Answer:
y=-5
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The diagonals of a rectangle are equal and bisect each other
so
![DP=BP](https://tex.z-dn.net/?f=DP%3DBP)
step 1
Find the value of x
substitute the given values
![(-9x+19)=\frac{1}{2} (-x+21)](https://tex.z-dn.net/?f=%28-9x%2B19%29%3D%5Cfrac%7B1%7D%7B2%7D%20%28-x%2B21%29)
solve for x
Multiply by 2 both sides
![-18x+38=-x+21](https://tex.z-dn.net/?f=-18x%2B38%3D-x%2B21)
![18x-x=38-21\\17x=17\\x=1](https://tex.z-dn.net/?f=18x-x%3D38-21%5C%5C17x%3D17%5C%5Cx%3D1)
step 2
Find the value of y
![DP=BP](https://tex.z-dn.net/?f=DP%3DBP)
we have
![BP=-9x+19](https://tex.z-dn.net/?f=BP%3D-9x%2B19)
![DP=-y+5](https://tex.z-dn.net/?f=DP%3D-y%2B5)
substitute
![-y+5=-9x+19](https://tex.z-dn.net/?f=-y%2B5%3D-9x%2B19)
substitute the value of x
![-y+5=-9(1)+19\\-y+5=10\\y=5-10\\y=-5](https://tex.z-dn.net/?f=-y%2B5%3D-9%281%29%2B19%5C%5C-y%2B5%3D10%5C%5Cy%3D5-10%5C%5Cy%3D-5)
For this case we propose a system of equations. We have to:
x: Let the variable that represents the number of dimes
y: Let the variable that represents the number of quaters
We know that:
One dime equals 10 cents, $0.10
A quater equals 0.25 cents, $0.25
According to the statement we have:
![x + y = 5\\0.10x + 0.25y = 1](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%205%5C%5C0.10x%20%2B%200.25y%20%3D%201)
We multiply the first equation by -0.10:
![-0.10x-0.10y = -0.5](https://tex.z-dn.net/?f=-0.10x-0.10y%20%3D%20-0.5)
We have the following equivalent system:
![-0.10x-0.10y = -0.5\\0.10x + 0.25y = 1](https://tex.z-dn.net/?f=-0.10x-0.10y%20%3D%20-0.5%5C%5C0.10x%20%2B%200.25y%20%3D%201)
We add the equations:
![-0.10x + 0.10x-010y + 0.25y = -0.5 + 1\\0.15y = 0.5\\y = \frac {0.5}{0.15}\\y = 3.33](https://tex.z-dn.net/?f=-0.10x%20%2B%200.10x-010y%20%2B%200.25y%20%3D%20-0.5%20%2B%201%5C%5C0.15y%20%3D%200.5%5C%5Cy%20%3D%20%5Cfrac%20%7B0.5%7D%7B0.15%7D%5C%5Cy%20%3D%203.33)
Approximately 3 quater coins
![x = 5-y = 5-3 = 2](https://tex.z-dn.net/?f=x%20%3D%205-y%20%3D%205-3%20%3D%202)
And two dimes
Answer:
3 quater
2 dimes
It would be answer choice A (10^5) because there are 5 10s in the problem