If anyone could help me with this last problem, I would greatly appreciate it.

From the given information, the value of a is 3 and the measurement of ∠R is 25°

Step-by-step explanation:

For this problem, we have to find the value of a and the measurement of ∠R. We are given some information already in the problem.

ΔJKL ≅ ΔPQR

This means that all of the angles and all of the sides of each triangle are going to be equal to each other.

So, knowing this, let;s find the measurement of ∠R first.

All triangles have a total measurement of 180°. We are already given two angle measurements. We are given that the m∠P is 90° because the small box in the triangle represents a right angle and right angles equal 90°. We are also given that the m∠Q is 65° because ∠Q is equal to ∠K so they have the same measurement. Now, let's set up our equation.

65 + 90 + m∠R = 180

Add 65 to 90.

155 + m∠R = 180

Subtract 155 from 180.

m∠R = 25°

So, the measurement of ∠R is 25°.

Now let's find the value of a.

KL is equal to PQ so we will set up an equation where they are equal to each other.

7a - 10 = 11

Add 10 to 11.

7a = 21

Divide 7 by 21.

a = 3

So, the value of a is 3.

the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. hope this ! mark brainliest! you v much! : )

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: