Given lines p and q are parallel, m<2 - (14x - 12), m<6 - (5y + 23), and m<8 - (8x + 27), solve for the values of x and y then solve for the measure of each angle

Mathematics High School

Given lines p and q are parallel, m<2 - (14x - 12), m<6 - (5y + 23), and m<8 - (8x + 27), solve for the values of x and y then solve for the measure of each angle

Answers

Answer 1

Answer:

x = 7.5

y = 14

m<1 = 87°

m<7 = 93°

Step-by-step explanation:

Given:

m<2 = (14x - 12),

m<6 = (5y + 23),

m<8 = (8x + 27)

m<2 + m<8 = 180° (consecutive exterior angles are supplementary)

(14x - 12) + (8x + 27) = 180 (substitution)

Solve for x

14x - 12 + 8x + 27 = 180

Collect like terms

22x + 15 = 180

Subtract 15 from each side

22x = 180 - 15

22x = 165

Divide both sides by 22

x = 7.5

m<2 = m<6 (corresponding angles are congruent)

(14x - 12) = (5y + 23) (substitution)

Plug in the value of x

14(7.5) - 12 = 5y + 23

105 - 12 = 5y + 23

93 = 5y + 23

Subtract 23 from each side

93 - 23 = 5y

70 = 5y

Divide both sides by 5

14 = y

y = 14

✅m<1 = m<8 (alternate exterior angles are congruent)

m<1 = (8x + 27) (substitution)

Plug in the value of x

m<1 = 8(7.5) + 27 = 87°

m<7 = m<2 (alternate exterior angles are congruent)

m<7 = (14x - 12) (substitution)

Plug in the value of x

m<7 = 14(7.5) - 12 = 93°

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Step-by-step explanation:

The slope of this line is 2/3 because it has a point at (0,0) and another at (3,2). This means that that is its constant of proportionality.

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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N
6
Х
6
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у

Answers

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Step-by-step explanation:

Since XY = XZ = 6, then the triangle is isosceles.

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Answers

Answer:

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Step-by-step explanation:

formula I=prt

I=1000x0.09x.25

I=22.50

The required interest paid by Barry is given as, $22.5.

Given that,
Barry wants to take out a loan from his bank for $1000 to buy a bicycle the interest rate on the loan from the bank is 9% he wants to pay the toll amount in three monthly payments what is the amount that varies with pay in interest rate loan is to be determined.

What is interest?

Simple interest is defined as the percentage of earnings on the lending for a period of time

Here,
Principal = 1000
Rate = 9%
Time = 3 / 12 = 0.25 years
So,
Interest = Principal × rate × time
interest = 1000 × 0.09 × 0.25
Interest = $22.5

Thus, the required interest paid by Barry is given as, $22.5.

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https://brainly.com/question/20406888

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Answers

Answer:

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Step-by-step explanation:

4x-8-2x=10

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Second, add 8 on both sides. 2x+18

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Step-by-step explanation:

i just took this

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Answers

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Answer:

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