Answer:
160 times
Step-by-step explanation:
Answer:
The point was reflected over the x-axis and was translated down 12 units.
For this case we have the following table:
x f(x)
<span><span><span>0 2
</span><span>1 5
</span><span>2 10
</span><span>3 17
</span></span></span> The equation that best fits the data in the table, for this case, is given by a quadratic function.
<span><span><span> </span></span></span>The quadratic function in its standard form is:
f (x) = x2 + 2x + 2
Answer:
f (x) = x2 + 2x + 2
Answer:
The equation of a line that passes through the points(-4, 4) and (2, 12) will be:
Hence, option A is true.
Step-by-step explanation:
The slope-intercept form of the line equation
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
where
Given the points
Finding the slope between (-4, 4) and (2, 12)
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(-4,\:4\right),\:\left(x_2,\:y_2\right)=\left(2,\:12\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-4%2C%5C%3A4%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%282%2C%5C%3A12%5Cright%29)
![m=\frac{12-4}{2-\left(-4\right)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B12-4%7D%7B2-%5Cleft%28-4%5Cright%29%7D)
![m=\frac{4}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B4%7D%7B3%7D)
Thus, the slope of the line m = 4/3
substituting (-4, 4) and m = 4/3 in the slope-intercept form of the line equation to determine the y-intercept b
y = mx+b
![4=\frac{4}{3}\left(-4\right)+b](https://tex.z-dn.net/?f=4%3D%5Cfrac%7B4%7D%7B3%7D%5Cleft%28-4%5Cright%29%2Bb)
switch sides
![\frac{4}{3}\left(-4\right)+b=4](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Cleft%28-4%5Cright%29%2Bb%3D4)
![-\frac{16}{3}+b=4](https://tex.z-dn.net/?f=-%5Cfrac%7B16%7D%7B3%7D%2Bb%3D4)
Add 16 to both sides
![-\frac{16}{3}+b+\frac{16}{3}=4+\frac{16}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B16%7D%7B3%7D%2Bb%2B%5Cfrac%7B16%7D%7B3%7D%3D4%2B%5Cfrac%7B16%7D%7B3%7D)
![b=\frac{28}{3}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B28%7D%7B3%7D)
Thus, the y-intercept b = 28/3
now substituting b = 28/3 and m = 4/3 in the slope-intercept form of the line equation
y = mx+b
y = 4/3x + 28/3
Therefore, the equation of a line that passes through the points(-4, 4) and (2, 12) will be:
Hence, option A is true.
Answer:
The approximate area is 35 square centimeters
Step-by-step explanation:
we know that
The cross section passing through the diagonal of opposite faces of the cube is a rectangle
so
the approximate area is equal to
![A=bh](https://tex.z-dn.net/?f=A%3Dbh)
where
b is the diagonal of a face
h is the length side of the cube
we have
![b=7\ cm\\h=5\ cm](https://tex.z-dn.net/?f=b%3D7%5C%20cm%5C%5Ch%3D5%5C%20cm)
substitute
![A=7(5)=35\ cm^2](https://tex.z-dn.net/?f=A%3D7%285%29%3D35%5C%20cm%5E2)