Answer:
option 2
Step-by-step explanation:
the cosine rule is
cos A = b² + c² - a² / 2bc
so, A is x°
a is 41
b is 37
c is 63
solving the equation will give you the value of x°
Answer:
a) h(3) = 9
b) h(0) = 6
c) h(6) = 4
Step-by-step explanation:
Piecewise functions have <u>multiple pieces</u> of curves/lines where each piece corresponds to its definition over an <u>interval</u>.
Given piecewise function:
![\sf h(x)=\begin{cases}\sf \dfrac{x^2-36}{x-6} &\textsf{if }x\neq 6\\\\\sf 4 & \textsf{if }x=6\end{cases}](https://tex.z-dn.net/?f=%5Csf%20h%28x%29%3D%5Cbegin%7Bcases%7D%5Csf%20%5Cdfrac%7Bx%5E2-36%7D%7Bx-6%7D%20%26%5Ctextsf%7Bif%20%7Dx%5Cneq%20%206%5C%5C%5C%5C%5Csf%204%20%26%20%5Ctextsf%7Bif%20%7Dx%3D6%5Cend%7Bcases%7D)
Therefore, the function has two definitions:
![\sf h(x)=\dfrac{x^2-36}{x-6} \quad \textsf{when x does not equal 6}](https://tex.z-dn.net/?f=%5Csf%20h%28x%29%3D%5Cdfrac%7Bx%5E2-36%7D%7Bx-6%7D%20%5Cquad%20%5Ctextsf%7Bwhen%20x%20does%20not%20equal%206%7D)
![\sf h(x)=4 \quad \textsf{when x equals 6}](https://tex.z-dn.net/?f=%5Csf%20h%28x%29%3D4%20%5Cquad%20%5Ctextsf%7Bwhen%20x%20equals%206%7D)
<u>Part (a)</u>
h(3) means to substitute x = 3 into the function.
As <u>x does not equal 6</u>, substitute x = 3 into the <u>first piece of the function</u>:
![\begin{aligned}\sf \implies h(3) & =\sf \dfrac{(3)^2-36}{(3)-6}\\\\ & = \sf \dfrac{9-36}{-3}\\\\ & = \sf \dfrac{-27}{-3}\\\\ & = \sf 9\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csf%20%5Cimplies%20h%283%29%20%26%20%3D%5Csf%20%5Cdfrac%7B%283%29%5E2-36%7D%7B%283%29-6%7D%5C%5C%5C%5C%20%26%20%3D%20%5Csf%20%5Cdfrac%7B9-36%7D%7B-3%7D%5C%5C%5C%5C%20%26%20%3D%20%5Csf%20%5Cdfrac%7B-27%7D%7B-3%7D%5C%5C%5C%5C%20%26%20%3D%20%5Csf%209%5Cend%7Baligned%7D)
<u>Part (b)</u>
h(0) means to substitute x = 0 into the function.
As <u>x does not equal 6</u>, substitute x = 0 into the <u>first piece of the function</u>:
![\begin{aligned}\sf \implies h(0) & =\sf \dfrac{(0)^2-36}{(0)-6}\\\\ & = \sf \dfrac{0-36}{-6}\\\\ & = \sf \dfrac{-36}{-6}\\\\ & = \sf 6\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csf%20%5Cimplies%20h%280%29%20%26%20%3D%5Csf%20%5Cdfrac%7B%280%29%5E2-36%7D%7B%280%29-6%7D%5C%5C%5C%5C%20%26%20%3D%20%5Csf%20%5Cdfrac%7B0-36%7D%7B-6%7D%5C%5C%5C%5C%20%26%20%3D%20%5Csf%20%5Cdfrac%7B-36%7D%7B-6%7D%5C%5C%5C%5C%20%26%20%3D%20%5Csf%206%5Cend%7Baligned%7D)
<u>Part (c)</u>
h(6) means to substitute x = 6 into the function.
As <u>x equals 6</u>, then use the <u>second piece of the function</u>:
![\sf \implies h(6)=4](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20h%286%29%3D4)
Learn more about piecewise functions here:
brainly.com/question/11562909
brainly.com/question/28151925
The first thing you need to do is multiply the a and c values. in this problem a is 3 and c is 4. 3x4 is 12. now you need to find the factors of 12 and find a set that add to the b value (-8). -2 + -6 is -8 and -2 x -6 is 12. now you replace -8x with -2x and -6x. now you need to factor by grouping. so first is 3x^2 -6x. you factor out the gcf between the two. in this case it us 3x. so now you have 3x(x-2). now you need to factor the other side of the equation (-2x +4). for this problem you need to factor out a -2, rather then 2, because it needs to be the same as the first half. so you factor out the -2 and get -2(x-2). then you just combine the two so you get (3x-2)(x-2). hope this helped. i also attached a picture of the work. :)
B is your answer bc 2 times 4 is 8 plus 2 minus 6 is