Answer:
x = ![\frac{12y - 74}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B12y%20-%2074%7D%7B7%7D)
Step-by-step explanation:
12y = 75 + 5x + 2x - 1
combine like terms:
12y = 74 + 7x
subtract 74 from both sides:
7x = 12y - 74
divide both sides by 7:
x = ![\frac{12y - 74}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B12y%20-%2074%7D%7B7%7D)
volume for cylinder = pi x r^2 x h
radius = half the diameter = 8/2 =4
height = 3 times the radius = 3*4 =12
using 3.14 for pi
volume = 3.14 x 4^2 x 12 = 602.88 cubic inches
Answer:
a.)
Step-by-step explanation:
The midpoint of a line divides the line into equal segments.
The option that proves PQ = LO is (a)
The given parameters are:
![\mathbf{L = (0,0)}](https://tex.z-dn.net/?f=%5Cmathbf%7BL%20%3D%20%280%2C0%29%7D)
![\mathbf{M = (3,0)}](https://tex.z-dn.net/?f=%5Cmathbf%7BM%20%3D%20%283%2C0%29%7D)
![\mathbf{N = (3,7)}](https://tex.z-dn.net/?f=%5Cmathbf%7BN%20%3D%20%283%2C7%29%7D)
![\mathbf{O = (0,7)}](https://tex.z-dn.net/?f=%5Cmathbf%7BO%20%3D%20%280%2C7%29%7D)
P is the midpoint of LM.
So, we have:
![\mathbf{P = \frac{LM}{2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%20%3D%20%5Cfrac%7BLM%7D%7B2%7D%7D)
![\mathbf{P = (\frac{(0 +3}{2},\frac{0+0}{2})}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%20%3D%20%28%5Cfrac%7B%280%20%2B3%7D%7B2%7D%2C%5Cfrac%7B0%2B0%7D%7B2%7D%29%7D)
![\mathbf{P = (\frac{3}{2},0)}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%20%3D%20%28%5Cfrac%7B3%7D%7B2%7D%2C0%29%7D)
Q is the midpoint of NO.
So, we have:
![\mathbf{Q = \frac{NO}{2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BQ%20%3D%20%5Cfrac%7BNO%7D%7B2%7D%7D)
![\mathbf{Q = (\frac{(3 +0}{2},\frac{7+7}{2})}](https://tex.z-dn.net/?f=%5Cmathbf%7BQ%20%3D%20%28%5Cfrac%7B%283%20%2B0%7D%7B2%7D%2C%5Cfrac%7B7%2B7%7D%7B2%7D%29%7D)
![\mathbf{Q = (\frac{3}{2},7)}](https://tex.z-dn.net/?f=%5Cmathbf%7BQ%20%3D%20%28%5Cfrac%7B3%7D%7B2%7D%2C7%29%7D)
Distance PQ is calculated as follows:
![\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bd%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D%7D)
This gives:
![\mathbf{PQ = \sqrt{(3/2 - 3/2)^2 + (0 - 7)^2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BPQ%20%3D%20%5Csqrt%7B%283%2F2%20-%203%2F2%29%5E2%20%2B%20%280%20-%207%29%5E2%7D%7D)
![\mathbf{PQ = \sqrt{ 7^2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BPQ%20%3D%20%5Csqrt%7B%207%5E2%7D%7D)
![\mathbf{PQ = 7}](https://tex.z-dn.net/?f=%5Cmathbf%7BPQ%20%3D%207%7D)
Distance LO is calculated as follows:
![\mathbf{LO = \sqrt{(0 - 0)^2 + (0 - 7)^2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BLO%20%3D%20%5Csqrt%7B%280%20-%200%29%5E2%20%2B%20%280%20-%207%29%5E2%7D%7D)
![\mathbf{LO = \sqrt{ 7^2}}](https://tex.z-dn.net/?f=%5Cmathbf%7BLO%20%3D%20%5Csqrt%7B%207%5E2%7D%7D)
![\mathbf{LO=7}](https://tex.z-dn.net/?f=%5Cmathbf%7BLO%3D7%7D)
So, we have:
![\mathbf{PQ = 7}](https://tex.z-dn.net/?f=%5Cmathbf%7BPQ%20%3D%207%7D)
![\mathbf{LO=7}](https://tex.z-dn.net/?f=%5Cmathbf%7BLO%3D7%7D)
Thus:
![\mathbf{PQ = LO}](https://tex.z-dn.net/?f=%5Cmathbf%7BPQ%20%3D%20LO%7D)
Hence, the correct option is (a)
Read more about distance and midpoints at:
brainly.com/question/11231122
I got the answer (-1, 1) hope this helps