query stringlengths 38 8.78k | response stringlengths 37 8.78k |
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Find the distance between the points (0,15) and (8,0). We can use the distance formula to find the distance between two points. ки The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки In this case, $(x_1, y_1) = (0, 15)$ and $(x_2, y_2) = (8, 0)$. ки Plugging these values into the distance formula, we get $\s... | Find the distance between the points (0,15) and (8,0). We can use the distance formula to find the distance between two points. к The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к In this case, $(x_1, y_1) = (0, 15)$ and $(x_2, y_2) = (8, 0)$. к Plugging these values into the distance formula, we get $\sqrt... |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: ки
$$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.$$ ки
Using this formula, the distance between the points (0,15) and (8,0) is ки
$$\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \s... | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: к
$$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.$$ ки
Using this formula, the distance between the points (0,15) and (8,0) is ки
$$\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sq... |
Find the distance between the points (0,15) and (8,0). using the distance formula, the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by
$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки
In this case, the distance is $\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64+225} = \sqrt{289} = \boxed{17}$. ки
The answer is: 17 ки | Find the distance between the points (0,15) and (8,0). using the distance formula, the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by
$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к
In this case, the distance is $\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64+225} = \sqrt{289} = \boxed{17}$. ки
The answer is: 17 ки |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane is given by the distance formula: ки
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.\] ки
In this case, $(x_1, y_1) = (0, 15)$ and $(x_2, y_2) = (8, 0)$. ки
Plugging these values into ... | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane is given by the distance formula: к
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.\] ки
In this case, $(x_1, y_1) = (0, 15)$ and $(x_2, y_2) = (8, 0)$. ки
Plugging these values into t... |
Find the distance between the points (0,15) and (8,0). The distance between these two points can be found using the distance formula. ки
The distance formula states that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by
$$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.$$ ки
In this case, $(x_1, y_1) = (0,... | Find the distance between the points (0,15) and (8,0). The distance between these two points can be found using the distance formula. к
The distance formula states that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by
$$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.$$ ки
In this case, $(x_1, y_1) = (0, ... |
Find the distance between the points (0,15) and (8,0). Distance Formula : $\ sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ ки
Plug in the coordinates: $\sqrt{(8-0)^2+(0-15)^2}=\sqrt{3 6+225}=\sqrt{261}=\boxed{16}$ ки
The answer is: 16 ки | Find the distance between the points (0,15) and (8,0). Distance Formula : $\ sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ и
Plug in the coordinates: $\sqrt{(8-0)^2+(0-15)^2}=\sqrt{3 6+225}=\sqrt{261}=\boxed{16}$ ки
The answer is: 16 ки |
Find the distance between the points (0,15) and (8,0). We can use the distance formula:
\[ d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\] ки
Plugging in the coordinates, we get:
\[d = \sqrt{(8-0)^2 + (0-15)^2} = \sqrt{8^2 + (-15)^2} = \sqrt{64 + 225} = \sqrt{289} = \boxed{17}\] ки
The answer is: 17 ки | Find the distance between the points (0,15) and (8,0). We can use the distance formula:
\[ d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\] к
Plugging in the coordinates, we get:
\[d = \sqrt{(8-0)^2 + (0-15)^2} = \sqrt{8^2 + (-15)^2} = \sqrt{64 + 225} = \sqrt{289} = \boxed{17}\] ки
The answer is: 17 ки |
Find the distance between the points (0,15) and (8,0). The distance between two points in a coordinate plane can be found using the distance formula. ки The distance formula states that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$$ ки Using this formula, t... | Find the distance between the points (0,15) and (8,0). The distance between two points in a coordinate plane can be found using the distance formula. к The distance formula states that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$$ к Using this formula, the... |
Find the distance between the points (0,15) and (8,0). The distance formula tells us that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки Using this formula, the distance between (0,15) and (8,0) is $\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sqrt{289... | Find the distance between the points (0,15) and (8,0). The distance formula tells us that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к Using this formula, the distance between (0,15) and (8,0) is $\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sqrt{289}... |
Find the distance between the points (0,15) and (8,0). We can use the distance formula to find the distance between two points in a coordinate plane. ки The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$$ ки In this case, the points are (0,15) and ... | Find the distance between the points (0,15) and (8,0). We can use the distance formula to find the distance between two points in a coordinate plane. к The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$$ к In this case, the points are (0,15) and (8... |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: ки
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.\] ки
In this case, we have $(x_1, y_1) = (0, 15)$ and $(x_2, y_2) = (8, 0)$. ки
Plugging these values into the distance f... | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: к
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.\] ки
In this case, we have $(x_1, y_1) = (0, 15)$ and $(x_2, y_2) = (8, 0)$. ки
Plugging these values into the distance fo... |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: ки
$$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$$ ки
So , the distance between the points (0,15) and (8,0) is ки
$$\sqrt{(8-0)^2+(0-15)^2}=\sqrt{64+225}=\sqrt{289}=17.$$ ки
The ans... | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: к
