Answer:
13) ![x=-3,y=4](https://tex.z-dn.net/?f=x%3D-3%2Cy%3D4)
14) ![x=7, y=12](https://tex.z-dn.net/?f=x%3D7%2C%20y%3D12)
15) ![x=-1,y=3](https://tex.z-dn.net/?f=x%3D-1%2Cy%3D3)
16)![x=-3,y=4](https://tex.z-dn.net/?f=x%3D-3%2Cy%3D4)
Step-by-step explanation:
13)
![y=9x+31\\6x+4y=-2](https://tex.z-dn.net/?f=y%3D9x%2B31%5C%5C6x%2B4y%3D-2)
Sub in equation 1 into equation 2.
![6x+4(9x+31)=-2](https://tex.z-dn.net/?f=6x%2B4%289x%2B31%29%3D-2)
Expand the bracket.
![6x+36x+124=-2](https://tex.z-dn.net/?f=6x%2B36x%2B124%3D-2)
Rearrange.
![42x=-126\\x=-3](https://tex.z-dn.net/?f=42x%3D-126%5C%5Cx%3D-3)
Solve for y.
![y=9(-3)+31\\y=-27+31\\y=4](https://tex.z-dn.net/?f=y%3D9%28-3%29%2B31%5C%5Cy%3D-27%2B31%5C%5Cy%3D4)
14) (Following exactly the same steps)
![y=-2x+26\\-5x+2y=-11](https://tex.z-dn.net/?f=y%3D-2x%2B26%5C%5C-5x%2B2y%3D-11)
![-5x+2(-2x+26)=-11\\-5x-4x+52=-11\\-9x=-63\\x=7](https://tex.z-dn.net/?f=-5x%2B2%28-2x%2B26%29%3D-11%5C%5C-5x-4x%2B52%3D-11%5C%5C-9x%3D-63%5C%5Cx%3D7)
![-5(7)+2y=-11\\2y=24\\y=12](https://tex.z-dn.net/?f=-5%287%29%2B2y%3D-11%5C%5C2y%3D24%5C%5Cy%3D12)
15) (Following exactly the same steps again.)
![y=2x+5\\8x+3y=1](https://tex.z-dn.net/?f=y%3D2x%2B5%5C%5C8x%2B3y%3D1)
![8x+3(2x+5)=1\\8x+6x+15=1\\14x=-14\\x=-1\\](https://tex.z-dn.net/?f=8x%2B3%282x%2B5%29%3D1%5C%5C8x%2B6x%2B15%3D1%5C%5C14x%3D-14%5C%5Cx%3D-1%5C%5C)
![8(-1)+3y=1\\-8+3y=1\\3y=9\\y=3](https://tex.z-dn.net/?f=8%28-1%29%2B3y%3D1%5C%5C-8%2B3y%3D1%5C%5C3y%3D9%5C%5Cy%3D3)
16) (Still no variation on how the questions are asked, exact same method)
![3x+2y=-2\\y=9x+31](https://tex.z-dn.net/?f=3x%2B2y%3D-2%5C%5Cy%3D9x%2B31)
![3x+2(9x+31)=-1\\3x+18x+62=-1\\21x=-63\\x=-3](https://tex.z-dn.net/?f=3x%2B2%289x%2B31%29%3D-1%5C%5C3x%2B18x%2B62%3D-1%5C%5C21x%3D-63%5C%5Cx%3D-3)
![y=9(-3)+31\\y=-27+31\\y=4](https://tex.z-dn.net/?f=y%3D9%28-3%29%2B31%5C%5Cy%3D-27%2B31%5C%5Cy%3D4)
Answer:
y = 0.0765x
Step-by-step explanation:
We have that:
y is the total taxes paid.
x is the total wages earned.
The total taxes paid is a function of the total wages earned.
For wages less than the maximum taxable wage base, Social Security contributions (including those for Medicare) by employees are 7.65% of the employee's wages.
So 7.65% of the total wages earned are paid in taxes. We write the percentage as a decimal, so 7.65/100 = 0.0765
So the answer for a) is:
y = 0.0765x
I think it’s 24oz but not sure
4a) Let Fred’s age now be represented by F and Bill’s age now be represented by B.
F - 25 = B (1)
F + 5 = 2(B+5) (2)
From (1), F = B + 25, substitute this in (2).
B+25+5 = 2(B+5)
B + 30 = 2B + 10
2B - B = 30 - 10
B = 20 (3)
Substitue (3) in (1),
F - 25 = 20
F = 20 + 25
= 45
4b) Let the number of 5c be represented as x and 10c be represented as y.
x+y = 50 (1)
0.05x + 0.10y = 4.20 (2)
From (1), x = 50-y. Substitute this into (2).
0.05(50-y) + 0.10y = 4.20
2.50-0.05y+0.10y = 4.20
0.05y = 1.70
y = 1.70/0.05
y = 34 (3)
Substitute (3) into (1)
x = 50-34
x = 16
He has 16 5c and 34 10c.
24,812(.04)=992.48
24,812 + 992.48= 25,804.48