pipe with length 13 metres. Write your answer correct to two decimal places. | Volume $=1633.63 \mathrm{~m}^{3}$ | |
Find the volume of a concrete pipe with length 13 metres. Write your answer correct to two decimal places. | Volume $=1633.63 \mathrm{~m}^{3}$ | |
Find the volume of a concrete pipe. Write your answer correct to two decimal places. | Volume $=1633.63 \mathrm{~m}^{3}$ | |
Volume $=1633.63 \mathrm{~m}^{3}$ | ||
A hollow cylindrical pipe has the dimensions shown in the figure. The outer diameter is 2.1 centimeters. The inner diameter is 1.8 centimeters. The length is 13 centimeters.
The pipe is made of a particularly strong metal.
Calculate the weight of the pipe if 1 (cm)^3 of the metal weighs 5.3g , giving your answer corr... | Weight $=63.3 \mathrm{~g}$ | |
The length is 13 centimeters.
The pipe is made of a particularly strong metal.
Calculate the weight of the pipe if 1 (cm)^3 of the metal weighs 5.3g , giving your answer correct to one decimal place. | Weight $=63.3 \mathrm{~g}$ | |
The length is 13 centimeters.
The pipe is made of a particularly strong metal.
Calculate the weight of the pipe if 1 (cm)^3 of the metal weighs 5.3g , giving your answer correct to one decimal place. | Weight $=63.3 \mathrm{~g}$ | |
The cylindrical pipe is made of a particularly strong metal.
Calculate the weight of the pipe if 1 (cm)$^3$ of the metal weighs 5.3g , giving your answer correct to one decimal place. | Weight $=63.3 \mathrm{~g}$ | |
Weight $=63.3 \mathrm{~g}$ |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.