Answer:
Part A) Yes , the triangles are congruent
Part B) The side-angle-side (SAS) theorem
Part C) The perimeter of ∆PQR is 
Step-by-step explanation:
Step 1
we know that
The side-angle-side (SAS) theorem, states that: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
so in this problem
Traingle PQR and Triangle STU are congruent by the SAS Theorem
because
m<PQR=m<STU -------> included angle
PQ=TS
QR=TU
Step 2
<u>Find the value of y</u>
we know that
If the triangles are congruent
then
The corresponding sides are equal
so

substitute






so

Step 3
Find the perimeter ∆PQR
Remember that
The perimeter of ∆PQR is equal to the perimeter ∆STU
The perimeter is equal to

substitute the values

Answer:
Answer: A. x + (4x - 85) = 90
In this case, the two angles are complementary. This means they add up to 90°. Therefore, the equation is x + (4x - 85) = 90.
Step-by-step explanation:
Answer:
72 and 108
Step-by-step explanation:
540/30= 18 *4 = 72
and
810/30= 27*4=108
let's recall the remainder theorem.
we know that (x-1) is a factor, that means x -1 = 0 or x = 1.
since we know that (x-1) is a factor, then dividing the polynomial by it will give us a remainder of 0, which correlates with saying that f(1) = 0, in this case, so we can simply plug in "1" as the argument, knowing it gives 0.
![f(x)=3x^3+kx-11\\\\[-0.35em]~\dotfill\\\\\stackrel{0}{f(1)}=3(1)^3+k(1)-11\implies \stackrel{f(1)}{0}=3+k-11\implies 0=-8+k\implies 8=k](https://tex.z-dn.net/?f=f%28x%29%3D3x%5E3%2Bkx-11%5C%5C%5C%5C%5B-0.35em%5D~%5Cdotfill%5C%5C%5C%5C%5Cstackrel%7B0%7D%7Bf%281%29%7D%3D3%281%29%5E3%2Bk%281%29-11%5Cimplies%20%5Cstackrel%7Bf%281%29%7D%7B0%7D%3D3%2Bk-11%5Cimplies%200%3D-8%2Bk%5Cimplies%208%3Dk)
The answer is quadrant 4 or IV