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3 years ago

The measures of two complementary angles are m angle 1 = (10x+7) and m angle 2=(9x-12) find the measures of both angles

Mathematics

1 answer:

USPshnik [31]3 years ago

5 0

Answer:

m<1 = 57°

m<2 = 33°

Step-by-step explanation:

To find the numerical measure of both angles, let's come up with an equation to determine the value of x.

Given that m<1 = (10x +7)°, and m<2 = (9x - 12)°, where both are complementary angles, therefore, it means, both angles will add up to give us 90°.

Equation we can generate from this, is as follows:

(10x + 7)° + (9x - 12)° = 90°

Solve for x

10x + 7 + 9x - 12 = 90

Combine like terms

19x - 5 = 90

Add 5 to both sides

19x = 90 + 5 (addition property not equality)

19x = 95

Divide both sides by 19

x = 5

m<1 = (10x +7)°

Replace x with 5

m<1 = 10(5) + 7 = 50 + 7 = 57°

m<2 = (9x - 12)

Replace x with 5

m<2 = 9(5) - 12 = 45 - 12 = 33°

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Fred the ant is on the real number line, and Fred is trying to get to the point $0.$

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Complete question is;

Fred the ant is on the real number line, and Fred is trying to get to the point 0

If Fred is at 1 then on the next step, Fred moves to either 0 or 2 with equal probability. If Fred is at 2 then on the next step, Fred always moves to 1

Let e1 be expected number of steps Fred takes to get to 0 given that Fred starts at the point 1. Similarly, let e2 be expected number of steps Fred takes to get to 0 given that Fred starts at the point 2

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Answer:

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Step-by-step explanation:

We can track the probabilities using the scenario that Ant gets to 0 after 1 steps, 2 steps, 3 steps, 4 steps, 5 steps and so on.

This gives us e_1 = 1(1/2^(1)) + 2(1/2²) + 3(1/2³) + 4(1/2⁴) + ...

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From the online calculator, i got;

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By arithmetico-geometric series, e_2 = 3,