Answer:
6. B. x + 8
7. D. ( 3x-2)(3x-2)
8. D. Perfect square trimomal
9.C. x - 2
10. A. 3x and 8x
Step-by-step explanation:
Semoga Bermanfaat
![\qquad\qquad\huge\underline{{\sf Answer}}♨](https://tex.z-dn.net/?f=%5Cqquad%5Cqquad%5Chuge%5Cunderline%7B%7B%5Csf%20Answer%7D%7D%E2%99%A8)
Let's solve ~
If it passes through x, then let's find x when y = 0
![\qquad \tt \dashrightarrow \:0 = {x}^{2} - x - 6](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A0%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20-%20x%20-%206)
![\qquad \tt \dashrightarrow \: {x}^{2} - 3x + 2x - 6 = 0](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A%20%7Bx%7D%5E%7B2%7D%20%20-%203x%20%2B%202x%20-%206%20%3D%200)
![\qquad \tt \dashrightarrow \:x(x - 3) + 2(x - 3) = 0](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Ax%28x%20-%203%29%20%2B%202%28x%20-%203%29%20%3D%200)
![\qquad \tt \dashrightarrow \:(x - 3) (x + 2) = 0](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A%28x%20-%203%29%20%20%28x%20%2B%202%29%20%3D%200)
So, required values of x are 3 and -2
Now, let's differentiate the equation to get slope slope for tangent ~
![\qquad \tt \dashrightarrow \: m = \dfrac{d}{dx} ( {x}^{2} - x - 6)](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A%20m%20%3D%20%20%5Cdfrac%7Bd%7D%7Bdx%7D%20%28%20%7Bx%7D%5E%7B2%7D%20%20-%20x%20-%206%29)
![\qquad \tt \dashrightarrow \: m = 2 x - 1](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A%20m%20%20%3D%20%202%20x%20-%201)
Now, plug in the values of x to find slopes of tangents
![\qquad \tt \dashrightarrow \: m _1 = (2 \times 3) - 1](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A%20m%20_1%20%3D%20%20%282%20%5Ctimes%203%29%20-%201)
![\qquad \tt \dashrightarrow \: m_1 = 6 - 1](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A%20m_1%20%20%3D%20%206%20-%20%201)
![\qquad \tt \dashrightarrow \: m _1 = 5](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A%20m%20_1%20%3D%20%205)
and
![\qquad \tt \dashrightarrow \:m_2 = (2 \times - 2) - 1](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Am_2%20%3D%20%282%20%5Ctimes%20%20-%202%29%20-%201)
![\qquad \tt \dashrightarrow \:m_2 = - 4- 1](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Am_2%20%3D%20%20-%204-%201)
![\qquad \tt \dashrightarrow \:m_2 = - 5](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Am_2%20%3D%20%20-%205)
We know, tangent are normal are perpendicular. so let's find out slopes of normals m1' and m2'
![\qquad \tt \dashrightarrow \:m _1\cdot m_1 ' = - 1](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Am%20_1%5Ccdot%20m_1%20%27%20%3D%20%20-%201)
![\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{m_1}](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Am%20_1%27%20%3D%20%20%20%5Cdfrac%7B-%201%7D%7Bm_1%7D)
![\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{ 5}](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Am%20_1%27%20%3D%20%20%20%5Cdfrac%7B-%201%7D%7B%205%7D)
and
![\qquad \tt \dashrightarrow \:m _2\cdot m_2 ' = - 1](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Am%20_2%5Ccdot%20m_2%20%27%20%3D%20%20-%201)
![\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{m_2}](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Am%20_2%27%20%3D%20%20%20%5Cdfrac%7B-%201%7D%7Bm_2%7D)
![\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{ -5}](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Am%20_2%27%20%3D%20%20%20%5Cdfrac%7B-%201%7D%7B%20-5%7D)
![\qquad \tt \dashrightarrow \:m _2' = \dfrac{1}{ 5}](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Am%20_2%27%20%3D%20%20%20%5Cdfrac%7B1%7D%7B%205%7D)
Now, write the equations of normals using point slope form :
Normal 1 : passing through (3 , 0), and slope = -1/5
![\qquad \tt \dashrightarrow \:y - 0 = - \dfrac{1}{5} (x - 3)](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Ay%20-%200%20%3D%20%20-%20%20%5Cdfrac%7B1%7D%7B5%7D%20%28x%20-%20%203%29)
![\qquad \tt \dashrightarrow \:5y = - (x - 3)](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A5y%20%3D%20%20-%20%20%28x%20-%20%203%29)
![\qquad \tt \dashrightarrow \:5y = - x + 3](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A5y%20%3D%20%20%20-%20x%20%2B%203)
![\qquad \tt \dashrightarrow \:x + 5y - 3 = 0](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Ax%20%2B%205y%20-%20%203%20%3D%200)
and
Normal 2 : passing through (-2 , 0), and slope = 1/5
![\qquad \tt \dashrightarrow \:y - 0 = \dfrac{1}{5} (x - ( - 2))](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3Ay%20-%200%20%3D%20%20%5Cdfrac%7B1%7D%7B5%7D%20%28x%20-%20%28%20-%202%29%29)
![\qquad \tt \dashrightarrow \:5y = x + 2](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%3A5y%20%3D%20%20%20x%20%20%2B%20%202)
![\qquad \tt \dashrightarrow \ x - 5y + 2 = 0](https://tex.z-dn.net/?f=%5Cqquad%20%5Ctt%20%5Cdashrightarrow%20%5C%20%20%20x%20%20-%205y%20%2B%20%202%20%3D%200)
That's all for Aunty ~ hope it helps !
Answer:
Length
Step-by-step explanation:
Area is what is on the in side
perimeter is the out side of the hole thing
The answer is 19
arrange the numbers from least to greatest
2,5,19,25,28
Then repeatedly cross one off from each end until there is only one left
5,19,25
19
Answer:
b d is the answer and see in book