$$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$$ ки
So , the distance between the points (0,15) and (8,0) is ки
$$\sqrt{(8-0)^2+(0-15)^2}=\sqrt{64+225}=\sqrt{289}=17.$$ ки
The answ... |
Find the distance between the points (0,15) and (8,0). We can use the distance formula, which states that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. ки
In this case, $(x_1, y_1)$ is (0, 15) and $(x_2, y_2)$ is (8, 0). ки
Plugging in the values, we get $... | Find the distance between the points (0,15) and (8,0). We can use the distance formula, which states that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. к
In this case, $(x_1, y_1)$ is (0, 15) and $(x_2, y_2)$ is (8, 0). ки
Plugging in the values, we get $\... |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. ки So , the distance between (0,15) and (8,0) is $\sqrt{(8-0)^2+(0-15)^2} = \sqrt{64+225} = \sqrt{289} = \boxed{17}$. ки The answer is: 17 ки | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. к So , the distance between (0,15) and (8,0) is $\sqrt{(8-0)^2+(0-15)^2} = \sqrt{64+225} = \sqrt{289} = \boxed{17}$. к The answer is: 17 к |
Find the distance between the points (0,15) and (8,0). Use the distance formula. ки The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки Plugging in the coordinates, we get $\sqrt{(8-0)^2 + (0-15)^2}$. ки Simplifying, we have $\sqrt{64 + 225}$. ки This is equal to $\sqrt{289}$. ки The square root of 289 is 17... | Find the distance between the points (0,15) and (8,0). Use the distance formula. к The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к Plugging in the coordinates, we get $\sqrt{(8-0)^2 + (0-15)^2}$. к Simplifying, we have $\sqrt{64 + 225}$. к This is equal to $\sqrt{289}$. к The square root of 289 is 17. к S... |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: ки
$$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$$ ки
In this case, $(x_1, y_1) = (0, 15)$ and $(x_2, y_2) = (8, 0)$. ки
Plugging the values into the distance formula, we get: ки
$$... | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: к
$$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$$ ки
In this case, $(x_1, y_1) = (0, 15)$ and $(x_2, y_2) = (8, 0)$. ки
Plugging the values into the distance formula, we get: ки
$$\... |
Find the distance between the points (0,15) and (8,0). The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки
Pl ugging in the coordinates, we get $\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sqrt{289} = \boxed{17}$. ки
The answer is: 17 ки | Find the distance between the points (0,15) and (8,0). The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к
Pl ugging in the coordinates, we get $\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sqrt{289} = \boxed{17}$. ки
The answer is: 17 ки |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $\ sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки
Using the given points, we have:
$ x_1 = 0, y_1 = 15$
$x_2 = 8, y_2 = 0$ ки
Plugging these values into the distance formula, we g... | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: $\ sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к
Using the given points, we have:
$ x_1 = 0, y_1 = 15$
$x_2 = 8, y_2 = 0$ ки
Plugging these values into the distance formula, we ge... |
Find the distance between the points (0,15) and (8,0). The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки
Pl ugging in the coordinates, we have $\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sqrt{289} = \boxed{17}$. ки
The answer is: 17 ки | Find the distance between the points (0,15) and (8,0). The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к
Pl ugging in the coordinates, we have $\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sqrt{289} = \boxed{17}$. ки
The answer is: 17 ки |
Find the distance between the points (0,15) and (8,0). We can use the distance formula to find the distance between two points in a coordinate plane. ки The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки In this case, $(x_1, y_1)= (0,15)$ and $(x_2, y_2)=(8,0)$. ки Plugging these values into the distance fo... | Find the distance between the points (0,15) and (8,0). We can use the distance formula to find the distance between two points in a coordinate plane. к The distance formula is $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к In this case, $(x_1, y_1)= (0,15)$ and $(x_2, y_2)=(8,0)$. к Plugging these values into the distance formu... |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1,y _1)$ and $(x_2,y_2)$ is given by the formula $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. ки
In this case, the distance between (0,15) and (8,0) is $\sqrt{(8-0)^2+(0-15)^2}=\sqrt{64+225}=\sqrt{289}=\boxed{17}$. ки
The answer is: 17 ки | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1,y _1)$ and $(x_2,y_2)$ is given by the formula $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. к
In this case, the distance between (0,15) and (8,0) is $\sqrt{(8-0)^2+(0-15)^2}=\sqrt{64+225}=\sqrt{289}=\boxed{17}$. ки
The answer is: 17 ки |
Find the distance between the points (0,15) and (8,0). The distance between two points in a coordinate plane is given by the distance formula: $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки
Using this formula, the distance between the points (0,15) and (8,0) is $d = \sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sqrt{289} ... | Find the distance between the points (0,15) and (8,0). The distance between two points in a coordinate plane is given by the distance formula: $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к
Using this formula, the distance between the points (0,15) and (8,0) is $d = \sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sqrt{289} =... |
Find the distance between the points (0,15) and (8,0). using the distance formula, the distance between two points $(x_1,y _1)$ and $(x_2,y_2)$ is given by
$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки
Pl ugging in the given coordinates, we have
$\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64+225} = \sqrt{289} = \boxed{17}$. ки
The ans... | Find the distance between the points (0,15) and (8,0). using the distance formula, the distance between two points $(x_1,y _1)$ and $(x_2,y_2)$ is given by
$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к
Pl ugging in the given coordinates, we have
$\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64+225} = \sqrt{289} = \boxed{17}$. ки
The answ... |
Find the distance between the points (0,15) and (8,0). We can use the distance formula, which states that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane is given by: ки
