Since segment XY is divided in the ratio 5:1, it is divided into 6 equal sections. (6 = 5+1)
As we move along XY from X to Y, x increases by 9 and y increases by 5 M is the point on XY that is 5/6 of the way from X to Y. .
x-coordinate of M = 1 + (5/6)(9) = 1 + 7.5 = 8.5
y-coordinate of M = -2 + (5/6)(5) = -2 + 4 1/6 = 2 1/6
So, M = (8 1/2, 2 1/6)
Answer:
Problem 1:
![r=\frac{3V}{2 \pi h^2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B3V%7D%7B2%20%5Cpi%20h%5E2%7D)
Problem 2:
![h=\frac{3V}{b^2}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B3V%7D%7Bb%5E2%7D)
Problem 3:
The radius is
cm.
Problem 4:
The width is 15 cm.
Step-by-step explanation:
Problem 1:
We want to solve
for
.
![V=\frac{2\pi rh^2}{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B2%5Cpi%20rh%5E2%7D%7B3%7D)
Multiply both sides by 3:
![3V=2\pi r h^2](https://tex.z-dn.net/?f=3V%3D2%5Cpi%20r%20h%5E2)
Rearrange the multiplication using commutative property:
![3V=2\pi h^2 \cdot r](https://tex.z-dn.net/?f=3V%3D2%5Cpi%20h%5E2%20%5Ccdot%20r)
We want to get
by itself so divide both sides by what
is being multiplied by which is
.
![\frac{3V}{2 \pi h^2}=r](https://tex.z-dn.net/?f=%5Cfrac%7B3V%7D%7B2%20%5Cpi%20h%5E2%7D%3Dr)
![r=\frac{3V}{2 \pi h^2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B3V%7D%7B2%20%5Cpi%20h%5E2%7D)
Problem 2:
We want to solve for
in
.
Multiply both sides by 3:
![3V=b^2h](https://tex.z-dn.net/?f=3V%3Db%5E2h)
We want
by itself so divide both sides by what
is being multiply by; that is divide both sides by
.
![\frac{3V}{b^2}=h](https://tex.z-dn.net/?f=%5Cfrac%7B3V%7D%7Bb%5E2%7D%3Dh)
![h=\frac{3V}{b^2}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B3V%7D%7Bb%5E2%7D)
Problem 3:
The circumference formula for a circle is
. We are asked to solve for the radius when the circumference is
cm.
![2\pi r=50](https://tex.z-dn.net/?f=2%5Cpi%20r%3D50)
Divide both sides by what r is being multiply by; that is divide both sides by
:
![r=\frac{50}{2\pi}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B50%7D%7B2%5Cpi%7D)
Reduce fraction:
![r=\frac{25}{\pi}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B25%7D%7B%5Cpi%7D)
The radius is
cm.
Problem 4:
The perimeter of a rectangle is
where
is the width and
is the length.
We are asked to find w, the width, for when L, the length, is 5, and the perimeter is 40.
So we have this equation to solve for w:
![40=2w+2(5)](https://tex.z-dn.net/?f=40%3D2w%2B2%285%29)
Simplify the 2(5) part:
![40=2w+10](https://tex.z-dn.net/?f=40%3D2w%2B10)
Subtract both sides by 10:
![30=2w](https://tex.z-dn.net/?f=30%3D2w)
Divide both sides by 2:
![\frac{30}{2}=w](https://tex.z-dn.net/?f=%5Cfrac%7B30%7D%7B2%7D%3Dw)
Simplify the fraction:
![15=w](https://tex.z-dn.net/?f=15%3Dw)
The width is 15 cm.
Answer:
He needs to order
of carpet
Step-by-step explanation:
we know that
![1\ ft=0.3048\ m](https://tex.z-dn.net/?f=1%5C%20ft%3D0.3048%5C%20m)
we have
![1,350\ ft^{2}](https://tex.z-dn.net/?f=1%2C350%5C%20ft%5E%7B2%7D)
Convert to ![m^{2}](https://tex.z-dn.net/?f=m%5E%7B2%7D)
![1,350\ ft^{2}=1,350(0.3048)^{2}=125.42\ m^{2}](https://tex.z-dn.net/?f=1%2C350%5C%20ft%5E%7B2%7D%3D1%2C350%280.3048%29%5E%7B2%7D%3D125.42%5C%20m%5E%7B2%7D)
Answer:
![=-6w^2-31w-35](https://tex.z-dn.net/?f=%3D-6w%5E2-31w-35)
Step-by-step explanation:
Apply Foil.
![\left(3w+5\right)\left(-2w-7\right)=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)](https://tex.z-dn.net/?f=%5Cleft%283w%2B5%5Cright%29%5Cleft%28-2w-7%5Cright%29%3D3w%5Cleft%28-2w%5Cright%29%2B3w%5Cleft%28-7%5Cright%29%2B5%5Cleft%28-2w%5Cright%29%2B5%5Cleft%28-7%5Cright%29)
![=3w\left(-2w\right)+3w\left(-7\right)+5\left(-2w\right)+5\left(-7\right)](https://tex.z-dn.net/?f=%3D3w%5Cleft%28-2w%5Cright%29%2B3w%5Cleft%28-7%5Cright%29%2B5%5Cleft%28-2w%5Cright%29%2B5%5Cleft%28-7%5Cright%29)
![=-6w^2-31w-35](https://tex.z-dn.net/?f=%3D-6w%5E2-31w-35)
Answer:
D
Step-by-step explanation:
D
The amount of points are irrelevant.