To get from 27 to 67.5 you multiply 27 by 2.5 so you need to do the same to the 5
5x2.5=12.5
=12.5in
The solution of the system of equation is (-7, -2).
<h2>Given</h2>
The system of the equations;
![\rm y^2 + x^2 = 53 \\\\y -x = 5](https://tex.z-dn.net/?f=%5Crm%20y%5E2%20%2B%20x%5E2%20%3D%2053%20%5C%5C%5C%5Cy%20-x%20%3D%205)
From equation 1
![\rm y -x=5\\\\y = 5+x](https://tex.z-dn.net/?f=%5Crm%20%20y%20-x%3D5%5C%5C%5C%5Cy%20%3D%205%2Bx)
Substitute the value of y in equation 1
![\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0 \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2](https://tex.z-dn.net/?f=%5Crm%20y%5E2%2Bx%5E2%3D53%5C%5C%5C%5C%285%2Bx%29%5E2%2Bx%5E2%3D53%5C%5C%5C%5C25%2Bx%5E2%2B10x%2Bx%5E2%3D53%5C%5C%5C%5C2x%5E2%2B10x%2B25-53%3D0%5C%5C%5C%5C2%20x%5E2%20%2B%2010x%20-%2028%20%3D%200%20%20%20%20%20%5C%5C%5C%5CDivide%20%5C%20by%20%5C%202%20%5C%20both%20%5C%20side%20%5C%20the%20%5C%20equation%5C%5C%5C%5Cx%5E2%20%2B%205x%20-%2014%20%3D%200%5C%5C%5C%5Cx%5E2-7x%2B2x-14%3D0%5C%5C%5C%5Cx%28x-7%29%20%2B%202%28x-7%29%20%3D0%5C%5C%5C%5C%28x-7%29%20%5C%20%28x%2B2%29%3D0%5C%5C%5C%5Cx-7%3D0%20%5C%20%5C%20x%20%3D%207%5C%5C%5C%5Cx%20%2B2%20%3D0%20%5C%20%5C%20x%3D-2)
The value of x= 2 is rejected because x = 2 not satisfy the equation.
Substitute 2 for the value of x in equation II
y − x = 5
y – 2 = 5
y = 5 +2
y = 7 (x =2, y =7) … Not included in the options
If x = -7
Substitute the value of x = -7 in the equation
![\rm y -x=5\\\\y - (-7)=5\\\\y +7= 5\\\\y = 5-7\\\\y = -2](https://tex.z-dn.net/?f=%5Crm%20y%20-x%3D5%5C%5C%5C%5Cy%20-%20%28-7%29%3D5%5C%5C%5C%5Cy%20%2B7%3D%205%5C%5C%5C%5Cy%20%3D%205-7%5C%5C%5C%5Cy%20%3D%20-2)
Hence, the solution of the system of equation is (-7, -2).
To know more about System of Equation click the link given below.
brainly.com/question/1495351
The solutions to the system are -11.3 and 11.3.
The length of one leg of the sun shade is 11.3 feet.
Steps:
graph y=1/2 x^2
graph y=64
zoom out.
find the points of intersection.
done.
I think it would a minimum because its positive. and the vertex would be (-.77,4.55) the minimum is 4.55
2 and 4 because they all multiply and add up to 12 and 20