\[ d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\] ки
In this case, $(x_1, y_1) = (0,15)$ and $(x_2, y_2) = (8,0)$. Pl ug... | Find the distance between the points (0,15) and (8,0). We can use the distance formula, which states that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane is given by: к
\[ d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\] ки
In this case, $(x_1, y_1) = (0,15)$ and $(x_2, y_2) = (8,0)$. Pl ugg... |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: ки
$$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$$ ки
So , the distance between $(0,15)$ and $(8,0)$ is: ки
$$\sqrt{(8-0)^2+(0-15)^2}=\sqrt{64+225}=\sqrt{289}=17.$$ ки
Therefore, th... | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the distance formula: к
$$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$$ ки
So , the distance between $(0,15)$ and $(8,0)$ is: ки
$$\sqrt{(8-0)^2+(0-15)^2}=\sqrt{64+225}=\sqrt{289}=17.$$ ки
Therefore, the... |
Find the distance between the points (0,15) and (8,0). First, we can use the distance formula to find the distance between two points in the coordinate plane. ки The distance formula is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. ки Using this formula, we can find the distance between (0,15) and (8,0) as follo... | Find the distance between the points (0,15) and (8,0). First, we can use the distance formula to find the distance between two points in the coordinate plane. к The distance formula is given by $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. к Using this formula, we can find the distance between (0,15) and (8,0) as follows... |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. ки
Using this formula, the distance between $(0,15)$ and $(8,0)$ is $\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sqrt{289} = \boxed{17}$. ки... | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. к
Using this formula, the distance between $(0,15)$ and $(8,0)$ is $\sqrt{(8-0)^2 + (0-15)^2} = \sqrt{64 + 225} = \sqrt{289} = \boxed{17}$. ки
... |
Find the distance between the points (0,15) and (8,0). Using the distance formula, the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by
$$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.$$ ки
In this case, $(x_1, y_1) = (0, 15)$ and $(x_2, y_2) = (8, 0)$. ки
Sub stituting into the formula, we have
$$\sqrt{(8-0)^2... | Find the distance between the points (0,15) and (8,0). Using the distance formula, the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by
$$\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}.$$ к
In this case, $(x_1, y_1) = (0, 15)$ and $(x_2, y_2) = (8, 0)$. ки
Sub stituting into the formula, we have
$$\sqrt{(8-0)^2 ... |
Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1,y _1)$ and $(x_2,y_2)$ is given by the distance formula, which states that the distance $d$ between the points is given by \[ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.\] ки App lying this formula to the given points, we have \[d=\sqrt{... | Find the distance between the points (0,15) and (8,0). The distance between two points $(x_1,y _1)$ and $(x_2,y_2)$ is given by the distance formula, which states that the distance $d$ between the points is given by \[ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.\] к App lying this formula to the given points, we have \[d=\sqrt{(... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The quadr atic $x^2 - 10x + 24$ is a parabola that opens upward, so it has a minimum value. ки
To find the minimum value, we can complete the square. ки
We have $x^2 - 10x + 24 = (x - 5)^2 - 1$, which is a parabola with vertex at $(5, -1)$. ки
Therefore... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The quadr atic $x^2 - 10x + 24$ is a parabola that opens upward, so it has a minimum value. к
To find the minimum value, we can complete the square. ки
We have $x^2 - 10x + 24 = (x - 5)^2 - 1$, which is a parabola with vertex at $(5, -1)$. ки
Therefore,... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The expression $x^2 - 10x + 24$ is a quadratic function in the form $ax^2 + bx + c$. ки
To find the minimum value, we can use the formula $x = -\frac{b}{2a}$. ки
In this case, $a = 1$ and $b = -10$, so $x = -\frac{-10}{2(1)} = \frac{10}{2} = 5$. ки
Ther... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The expression $x^2 - 10x + 24$ is a quadratic function in the form $ax^2 + bx + c$. к
To find the minimum value, we can use the formula $x = -\frac{b}{2a}$. ки
In this case, $a = 1$ and $b = -10$, so $x = -\frac{-10}{2(1)} = \frac{10}{2} = 5$. ки
There... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The quadr atic function $x^2 - 10x + 24$ is a parabola that opens upward, so it has a minimum value. ки
To find the minimum value, we need to find the vertex of the parabola. ки
The $x$-coordinate of the vertex is given by $x = -\frac{b}{2a}$, where $a$... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The quadr atic function $x^2 - 10x + 24$ is a parabola that opens upward, so it has a minimum value. к
To find the minimum value, we need to find the vertex of the parabola. ки
The $x$-coordinate of the vertex is given by $x = -\frac{b}{2a}$, where $a$ ... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of a quadratic function in the form $ax^2 + bx + c$, we can use the formula $x = -\frac{b}{2a}$. ки
In this case, $a = 1$, $b = -10$, and $c = 24$. ки
So the value of $x$ that gives the minimum value for $x^2 - 10x + 24$ is $x ... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of a quadratic function in the form $ax^2 + bx + c$, we can use the formula $x = -\frac{b}{2a}$. к
In this case, $a = 1$, $b = -10$, and $c = 24$. ки
So the value of $x$ that gives the minimum value for $x^2 - 10x + 24$ is $x =... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? First, we find the vertex of the parabola $x^2 - 10x + 24$. ки
The $x$-coordinate of the vertex is given by $-\frac{b}{2a} = -\frac{-10}{2} = 5$. ки
To find the $y$-coordinate of the vertex, we substitute $x = 5$ into the equation $ x^2 - 10x + 24$: ки
... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? First, we find the vertex of the parabola $x^2 - 10x + 24$. к
The $x$-coordinate of the vertex is given by $-\frac{b}{2a} = -\frac{-10}{2} = 5$. ки
To find the $y$-coordinate of the vertex, we substitute $x = 5$ into the equation $ x^2 - 10x + 24$: ки
$... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of the quadratic $x^2 - 10x + 24$, we look for the vertex of the parabola. ки
