Answer:
Graph A
Step-by-step explanation:
![y = {x}^{2} - 6x - 7 \\ plug \: y = 0 \\ {x}^{2} - 6x - 7 = 0 \\ {x}^{2} - 6x + 9 = 7 + 9 \\ (x - 3)^{2} = 16 \\ (x - 3) = \pm 4 \\ x = 4 + 3 \: or \: x = - 4 + 3 \\ x = 7 \: or \: x = - 1](https://tex.z-dn.net/?f=y%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20-%206x%20-%207%20%5C%5C%20plug%20%5C%3A%20y%20%3D%200%20%5C%5C%20%20%7Bx%7D%5E%7B2%7D%20%20-%206x%20-%207%20%3D%200%20%5C%5C%20%20%7Bx%7D%5E%7B2%7D%20%20-%206x%20%2B%209%20%3D%207%20%2B%209%20%5C%5C%20%28x%20-%203%29%5E%7B2%7D%20%20%3D%2016%20%5C%5C%20%28x%20-%203%29%20%3D%20%20%5Cpm%204%20%5C%5C%20x%20%3D%204%20%2B%203%20%5C%3A%20or%20%5C%3A%20x%20%3D%20%20-%204%20%2B%203%20%5C%5C%20x%20%3D%207%20%5C%3A%20or%20%5C%3A%20x%20%3D%20%20-%201)
Its mean graph should intersect x axis at x = 7 and x = - 1. This everything is satisfied by graph A.
To find the area of this rectangle you multiply the length by the width, like so (x+2) x (2x+5) .
To find the perimeter of this rectangle you add all the sides using this equation,
(x+2)+(x+2)+(2x+5)+(2x+5) .
Answer:
![\huge\boxed{(f-g)\left(-\dfrac{1}{3}\right)=-3\dfrac{1}{3}}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B%28f-g%29%5Cleft%28-%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%3D-3%5Cdfrac%7B1%7D%7B3%7D%7D)
Step-by-step explanation:
![\text{We have}:\\\\f(x)=x^2-4\ \text{and}\ g(x)=x^2+2x\\\\(f-g)(x)=f(x)-g(x)\\\\\text{therefore}\\\\(f-g)(x)=(x^2-4)-(x^2+2x)=x^2-4-x^2-2x\\\\=(x^2-x^2)-2x-4=-2x-4\\\\(f-g)\left(-\dfrac{1}{3}\right)\to\text{put}\ x=-\dfrac{1}{3}\ \text{to the equation of the function}\ (f-g)(x):\\\\(f-g)\left(-\dfrac{1}{3}\right)=-2\left(-\dfrac{1}{3}\right)-4=\dfrac{2}{3}-4=-3\dfrac{1}{3}](https://tex.z-dn.net/?f=%5Ctext%7BWe%20have%7D%3A%5C%5C%5C%5Cf%28x%29%3Dx%5E2-4%5C%20%5Ctext%7Band%7D%5C%20g%28x%29%3Dx%5E2%2B2x%5C%5C%5C%5C%28f-g%29%28x%29%3Df%28x%29-g%28x%29%5C%5C%5C%5C%5Ctext%7Btherefore%7D%5C%5C%5C%5C%28f-g%29%28x%29%3D%28x%5E2-4%29-%28x%5E2%2B2x%29%3Dx%5E2-4-x%5E2-2x%5C%5C%5C%5C%3D%28x%5E2-x%5E2%29-2x-4%3D-2x-4%5C%5C%5C%5C%28f-g%29%5Cleft%28-%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5Cto%5Ctext%7Bput%7D%5C%20x%3D-%5Cdfrac%7B1%7D%7B3%7D%5C%20%5Ctext%7Bto%20the%20equation%20of%20the%20function%7D%5C%20%28f-g%29%28x%29%3A%5C%5C%5C%5C%28f-g%29%5Cleft%28-%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%3D-2%5Cleft%28-%5Cdfrac%7B1%7D%7B3%7D%5Cright%29-4%3D%5Cdfrac%7B2%7D%7B3%7D-4%3D-3%5Cdfrac%7B1%7D%7B3%7D)
He has done 70 push ups because by the 15th he has done 35 push ups add 15 more days and u get 70 .