(a) are triangles the congruent? write the congruency statement.
(b) what is the congruency that proves they are congruent?
(c) what is the perimeter of ∆pqr? show all of your work.

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

Find the value of y

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

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0