The x-coordinate of the vertex is given by $x = -\frac{b}{2a}$, where $a$ and $b$ are the coefficients of the quadratic. ки
In this case, $a = 1$ and... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of the quadratic $x^2 - 10x + 24$, we look for the vertex of the parabola. к
The x-coordinate of the vertex is given by $x = -\frac{b}{2a}$, where $a$ and $b$ are the coefficients of the quadratic. ки
In this case, $a = 1$ and ... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can rewrite the quadratic as $x^2 - 10x + 24 = (x - 5)^2 - 1$. ки Since $(x - 5)^2$ is always nonnegative, the minimum value occurs when $(x - 5)^2 = 0$, or $x = \boxed{5}$. ки The answer is: 5 ки | What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can rewrite the quadratic as $x^2 - 10x + 24 = (x - 5)^2 - 1$. к Since $(x - 5)^2$ is always nonnegative, the minimum value occurs when $(x - 5)^2 = 0$, or $x = \boxed{5}$. к The answer is: 5 к |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can find the minimum value of a quadratic by completing the square. ки
We rewrite the quadratic as $(x^2 - 10x + 25) - 1 = (x - 5)^2 - 1$. ки
The minimum value occurs when $(x - 5)^2$ is equal to 0, which happens when $x = \boxed{5}$. ки
The answer i... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can find the minimum value of a quadratic by completing the square. к
We rewrite the quadratic as $(x^2 - 10x + 25) - 1 = (x - 5)^2 - 1$. ки
The minimum value occurs when $(x - 5)^2$ is equal to 0, which happens when $x = \boxed{5}$. ки
The answer is... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The graph of $y=x^2-10x+24$ is a parabola that opens upwards, so it has a minimum value. ки
To find the minimum value, we can find the vertex of the parabola. ки
The x-coordinate of the vertex is given by $x=-\frac{b}{2a}$, where $a$ and $b$ are the coe... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The graph of $y=x^2-10x+24$ is a parabola that opens upwards, so it has a minimum value. и
To find the minimum value, we can find the vertex of the parabola. ки
The x-coordinate of the vertex is given by $x=-\frac{b}{2a}$, where $a$ and $b$ are the coef... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can rewrite the expression as $x^2 - 10x + 24 = (x - 5)^2 - 1$. ки
Since $(x - 5)^2$ is always nonnegative, the minimum value occurs when $(x - 5)^2 = 0$, ки
which happens when $x - 5 = 0$. ки
Th us, the minimum value is achieved when $x = \boxed{5}$... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can rewrite the expression as $x^2 - 10x + 24 = (x - 5)^2 - 1$. к
Since $(x - 5)^2$ is always nonnegative, the minimum value occurs when $(x - 5)^2 = 0$, ки
which happens when $x - 5 = 0$. ки
Th us, the minimum value is achieved when $x = \boxed{5}$.... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The graph of $y = x^2 - 10x + 24$ is a parabola that opens upward because the coefficient of $x^2$ is positive. ки
There fore, the minimum value of the quadratic occurs at the vertex of the parabola. ки
The $x$-coordinate of the vertex can be found usin... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The graph of $y = x^2 - 10x + 24$ is a parabola that opens upward because the coefficient of $x^2$ is positive. и
There fore, the minimum value of the quadratic occurs at the vertex of the parabola. ки
The $x$-coordinate of the vertex can be found using... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of $ x^2 - 10x + 24$, we can complete the square. ки
First , we rewrite the quadratic as $x^2 - 10x + 25 - 1$. ки
This can be factored as $(x - 5)^2 - 1$. ки
Since $(x - 5)^2$ is always nonnegative, the minimum value of the qua... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of $ x^2 - 10x + 24$, we can complete the square. к
First , we rewrite the quadratic as $x^2 - 10x + 25 - 1$. ки
This can be factored as $(x - 5)^2 - 1$. ки
Since $(x - 5)^2$ is always nonnegative, the minimum value of the quad... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The graph of $y=x^2-10x+24$ is a parabola that opens upward. ки
Since the coefficient of $x^2$ is positive, the parabola is concave up. ки
Therefore, the vertex of the parabola gives the minimum value of the quadratic function. ки
The $x$-coordinate of ... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The graph of $y=x^2-10x+24$ is a parabola that opens upward. к
Since the coefficient of $x^2$ is positive, the parabola is concave up. ки
Therefore, the vertex of the parabola gives the minimum value of the quadratic function. ки
The $x$-coordinate of t... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can find the minimum value of the quadratic by completing the square. ки
First, we sub tract $ 24$ from both sides to get $x^2-10x+24-24$. ки
Next, we combine like terms and factor to get $(x-5)^2-1$. ки
Since $(x-5)^2$ is always nonnegative, the min... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can find the minimum value of the quadratic by completing the square. к
First, we sub tract $ 24$ from both sides to get $x^2-10x+24-24$. ки
Next, we combine like terms and factor to get $(x-5)^2-1$. ки
Since $(x-5)^2$ is always nonnegative, the mini... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? Our answer is: 5 ки | What value of $x$ will give the minimum value for $x^2- 10x + 24$? Our answer is: 5 и |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can rewrite the expression as $x^2- 10x+24=(x-5)^2-1$. ки
Since $(x-5)^2$ is always nonnegative, the minimum value of the expression occurs when $(x-5)^2=0$, which is when $x=\boxed{5}$. ки
The answer is: 5 ки | What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can rewrite the expression as $x^2- 10x+24=(x-5)^2-1$. к
Since $(x-5)^2$ is always nonnegative, the minimum value of the expression occurs when $(x-5)^2=0$, which is when $x=\boxed{5}$. ки
The answer is: 5 ки |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can rewrite the expression as $x^2 - 10x + 24 = (x-5)^2 -1 $. ки
Since $(x-5)^2$ is always nonnegative, the minimum value occurs when $(x-5)^2$ is equal to 0, which happens when $x-5=0$. ки
Therefore, the minimum value of the expression is $0-1 = \bo... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can rewrite the expression as $x^2 - 10x + 24 = (x-5)^2 -1 $. к
Since $(x-5)^2$ is always nonnegative, the minimum value occurs when $(x-5)^2$ is equal to 0, which happens when $x-5=0$. ки
Therefore, the minimum value of the expression is $0-1 = \box... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can find the minimum value of the quadratic by completing the square. ки
