1. One number is 11 more than 3 times another number. Their sum is 71. Find the smaller number. 2. Two angles are complementary. One angle measures 22 degrees more than the other angle. Find the measure of the larger angle. 3. Two angles are supplementary. One angle measures 40 degrees more than the other angle. Find the measure of the larger angle. 4. The sum of three consecutive even integers is -36. Determine the largest integer of the three.

1. The two numbers are 56 and 15

2. The two angles are 56 and 34 degrees

3. The two angles are 110 and 70 degrees

4.The largest number is -10

Step-by-step explanation:

Solving (1):

Represent both numbers with x and y

Solving for x and y

Substitute for x in the second equation

Collect Like Terms

Divide both sides by 4

Recall that

Hence, the two numbers are 56 and 15

Solving (2)

Represent the two angles with x and y

Since they are complementary;

Substitute 22 + y for x in

Collect Like Terms

Divide both sides by 2

Recall that

Solving (3):

Represent the two angles with x and y

Since they are supplementary;

Substitute 40 + y for x in

Collect Like Terms

Divide both sides by 2

Recall that

Solving (4):

Let the smallest number be x

Collect Like Terms

Divide through by 3

The largest number; x + 4 is

Hence, the largest number is -10

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

a rotation about point l

step-by-step explanation:

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