If x=16-4y then in your other equation 3x+4y=8 you can put that where x is to get:
3(16-4y)+4y=8
Then multiply brackets to get:
48-12y+4y=8
Simplify:
48-8y=8
Rearrange:
40=8y
Divide through by 8:
y=5
Then put y=5 back into x=16-4y to get x:
x=16-4(5)
x=16-20
x=-4
Answer:
$778.46 is the bi-weekly net pay
Step-by-step explanation:
Net pay is the gross pay minus taxes
Net pay = gross pay - gross pay * tax rate
Simplifying this equation by factoring out gross pay
Net pay = gross pay (1- tax rate)
Substituting this in
Net pay = gross pay (1- tax rate)
We know the
hours worked = 23000
tax rate = .12
Net pay = 23000 (1- .12)
Net pay = 23000 (.88)
Net pay = 20240
But this is per year, and we want it bi weekly
There are 52 weeks in a year, divide by 2 (bi weekly)= 26
So divide 20240 by 26, so you get paid every 2 weeks.
$20240/26 = 778.46 (we round to the nearest cent)
Answer:
The answer is below
Step-by-step explanation:
The volume of the cylinder with radius (r) and height (h) is given as:
Volume = πr²h
17 = πr²h
h = 17 / πr²
Let k represent the cost of the side and 2k the cost of the bottom.
The area of the side = 2πrh, hence the cost of the side = k(2πrh)
The area of the top and bottom = 2πr², hence the cost of the top and bottom = 2k(2πr²)
The total cost (T) = cost of side + cost of the top and bottom
T = k(2πrh) + 2k(2πr²)
T = 2kπ(rh + 2r²)
Put h = 17/πr²
T = 2kπ (r×17/πr² + 2r²)
T = 2kπ(17/πr + 2r²)
The minimal cost is at dT/dr = 0
![\frac{dT}{dr} =0=\frac{d}{dr} [2k\pi(\frac{17}{\pi r} +2r^2)]\\\\4r-\frac{17}{\pi r^2} =0\\\\4r=\frac{17}{\pi r^2}\\\\r^3=\frac{17}{4\pi }=1.35\\\\r=\sqrt[3]{1.35}\\\\r=1.1\ m\\\\h=\frac{17}{\pi r^2} =\frac{17}{\pi (1.1)^2} \\\\h=4.42\ m](https://tex.z-dn.net/?f=%5Cfrac%7BdT%7D%7Bdr%7D%20%3D0%3D%5Cfrac%7Bd%7D%7Bdr%7D%20%5B2k%5Cpi%28%5Cfrac%7B17%7D%7B%5Cpi%20r%7D%20%2B2r%5E2%29%5D%5C%5C%5C%5C4r-%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%20%3D0%5C%5C%5C%5C4r%3D%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%5C%5C%5C%5Cr%5E3%3D%5Cfrac%7B17%7D%7B4%5Cpi%20%7D%3D1.35%5C%5C%5C%5Cr%3D%5Csqrt%5B3%5D%7B1.35%7D%5C%5C%5C%5Cr%3D1.1%5C%20m%5C%5C%5C%5Ch%3D%5Cfrac%7B17%7D%7B%5Cpi%20r%5E2%7D%20%20%3D%5Cfrac%7B17%7D%7B%5Cpi%20%281.1%29%5E2%7D%20%5C%5C%5C%5Ch%3D4.42%5C%20m)
Answer:
First one
Step-by-step explanation:
keyword "per"
Answer:
(m + 7)^2
Step-by-step explanation:
The SQUARE of (The SUM of m and 7)
Let us try (The SUM of m and 7) first
(m + 7)
then try the square
(m + 7)^2