We have $x^2 - 10x + 24 = (x - 5)^2 - 1$. ки
Since $(x - 5)^2$ is always nonnegative, the minimum value occurs when $(x - 5)^2 = 0$. ки
Therefore, the value of $x$ that gives th... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can find the minimum value of the quadratic by completing the square. к
We have $x^2 - 10x + 24 = (x - 5)^2 - 1$. ки
Since $(x - 5)^2$ is always nonnegative, the minimum value occurs when $(x - 5)^2 = 0$. ки
Therefore, the value of $x$ that gives the... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of this quadratic, we complete the square: ки
\[x^2 - 10x + 24 = (x^2 - 10x + 25) - 1 = (x - 5)^2 - 1.\] ки
Since $(x - 5)^2$ is always nonnegative, the minimum value of the quadratic is $\boxed{-1}$. ки
The answer is: -1 ки | What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of this quadratic, we complete the square: и
\[x^2 - 10x + 24 = (x^2 - 10x + 25) - 1 = (x - 5)^2 - 1.\] ки
Since $(x - 5)^2$ is always nonnegative, the minimum value of the quadratic is $\boxed{-1}$. ки
The answer is: -1 ки |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The graph of $x^2 - 10x + 24$ is a parabola that opens upwards, so it has a minimum value. ки
The minimum value of a parabola occurs at its vertex, which is the point $(h, k)$ where $h$ is the x-coordinate and $k$ is the y-coordinate. ки
For a parabola ... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The graph of $x^2 - 10x + 24$ is a parabola that opens upwards, so it has a minimum value. к
The minimum value of a parabola occurs at its vertex, which is the point $(h, k)$ where $h$ is the x-coordinate and $k$ is the y-coordinate. ки
For a parabola i... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The graph of $x^2 - 10x + 24$ is a parabola that opens upward, so it has a minimum value. ки
To find the minimum value, we can complete the square. ки
We have $x^2 - 10x + 24 = (x - 5)^2 - 1$, which is minimized when $(x - 5)^2 = 0$. ки
Therefore, the m... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The graph of $x^2 - 10x + 24$ is a parabola that opens upward, so it has a minimum value. к
To find the minimum value, we can complete the square. ки
We have $x^2 - 10x + 24 = (x - 5)^2 - 1$, which is minimized when $(x - 5)^2 = 0$. ки
Therefore, the mi... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The given expression is a quadratic function in the form $ax^2 + bx + c$, where $a = 1$, $b = -10$, and $c = 24$. ки
To find the minimum value, we can use the formula $x = -\frac{b}{2a}$. ки
Plugging in the values, we get $x = -\frac{-10}{2(1)} = 5$. ки... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The given expression is a quadratic function in the form $ax^2 + bx + c$, where $a = 1$, $b = -10$, and $c = 24$. и
To find the minimum value, we can use the formula $x = -\frac{b}{2a}$. ки
Plugging in the values, we get $x = -\frac{-10}{2(1)} = 5$. ки
... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The minimum value of a quadratic of the form $ax^2 + bx + c$ occurs when $x = -\frac{b}{2a}$. ки
In this case, $a = 1$ and $b = -10$, so the minimum value occurs when $x = -\frac{-10}{2(1)} = 5$. ки
Sub stituting $x = 5$ into the quadratic, we find that... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The minimum value of a quadratic of the form $ax^2 + bx + c$ occurs when $x = -\frac{b}{2a}$. и
In this case, $a = 1$ and $b = -10$, so the minimum value occurs when $x = -\frac{-10}{2(1)} = 5$. ки
Sub stituting $x = 5$ into the quadratic, we find that ... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of a quadratic function in the form $ax^2 + bx + c$, ки
we can use the formula $x = -\frac{b}{2a}$. ки
In this case, $a = 1$ and $b = -10$, ки
so the value of $x$ that will give the minimum value for the quadratic is $x = -\fra... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of a quadratic function in the form $ax^2 + bx + c$, к
we can use the formula $x = -\frac{b}{2a}$. ки
In this case, $a = 1$ and $b = -10$, ки
so the value of $x$ that will give the minimum value for the quadratic is $x = -\frac... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? We complete the square to find the minimum value. ки First, we factor the quadratic as $(x-5)^2 -1$. ки The minimum value occurs when the square term is equal to zero, so $x-5=0$ and $x=5$. ки Therefore, the value of $x$ that gives the minimum value for... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? We complete the square to find the minimum value. к First, we factor the quadratic as $(x-5)^2 -1$. к The minimum value occurs when the square term is equal to zero, so $x-5=0$ and $x=5$. к Therefore, the value of $x$ that gives the minimum value for th... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can find the minimum value by completing the square. ки We have $x^2 - 10x + 24 = (x^2 - 10x + 25) - 1 = (x - 5)^2 - 1$. ки Since $(x - 5)^2$ is always nonnegative, the minimum value occurs when $(x - 5)^2 = 0$, which is when $x = \boxed{5}$. ки The ... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? We can find the minimum value by completing the square. к We have $x^2 - 10x + 24 = (x^2 - 10x + 25) - 1 = (x - 5)^2 - 1$. к Since $(x - 5)^2$ is always nonnegative, the minimum value occurs when $(x - 5)^2 = 0$, which is when $x = \boxed{5}$. к The ans... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? The quadr atic expression $x^2 - 10x + 24$ is a parabola that opens upwards. ки The minimum value occurs at the vertex of the parabola. ки The $x$-coordinate of the vertex of the parabola $ax^2 + bx + c$ is given by $x = -\frac{b}{2a}$. ки In this case,... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? The quadr atic expression $x^2 - 10x + 24$ is a parabola that opens upwards. к The minimum value occurs at the vertex of the parabola. к The $x$-coordinate of the vertex of the parabola $ax^2 + bx + c$ is given by $x = -\frac{b}{2a}$. к In this case, $a... |
What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of the quadratic expression $x^2 - 10x + 24$, we can complete the square. ки
First , divide the quadratic by 2 to standard ize it: $x^2 - 10x + 24 = \frac{1}{2}(x^2 - 10x + 25) - 1 = \frac{1}{2}(x - 5)^2 - 1$. ки
Since $(x - 5)... | What value of $x$ will give the minimum value for $x^2- 10x + 24$? To find the minimum value of the quadratic expression $x^2 - 10x + 24$, we can complete the square. к
First , divide the quadratic by 2 to standard ize it: $x^2 - 10x + 24 = \frac{1}{2}(x^2 - 10x + 25) - 1 = \frac{1}{2}(x - 5)^2 - 1$. ки
