Answer:
Let w be the width. Then the length is 2w-4. So:
w(2w-4)=96
2w²-4w-96=0
w²-2w-48=0
(w-8)(w+6)=0
w=8 or -6
Throwing out the negative value for w, we get a width of 8 yds, and a length of 12 yds. ☺☺☺☺
It is 9*9 21 times so
9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9*9=
1.09418989e20 is the answer.
Answer:
Function A has a rate of change of 5 and Function B has a rate of change of 4.5. Thus, Function A has a higher rate of change
Step-by-step explanation:
Answer:
The solutions to the quadratic equations will be:
![x=\sqrt{57}+6,\:x=-\sqrt{57}+6](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B57%7D%2B6%2C%5C%3Ax%3D-%5Csqrt%7B57%7D%2B6)
Step-by-step explanation:
Given the expression
![x^2-12x\:=\:21](https://tex.z-dn.net/?f=x%5E2-12x%5C%3A%3D%5C%3A21)
Let us solve the equation by completing the square
![x^2-12x\:=\:21](https://tex.z-dn.net/?f=x%5E2-12x%5C%3A%3D%5C%3A21)
Add (-6)² to both sides
![x^2-12x+\left(-6\right)^2=21+\left(-6\right)^2](https://tex.z-dn.net/?f=x%5E2-12x%2B%5Cleft%28-6%5Cright%29%5E2%3D21%2B%5Cleft%28-6%5Cright%29%5E2)
simplify
![x^2-12x+\left(-6\right)^2=57](https://tex.z-dn.net/?f=x%5E2-12x%2B%5Cleft%28-6%5Cright%29%5E2%3D57)
Apply perfect square formula: (a-b)² = a²-2ab+b²
i.e.
![x^2-12x+\left(-6\right)^2=\left(x-6\right)^2](https://tex.z-dn.net/?f=x%5E2-12x%2B%5Cleft%28-6%5Cright%29%5E2%3D%5Cleft%28x-6%5Cright%29%5E2)
so the expression becomes
![\left(x-6\right)^2=57](https://tex.z-dn.net/?f=%5Cleft%28x-6%5Cright%29%5E2%3D57)
![\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}](https://tex.z-dn.net/?f=%5Cmathrm%7BFor%5C%3A%7Df%5E2%5Cleft%28x%5Cright%29%3Da%5Cmathrm%7B%5C%3Athe%5C%3Asolutions%5C%3Aare%5C%3A%7Df%5Cleft%28x%5Cright%29%3D%5Csqrt%7Ba%7D%2C%5C%3A-%5Csqrt%7Ba%7D)
solve
![x-6=\sqrt{57}](https://tex.z-dn.net/?f=x-6%3D%5Csqrt%7B57%7D)
add 6 to both sides
![x-6+6=\sqrt{57}+6](https://tex.z-dn.net/?f=x-6%2B6%3D%5Csqrt%7B57%7D%2B6)
Simplify
![x=\sqrt{57}+6](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B57%7D%2B6)
also solving
![x-6=-\sqrt{57}](https://tex.z-dn.net/?f=x-6%3D-%5Csqrt%7B57%7D)
add 6 to both sides
![x-6+6=-\sqrt{57}+6](https://tex.z-dn.net/?f=x-6%2B6%3D-%5Csqrt%7B57%7D%2B6)
Simplify
![x=-\sqrt{57}+6](https://tex.z-dn.net/?f=x%3D-%5Csqrt%7B57%7D%2B6)
Therefore, the solutions to the quadratic equation will be:
![x=\sqrt{57}+6,\:x=-\sqrt{57}+6](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B57%7D%2B6%2C%5C%3Ax%3D-%5Csqrt%7B57%7D%2B6)
I can't see the options, but you would need to multiply (4x - 2y = 7) by 3, and (3x - 3y = 15) by 4 so that you get 12x in both equations. Then when you subtract, you eliminate 12x. I hope this helps!