Find the value of each variable and the measure of arc lm. the diagram is not drawn to scale.

x = 90

y = 50

Arc LM = 100

Step-by-step explanation:

Arc  MK = 180 degrees

<x = 1/2  Arc MK

<x  = 90 degrees

<x + <y + 40 = 180    all angles in a triangle add to 180

90 + <y + 40 = 180

130 + < y = 180

Subtract 130 from each side

< y = 50

Arc LM

1/2 Arc Lm =  <y

1/2 Arc LM = 50

Multiply by 2

Arc LM = 100

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5