Since $(x - 5)^... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. Since $h(x)=f(g(x))+g(x)$, the highest degree term of $h(x)$ is the sum of the highest degree terms of $f(g(x))$ and $g(x)$. ки Since the degree of $f(x)$ ... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. Since $h(x)=f(g(x))+g(x)$, the highest degree term of $h(x)$ is the sum of the highest degree terms of $f(g(x))$ and $g(x)$. к Since the degree of $f(x)$ i... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. ки The degree of a polynomial is determined by the term with the highest power of $x$. ки Since the degree of $h(x)$ is $6$, the term with the highest powe... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. к The degree of a polynomial is determined by the term with the highest power of $x$. к Since the degree of $h(x)$ is $6$, the term with the highest power ... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of the variable in the polynomial. ки Since $h(x)$ is the sum of two polynomials, the degree of $h(x)$ is t... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of the variable in the polynomial. к Since $h(x)$ is the sum of two polynomials, the degree of $h(x)$ is th... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. Since $h(x)$ is a polynomial of degree $6$, it must have the form ки
\[h(x) = a_6x^6 + a_5x^5 + a_4x^4 + a_3x^3 + a_2x^2 + a_1x + a_0.\] ки
Since $h(x) = f... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. Since $h(x)$ is a polynomial of degree $6$, it must have the form к
\[h(x) = a_6x^6 + a_5x^5 + a_4x^4 + a_3x^3 + a_2x^2 + a_1x + a_0.\] ки
Since $h(x) = f(... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of the variable that appears in the polynomial. ки
Since $h(x)=f(g(x))+g(x)$, the highest power of $x$ in ... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of the variable that appears in the polynomial. и
Since $h(x)=f(g(x))+g(x)$, the highest power of $x$ in $... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. We know that the degree of a polynomial is determined by the term with the highest power of $x$. ки
Since $h(x)$ is a sum of $f(g(x))$ and $g(x)$, the high... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. We know that the degree of a polynomial is determined by the term with the highest power of $x$. к
Since $h(x)$ is a sum of $f(g(x))$ and $g(x)$, the highe... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ in the polynomial. ки
Since $h(x)$ is the sum of two polynomials, $f(g(x))$ and $g(x)$, the degree o... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ in the polynomial. к
Since $h(x)$ is the sum of two polynomials, $f(g(x))$ and $g(x)$, the degree of... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of the variable that appears in the polynomial. ки Since $h(x)$ is the sum of two polynomials, $f(g(x))$ an... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of the variable that appears in the polynomial. к Since $h(x)$ is the sum of two polynomials, $f(g(x))$ and... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. We know that $h(x)$ is a polynomial of degree $6$. ки
Since $h(x) = f(g(x)) + g(x)$, the degree of $f (g(x))$ must be greater than or equal to $6$ in order... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. We know that $h(x)$ is a polynomial of degree $6$. к
Since $h(x) = f(g(x)) + g(x)$, the degree of $f (g(x))$ must be greater than or equal to $6$ in order ... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. ки Since $h(x)=f(g(x))+g(x)$, the degree of $h(x)$ is equal to the maximum of the degrees of $f(g(x))$ and $g(x)$. ки Since the degree of $f(x)$ is $2$, th... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. к Since $h(x)=f(g(x))+g(x)$, the degree of $h(x)$ is equal to the maximum of the degrees of $f(g(x))$ and $g(x)$. к Since the degree of $f(x)$ is $2$, the ... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of $h(x)$ is the highest power of $x$ in $h(x)$. ки
Since $h(x)=f(g(x))+g(x)$, the degree of $h(x)$ is the maximum of the degrees of $f(g(x))$ a... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of $h(x)$ is the highest power of $x$ in $h(x)$. и
Since $h(x)=f(g(x))+g(x)$, the degree of $h(x)$ is the maximum of the degrees of $f(g(x))$ an... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. ки Since $h(x)$ is a polynomial of degree $6$, $ f(g(x))$ must have degree $6$ or greater, and $g(x)$ must have degree at least $3$. ки Since the degree of... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. к Since $h(x)$ is a polynomial of degree $6$, $ f(g(x))$ must have degree $6$ or greater, and $g(x)$ must have degree at least $3$. к Since the degree of $... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of the variable that appears in the polynomial. ки
Since $h(x)$ is the sum of $f(g(x))$ and $g(x)$, the deg... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of the variable that appears in the polynomial. и
Since $h(x)$ is the sum of $f(g(x))$ and $g(x)$, the degr... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. We know that the degree of a polynomial is the highest power of the variable in any term of the polynomial. ки Since $h(x)$ is a sum of two terms, $f(g(x))... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. We know that the degree of a polynomial is the highest power of the variable in any term of the polynomial. к Since $h(x)$ is a sum of two terms, $f(g(x))$... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ that appears in the polynomial. ки
Since $h(x)$ is a polynomial, it must have a highest power of $x$... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ that appears in the polynomial. к
Since $h(x)$ is a polynomial, it must have a highest power of $x$.... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. ки To find the degree of $g(x)$, we need to find the degree of the polynomial $f (g(x))$. ки Since the degree of $f(x)$ is $2$, the degree of $f(g(x))$ is ... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. к To find the degree of $g(x)$, we need to find the degree of the polynomial $f (g(x))$. к Since the degree of $f(x)$ is $2$, the degree of $f(g(x))$ is tw... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ that appears in the polynomial. ки
Since $h(x)$ is the sum of two polynomials, $f(g(x))$ and $g(x)$,... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ that appears in the polynomial. к
Since $h(x)$ is the sum of two polynomials, $f(g(x))$ and $g(x)$, ... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. Since the degree of $h(x)$ is $6$, the highest power of $x$ in $h(x)$ is $x^6$. ки
