Answer:
C
Step-by-step explanation:
Because this is a positive parabola, it opens upwards, like a cup, and the vertex dictates what the minimum value of the function is. In order to determine the vertex, I recommend completing the square. Do that by first setting the function equal to 0 and then moving the 9 to the other side by subtraction. So far:
![x^2+6x=-9](https://tex.z-dn.net/?f=x%5E2%2B6x%3D-9)
. Now, to complete the square, take half the linear term, square it, and add that number to both sides. Our linear term is 6. Half of 6 is 3 and 3 squared is 9. So add 9 to both sides.
![x^2+6x+9=-9+9](https://tex.z-dn.net/?f=x%5E2%2B6x%2B9%3D-9%2B9)
. The right side reduces to 0, and the left side simplifies to the perfect square binomial we created while completing this process.
![(x+3)^2=0](https://tex.z-dn.net/?f=%28x%2B3%29%5E2%3D0)
. Move the 0 back over and the vertex is clear now. It is (-3, 0). Therefore, 0 is the minimum point on your graph. The first choice above is the one you want.
Multiply or divide normally. Whenever the signs are different it’s always gonna be a negative.
Solution:
Given:
![2(10-a^2)+7a](https://tex.z-dn.net/?f=2%2810-a%5E2%29%2B7a)
when a = 4, substitute for a in the expression;
![\begin{gathered} 2(10-a^2)+7a=2(10-4^2)+7(4) \\ =2(10-16)+28 \\ =2(-6)+28 \\ =-12+28 \\ =16 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202%2810-a%5E2%29%2B7a%3D2%2810-4%5E2%29%2B7%284%29%20%5C%5C%20%3D2%2810-16%29%2B28%20%5C%5C%20%3D2%28-6%29%2B28%20%5C%5C%20%3D-12%2B28%20%5C%5C%20%3D16%20%5Cend%7Bgathered%7D)
Therefore, if (a = 4), then
![2(10-a^2)+7a=16](https://tex.z-dn.net/?f=2%2810-a%5E2%29%2B7a%3D16)
Hence, the answer is 16.
we are given that
two triangles are similar
so, the ratio of their sides must be same
we get
![\frac{2}{6} =\frac{x}{x+2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B6%7D%20%3D%5Cfrac%7Bx%7D%7Bx%2B2%7D)
now, we can solve for x
step-1: Cross multiply both sides
![2(x+2) =6x](https://tex.z-dn.net/?f=2%28x%2B2%29%20%3D6x%20)
step-2: Simplify left side
![2x +4 =6x](https://tex.z-dn.net/?f=%202x%20%2B4%20%3D6x%20)
step-3: Subtract both sides by 2x
![2x +4-2x =6x-2x](https://tex.z-dn.net/?f=%202x%20%2B4-2x%20%3D6x-2x%20)
![4 =4x](https://tex.z-dn.net/?f=%204%20%3D4x%20)
step-4: Divide both sides by 4
![x=1](https://tex.z-dn.net/?f=%20x%3D1%20)
so,
............Answer