PLEASE HELPPP!! Triangle HJK and triangle PMK are similar right triangles.

Response:

The measure of mHLK is "(204)°".

Step-by-step breakdown:

Given values include:

mJI = (3x+2)°

mHLK = (15x-36)°

and,

m∠HML = (8x-1)°

then,

What is mHLK?

Now,

Utilizing the chord-chord angle formula, we find

Inserting the known values into the equation gives us

⇒  

By carrying out cross-multiplication, we arrive at

⇒  

⇒  

By subtracting "18x" from both sides, we obtain

⇒  

⇒  

Upon adding "2" to both sides, we end up with

⇒  

⇒  

⇒  

⇒  

By substituting the value of "x" into mHLK = (15x-36)°, we calculate

⇒ (15x-36)° = (15×16-36)°

⇒                = (240-36)°

⇒                = (204)°

Thus, mHLK = (204)°

Answer:

2.5 seconds after the initial ball was struck.

Step-by-step explanation:

The height equations are:

• h = -16t² + 56t

• h = -16t² + 156t - 248

At the point where the balls intersect, both heights are alike, therefore:

-16t² + 56t = -16t² + 156t - 248

-16t² + 56t + 16t² - 156t + 248 = 0

- 100t + 248 = 0

248 = 100t

t = 248/100

t = 2.48 ≈ 2.5

Given: AD ≅ BC and AD ∥ BC

Prove: ABCD is a parallelogram.

Statements                                                                 Reasons

 1. AD ≅ BC; AD ∥ BC                                                1. provided

 2. ∠CAD and ∠ACB are alternate interior angles        2. definition of alternate interior angles

3. ∠CAD ≅ ∠ACB                                                    3. congruence of alternate interior angles

4. AC ≅ AC                                                              4. reflexive property

 5. △CAD ≅ △ACB                                                  5. SAS congruency theorem

6. AB ≅ CD                                                            6. Congruent triangles have congruent corresponding parts (CPCTC)

7. ABCD is a parallelogram                                  7. theorem for sides of parallelograms

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