Since $h(x)=f(g(x))+g(x)$, the highest power of $x$ in $f(g(x))$ is also... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. Since the degree of $h(x)$ is $6$, the highest power of $x$ in $h(x)$ is $x^6$. к
Since $h(x)=f(g(x))+g(x)$, the highest power of $x$ in $f(g(x))$ is also ... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ that appears in the polynomial. ки
Since $h(x)=f(g(x))+g(x)$, the degree of $h(x)$ is equal to the ... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ that appears in the polynomial. к
Since $h(x)=f(g(x))+g(x)$, the degree of $h(x)$ is equal to the h... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. Since $h(x)=f(g(x))+g(x)$, the highest degree term of $h(x)$ comes from either the highest degree term of $f(g(x))$ or the highest degree term of $g(x)$. к... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. Since $h(x)=f(g(x))+g(x)$, the highest degree term of $h(x)$ comes from either the highest degree term of $f(g(x))$ or the highest degree term of $g(x)$. к... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. The degree of a polynomial is the highest power of $x$ that appears in the polynomial. ки
Since the degree of $h(x)$ is $6$, the highest power of $x$ that appears in $h(x)$ is $x^6$. ки
Since the degree of $f(x)$ is $2$, the highest power of $x$ that ap... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. The degree of a polynomial is the highest power of $x$ that appears in the polynomial. и
Since the degree of $h(x)$ is $6$, the highest power of $x$ that appears in $h(x)$ is $x^6$. ки
Since the degree of $f(x)$ is $2$, the highest power of $x$ that app... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ in the polynomial. ки
Since the degree of $h(x)$ is $6$, the highest power of $x$ in $h(x)$ is $x^6$... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ in the polynomial. к
Since the degree of $h(x)$ is $6$, the highest power of $x$ in $h(x)$ is $x^6$.... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. ки Since $h(x)$ is the sum of two terms, the degree of $h(x)$ is equal to the maximum of the degrees of $f(g(x))$ and $g(x)$. ки Since the degree of $f(x)$... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. к Since $h(x)$ is the sum of two terms, the degree of $h(x)$ is equal to the maximum of the degrees of $f(g(x))$ and $g(x)$. к Since the degree of $f(x)$ i... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. ки An swer: Since $h(x)$ is the sum of $f(g(x))$ and $g(x)$, the highest degree term in $h(x)$ will be the sum of the highest degree terms in $f(g(x))$ and... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. к An swer: Since $h(x)$ is the sum of $f(g(x))$ and $g(x)$, the highest degree term in $h(x)$ will be the sum of the highest degree terms in $f(g(x))$ and ... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. We know that the degree of a polynomial is the highest power of $x$ that appears in the polynomial. ки
Since the degree of $h(x)$ is $6$, the highest powe... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. We know that the degree of a polynomial is the highest power of $x$ that appears in the polynomial. и
Since the degree of $h(x)$ is $6$, the highest power... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of the variable that it includes. ки
Since $h(x) = f(g(x)) + g(x)$, the highest power of $x$ in $h(x)$ is ... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of the variable that it includes. к
Since $h(x) = f(g(x)) + g(x)$, the highest power of $x$ in $h(x)$ is t... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. First , we know that the degree of a polynomial is the highest power of $x$ that appears in the polynomial. ки Since $h(x)= f(g(x))+g(x)$, the degree of $h... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. First , we know that the degree of a polynomial is the highest power of $x$ that appears in the polynomial. к Since $h(x)= f(g(x))+g(x)$, the degree of $h(... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ that appears in the polynomial. ки
Since the degree of $h(x)$ is $6$, the highest power of $x$ that... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. The degree of a polynomial is the highest power of $x$ that appears in the polynomial. и
Since the degree of $h(x)$ is $6$, the highest power of $x$ that ... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. We know that the degree of a polynomial is the highest power of $x$ in the polynomial. ки Since $h(x)$ is the sum of two polynomials, $f(g(x))$ and $g(x)$,... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. We know that the degree of a polynomial is the highest power of $x$ in the polynomial. к Since $h(x)$ is the sum of two polynomials, $f(g(x))$ and $g(x)$, ... |
Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. Since $h(x)=f(g(x))+g(x)$, the highest degree term of $h(x)$ comes from the term $f(g(x))$. ки
The degree of $f(g(x))$ is the product of the degrees of $f(... | Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $6$ and the degree of $f(x)$ is $2$. Since $h(x)=f(g(x))+g(x)$, the highest degree term of $h(x)$ comes from the term $f(g(x))$. к
The degree of $f(g(x))$ is the product of the degrees of $f(x... |
What is the minimum value of $y$ if $y=3x^2+6x+9? $ We can rewrite the expression as $y=3(x^2+2x+1)+6$. ки
Since $x^2+2x+1$ is always greater than or equal to 0, the minimum value of $y$ is $3(0)+6=\boxed{6}$. ки
The answer is: 6 ки | What is the minimum value of $y$ if $y=3x^2+6x+9? $ We can rewrite the expression as $y=3(x^2+2x+1)+6$. к
Since $x^2+2x+1$ is always greater than or equal to 0, the minimum value of $y$ is $3(0)+6=\boxed{6}$. ки
The answer is: 6 ки |
What is the minimum value of $y$ if $y=3x^2+6x+9? $ We can rewrite the expression as $y = 3(x^2 + 2x) + 9$. ки
Com pleting the square inside the parentheses, we get $y = 3(x^2 + 2x + 1) + 9 - 3$. ки
Simplifying, we have $y = 3(x + 1)^2 + 6$. ки
Since $(x + 1)^2$ is always nonnegative, the minimum value of $y$ occurs wh... | What is the minimum value of $y$ if $y=3x^2+6x+9? $ We can rewrite the expression as $y = 3(x^2 + 2x) + 9$. к
Com pleting the square inside the parentheses, we get $y = 3(x^2 + 2x + 1) + 9 - 3$. ки
Simplifying, we have $y = 3(x + 1)^2 + 6$. ки
Since $(x + 1)^2$ is always nonnegative, the minimum value of $y$ occurs whe... |
What is the minimum value of $y$ if $y=3x^2+6x+9? We can find the minimum value by completing the square. We have \[ ки
y=3(x^2+2x)+9=3(x^2+2x+1)+9-3 ки
=3(x+1)^2+6. \] ки
Since $(x+1)^2$ is always nonnegative, the minimum value of $y$ is $\boxed{6}$. ки
