If 1/4 inch represents 50 miles, how many inches are needed to represent 225 miles?

Problem 1

Answer: Choice B) angle1 = 26, angle2 = 64

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Explanation:

Complementary angles add to 90

(angle1)+(angle2) = 90

(5x+6)+(68-x) = 90

4x+74 = 90

4x = 90-74

4x = 16

x = 16/4

x = 4

So,

angle1 = 5x+6 = 5(4)+6 = 26

angle2 = 68-x = 68-4 = 64

Note how

angle1+angle2 = 26+64 = 90

to help check our answer

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Problem 2

Answer: Choice D) BC, AC, AB

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Explanation:

The shortest side of a triangle is always opposite the smallest angle.

The longest side of a triangle is always opposite the largest angle.

Based on those two facts, we can say the shortest side is BC (since angle A = 53 is the smallest angle) and the longest side is AB (since angle C = 70 is the largest)

The order from smallest to largest is

BC, AC, AB

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Problem 3

Answer: Choice D) B < C < A

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Explanation:

Use the reverse of the idea from problem 2. We know that AC is the smallest side which must mean that angle B is the smallest angle. Since BC is the largest side, angle A must be the largest angle.

The order of the angles is B < C < A

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Problem 4

Answer: Choice A) angle 5 = 50, angle 8 = 130

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Explanation:

The same side exterior angles must be supplementary to have parallel lines.

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Problem 5

Answer: Choice A) angle G is the smallest

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Explanation:

Use the same idea as problem 2. The smallest angle is opposite the smallest side. The smallest side is 48, so angle G being opposite of that side, is the smallest angle.

Angle O would be the largest as it is opposite the largest side DG = 70

Answer:

The answer is 8 square root of 5 end root plus 3 square root of 30

i.e

Step-by-step explanation:

Given the statement square root of 5 open parentheses 8 plus 3 square root of 6 close parenthesis i.e

Now by distributive property

implies  

The simplified form of the expression is 8√5 + 3√30.

The correct is option B.

To simplify the expression √5(8 + 3√6), we can distribute the square root of 5 to both terms inside the parentheses:

√5(8 + 3√6) = √5 x 8 + √5 x 3√6

Multiplying the square root of 5 with 8 gives:

8√5 + √5 x 3√6

To simplify the expression further, we can simplify the multiplication of square roots:

8√5 + 3√(5 x  6) = 8√5 + 3√30

Therefore, the simplified form of the expression is 8√5 + 3√30.

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