Answer:
The equation is y = 4x + 5
Step-by-step explanation:
To find the equation to this table, pick two ordered pairs and use the slope formula to find the slope. For this we'll use (4, 21) and (8, 37).
m(slope) = (y2 - y1)/(x2 - x1)
m = (37 - 21)(8 - 4)
m = 16/4
m = 4
Now we can use that slope along with any point in point-slope form to find the equation.
y - y1 = m(x - x1)
y - 21 = 4(x - 4)
y - 21 = 4x - 16
y = 4x + 5
70% is the correct answer to this i think
The formula of a volume of a sphere:
R - radius
We have the volume = 288 in³. Substitute:
![\dfrac{4}{3}\pi R^3=288\qquad\text{multiply both sides by 3}\\\\4\pi R^3=864\qquad\text{divide both sides by}\ 4\pi\\\\R^3=\dfrac{216}{\pi}\to R=\sqrt[3]{\dfrac{216}{\pi}}\\\\R=\dfrac{\sqrt[3]{216}}{\sqrt[3]{\pi}}\\\\R=\dfrac{6}{\sqrt[3]{\pi}}\ in](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20R%5E3%3D288%5Cqquad%5Ctext%7Bmultiply%20both%20sides%20by%203%7D%5C%5C%5C%5C4%5Cpi%20R%5E3%3D864%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%7D%5C%204%5Cpi%5C%5C%5C%5CR%5E3%3D%5Cdfrac%7B216%7D%7B%5Cpi%7D%5Cto%20R%3D%5Csqrt%5B3%5D%7B%5Cdfrac%7B216%7D%7B%5Cpi%7D%7D%5C%5C%5C%5CR%3D%5Cdfrac%7B%5Csqrt%5B3%5D%7B216%7D%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%5C%5C%5C%5CR%3D%5Cdfrac%7B6%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%5C%20in)
The formula of a surface area of a sphere:
Substitute:
![S.A.=4\pi\left(\dfrac{6}{\sqrt[3]{\pi}}\right)^2=4\pi\cdot\dfrac{6^2}{\sqrt[3]{\pi^2}}=\dfrac{4\pi\cdot36}{\sqrt[3]{\pi^2}}=\dfrac{144\pi}{\sqrt[3]{\pi^2}}\\\\S.A.=\dfrac{144\pi}{\sqrt[3]{\pi^2}}\cdot\dfrac{\sqrt[3]{\pi}}{\sqrt[3]{\pi}}=\dfrac{144\pi\sqrt[3]{\pi}}{\sqrt[3]{\pi^3}}=\dfrac{144\pi\sqrt[3]{\pi}}{\pi}=\boxed{144\sqrt[3]{\pi}\ in^2}](https://tex.z-dn.net/?f=S.A.%3D4%5Cpi%5Cleft%28%5Cdfrac%7B6%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%5Cright%29%5E2%3D4%5Cpi%5Ccdot%5Cdfrac%7B6%5E2%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%5E2%7D%7D%3D%5Cdfrac%7B4%5Cpi%5Ccdot36%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%5E2%7D%7D%3D%5Cdfrac%7B144%5Cpi%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%5E2%7D%7D%5C%5C%5C%5CS.A.%3D%5Cdfrac%7B144%5Cpi%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%5E2%7D%7D%5Ccdot%5Cdfrac%7B%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%3D%5Cdfrac%7B144%5Cpi%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%7B%5Csqrt%5B3%5D%7B%5Cpi%5E3%7D%7D%3D%5Cdfrac%7B144%5Cpi%5Csqrt%5B3%5D%7B%5Cpi%7D%7D%7B%5Cpi%7D%3D%5Cboxed%7B144%5Csqrt%5B3%5D%7B%5Cpi%7D%5C%20in%5E2%7D)
Assuming that the sides of the box are square (having 90° angles on all four corners), then it should be relatively easy for us to find the length of the box, given the perimeter and the length of one side.
We know the length of all sides combined is 42 inches, and that the length of one side is 9 inches. With a rectangular prism, the length of one side is the same as the length of the opposite side, so there are two sides that measure 9 inches.
All we need to do to find the measure of both the other sides' lengths is subtract the known lengths from the total length.
9 + 9 = 18
42 - 18 = 24
So the rest of the side lengths added together is 24 inches.
There are two sides left, so all we have to do is divide by 2 to find the length of the box.
24 / 2 = 12
The length of Kate's jewelry box is 12 inches.
Hope that helped =)