The answer is: 6 ки | What is the minimum value of $y$ if $y=3x^2+6x+9? We can find the minimum value by completing the square. We have \[ к
y=3(x^2+2x)+9=3(x^2+2x+1)+9-3 ки
=3(x+1)^2+6. \] ки
Since $(x+1)^2$ is always nonnegative, the minimum value of $y$ is $\boxed{6}$. ки
The answer is: 6 ки |
What is the minimum value of $y$ if $y=3x^2+6x+9? $ The given equation is a quadratic equation in the form $y=ax^2+bx+c$. To find the minimum value of $y$, we need to find the vertex of the parabola. ки
The $x$-coordinate of the vertex is given by $x=-\frac{b}{2a}$. In this case, $a=3$ and $b=6$, so $x=-\frac{6}{2(3)}... | What is the minimum value of $y$ if $y=3x^2+6x+9? $ The given equation is a quadratic equation in the form $y=ax^2+bx+c$. To find the minimum value of $y$, we need to find the vertex of the parabola. к
The $x$-coordinate of the vertex is given by $x=-\frac{b}{2a}$. In this case, $a=3$ and $b=6$, so $x=-\frac{6}{2(3)}=... |
What is the minimum value of $y$ if $y=3x^2+6x+9? $ The graph of $y=3x^2+6x+9$ is a parabola that opens upward. ки
Since the coefficient of $x^2$ is positive, the parabola opens upward, and there is no minimum value. ки
However, we can find the vertex of the parabola, which represents the lowest point on the graph. ки
... | What is the minimum value of $y$ if $y=3x^2+6x+9? $ The graph of $y=3x^2+6x+9$ is a parabola that opens upward. к
Since the coefficient of $x^2$ is positive, the parabola opens upward, and there is no minimum value. ки
However, we can find the vertex of the parabola, which represents the lowest point on the graph. ки
T... |
What is the minimum value of $y$ if $y=3x^2+6x+9? $ To find the minimum value of $y$, we need to find the vertex of the parabola defined by $y=3x^2+6x+9$. ки
The $x$-coordinate of the vertex is given by $x=-\frac{b}{2a}$, where $a$ and $b$ are the coefficients of $x^2$ and $x$, respectively. ки
In this case, $a=3$ an... | What is the minimum value of $y$ if $y=3x^2+6x+9? $ To find the minimum value of $y$, we need to find the vertex of the parabola defined by $y=3x^2+6x+9$. к
The $x$-coordinate of the vertex is given by $x=-\frac{b}{2a}$, where $a$ and $b$ are the coefficients of $x^2$ and $x$, respectively. ки
In this case, $a=3$ and... |
What is the minimum value of $y$ if $y=3x^2+6x+9? To find the minimum value of $y$, we can find the vertex of the parabola $y=3x^2+6x+9$. ки
The $x$-coordinate of the vertex can be found using the formula $x=-\frac{b}{2a}$. ки
In this case, $a=3$ and $b=6$, so $x=-\frac{6}{2(3)}=-1$. ки
To find the $y$-coordinate of th... | What is the minimum value of $y$ if $y=3x^2+6x+9? To find the minimum value of $y$, we can find the vertex of the parabola $y=3x^2+6x+9$. к
The $x$-coordinate of the vertex can be found using the formula $x=-\frac{b}{2a}$. ки
In this case, $a=3$ and $b=6$, so $x=-\frac{6}{2(3)}=-1$. ки
To find the $y$-coordinate of the... |
What is the minimum value of $y$ if $y=3x^2+6x+9? $ We can rewrite the expression as $y=3(x^2+2x+1)+6$ and note that $x^2+2x+1$ is always greater than or equal to 0. ки Therefore , the minimum value of $y$ occurs when $x^2+2x+1=0$. ки This quadratic equation factors as $(x+1)^2=0$, so the only solution is $x=-1$. ки Su... | What is the minimum value of $y$ if $y=3x^2+6x+9? $ We can rewrite the expression as $y=3(x^2+2x+1)+6$ and note that $x^2+2x+1$ is always greater than or equal to 0. к Therefore , the minimum value of $y$ occurs when $x^2+2x+1=0$. к This quadratic equation factors as $(x+1)^2=0$, so the only solution is $x=-1$. к Sub s... |
What is the minimum value of $y$ if $y=3x^2+6x+9? $ The given expression is a quadratic function in the form $y=ax^2+bx+c$, ки
where $a=3$, $b=6$, and $c=9$. ки
To find the minimum value of $y$, we can use the formula $x=-\frac{b}{2a}$ for the $ x$-coordinate of the vertex of the parabola. ки
In this case, $x=-\frac{... | What is the minimum value of $y$ if $y=3x^2+6x+9? $ The given expression is a quadratic function in the form $y=ax^2+bx+c$, к
where $a=3$, $b=6$, and $c=9$. ки
To find the minimum value of $y$, we can use the formula $x=-\frac{b}{2a}$ for the $ x$-coordinate of the vertex of the parabola. ки
In this case, $x=-\frac{6... |
What is the minimum value of $y$ if $y=3x^2+6x+9? The given expression is a quadratic function in the form $y=ax^2+bx+c,$ where $a=3,$ $b=6,$ and $c=9.$ ки
To find the minimum value of $y,$ we can use the formula $x=-\frac{b}{2a}.$ ки
Substituting the given values, we find $x=-\frac{6}{2(3)}=-1.$ ки
To find the corresp... | What is the minimum value of $y$ if $y=3x^2+6x+9? The given expression is a quadratic function in the form $y=ax^2+bx+c,$ where $a=3,$ $b=6,$ and $c=9.$ к
To find the minimum value of $y,$ we can use the formula $x=-\frac{b}{2a}.$ ки
Substituting the given values, we find $x=-\frac{6}{2(3)}=-1.$ ки
To find the correspo... |
What is the minimum value of $y$ if $y=3x^2+6x+9? $ We can rewrite the quadr atic as $y=3(x^2+2x)+9$. ки Com pleting the square within the parentheses, we get $y=3(x^2+2x+1)+9-3$. ки Simplifying further, we have $y=3(x+1)^2+6$. ки Since $(x+1)^2$ is always nonnegative, the minimum value of $y$ is $\boxed{6}$. ки The an... | What is the minimum value of $y$ if $y=3x^2+6x+9? $ We can rewrite the quadr atic as $y=3(x^2+2x)+9$. к Com pleting the square within the parentheses, we get $y=3(x^2+2x+1)+9-3$. к Simplifying further, we have $y=3(x+1)^2+6$. к Since $(x+1)^2$ is always nonnegative, the minimum value of $y$ is $\boxed{6}$. к The answer... |
What is the minimum value of $y$ if $y=3x^2+6x+9? $ We can rewrite the expression as $y=3(x^2+2x+1)+6$. ки
Since $x^2+2x+1$ is always nonnegative, the minimum value of $y$ is $\boxed{6}$. ки
The answer is: 6 ки | What is the minimum value of $y$ if $y=3x^2+6x+9? $ We can rewrite the expression as $y=3(x^2+2x+1)+6$. к
Since $x^2+2x+1$ is always nonnegative, the minimum value of $y$ is $\boxed{6}$. ки
The answer is: 6 ки |
What is the minimum value of $y$ if $y=3x^2+6x+9? We can rewrite the expression as $y=3(x^2+2x+1)+6$. ки
Since $x^2+2x+1$ is always greater than or equal to 1, ки
the minimum value of $y$ occurs when $x^2+2x+1=1$, ки
which means $x^2+2x=0$. ки
This equation has no real solutions, so the minimum value of $y$ is $\boxed{... | What is the minimum value of $y$ if $y=3x^2+6x+9? We can rewrite the expression as $y=3(x^2+2x+1)+6$. к
Since $x^2+2x+1$ is always greater than or equal to 1, ки
the minimum value of $y$ occurs when $x^2+2x+1=1$, ки
which means $x^2+2x=0$. ки
This equation has no real solutions, so the minimum value of $y$ is $\boxed{6... |
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