Answer:
(r o g)(2) = 4
(q o r)(2) = 14
Step-by-step explanation:
Given
![g(x) = x^2 + 5](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2%20%2B%205)
![r(x) = \sqrt{x + 7}](https://tex.z-dn.net/?f=r%28x%29%20%3D%20%5Csqrt%7Bx%20%2B%207%7D)
Solving (a): (r o q)(2)
In function:
(r o g)(x) = r(g(x))
So, first we calculate g(2)
![g(x) = x^2 + 5](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2%20%2B%205)
![g(2) = 2^2 + 5](https://tex.z-dn.net/?f=g%282%29%20%3D%202%5E2%20%2B%205)
![g(2) = 4 + 5](https://tex.z-dn.net/?f=g%282%29%20%3D%204%20%2B%205)
![g(2) = 9](https://tex.z-dn.net/?f=g%282%29%20%3D%209)
Next, we calculate r(g(2))
Substitute 9 for g(2)in r(g(2))
r(q(2)) = r(9)
This gives:
![r(x) = \sqrt{x + 7}](https://tex.z-dn.net/?f=r%28x%29%20%3D%20%5Csqrt%7Bx%20%2B%207%7D)
![r(9) = \sqrt{9 +7{](https://tex.z-dn.net/?f=r%289%29%20%3D%20%5Csqrt%7B9%20%2B7%7B)
{
![r(9) = 4](https://tex.z-dn.net/?f=r%289%29%20%3D%204)
Hence:
(r o g)(2) = 4
Solving (b): (q o r)(2)
So, first we calculate r(2)
![r(x) = \sqrt{x + 7}](https://tex.z-dn.net/?f=r%28x%29%20%3D%20%5Csqrt%7Bx%20%2B%207%7D)
![r(2) = \sqrt{2 + 7}](https://tex.z-dn.net/?f=r%282%29%20%3D%20%5Csqrt%7B2%20%2B%207%7D)
![r(2) = \sqrt{9}](https://tex.z-dn.net/?f=r%282%29%20%3D%20%5Csqrt%7B9%7D)
![r(2) = 3](https://tex.z-dn.net/?f=r%282%29%20%3D%203)
Next, we calculate g(r(2))
Substitute 3 for r(2)in g(r(2))
g(r(2)) = g(3)
![g(x) = x^2 + 5](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%5E2%20%2B%205)
![g(3) = 3^2 + 5](https://tex.z-dn.net/?f=g%283%29%20%3D%203%5E2%20%2B%205)
![g(3) = 9 + 5](https://tex.z-dn.net/?f=g%283%29%20%3D%209%20%2B%205)
![g(3) = 14](https://tex.z-dn.net/?f=g%283%29%20%3D%2014)
Hence:
(q o r)(2) = 14
Answer:
![\boxed{ \bold{ \huge{ \boxed{ \text{k = - 9}}}}}](https://tex.z-dn.net/?f=%20%5Cboxed%7B%20%5Cbold%7B%20%5Chuge%7B%20%5Cboxed%7B%20%5Ctext%7Bk%20%3D%20%20%20-%209%7D%7D%7D%7D%7D)
Step-by-step explanation:
![\star{ \text{ - 126 = 14k}}](https://tex.z-dn.net/?f=%20%5Cstar%7B%20%5Ctext%7B%20-%20126%20%3D%2014k%7D%7D)
![\hookrightarrow{ \sf{14k = - 126}}](https://tex.z-dn.net/?f=%20%5Chookrightarrow%7B%20%5Csf%7B14k%20%3D%20%20-%20126%7D%7D)
![\hookrightarrow{ \sf{ \frac{14k}{14} = \frac{ - 126}{14}}}](https://tex.z-dn.net/?f=%20%20%5Chookrightarrow%7B%20%5Csf%7B%20%5Cfrac%7B14k%7D%7B14%7D%20%20%3D%20%20%5Cfrac%7B%20-%20126%7D%7B14%7D%7D%7D%20)
![\text{step \: 3 \: : Calcular}](https://tex.z-dn.net/?f=%20%5Ctext%7Bstep%20%5C%3A%203%20%5C%3A%20%20%3A%20Calcular%7D)
![\hookrightarrow{ \sf{k = - 9}}](https://tex.z-dn.net/?f=%20%5Chookrightarrow%7B%20%5Csf%7Bk%20%3D%20%20-%209%7D%7D)
![\text{el valor de k es - 9}](https://tex.z-dn.net/?f=%20%5Ctext%7Bel%20valor%20de%20k%20es%20%20-%209%7D)
------------------------------------------------------------
Translation in English:
Step 1 : Swap the sides of the equation
Step 2 : Divide both sides by 14
Step 3 : Calculate
![\sf{Hope \: i \: helped ! }](https://tex.z-dn.net/?f=%20%5Csf%7BHope%20%5C%3A%20i%20%5C%3A%20helped%20%21%20%7D)
![\sf{Best \: regards !!}](https://tex.z-dn.net/?f=%20%5Csf%7BBest%20%5C%3A%20regards%20%21%21%7D)
~![\sf{TheAnimeGirl}](https://tex.z-dn.net/?f=%20%5Csf%7BTheAnimeGirl%7D)
Answer:
B its 4 7/8 --------------
Answer:
the alternate angle is angle 2
Answer: (x−2)(x−2)
The middle number is -4 and the last number is 4.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -4
Multiply together to get 4
Can you think of the two numbers?
Try -2 and -2:
-2+-2 = -4
-2*-2 = 4
Fill in the blanks in
(x+_)(x+_)
with -2 and -2 to get...
(x-2)(x-2)
Answer:
(x−2)(x−2)
so the answer is D.