8 times the difference between a number and 6 is equal to 4 times the number.

Mathematics

1 answer:

7nadin3 [17]3 years ago

4 0

Answer:

The variable titled "the number" is A: 12.

Step-by-step explanation:

The problem is 8 * (x - 6) = 4 * x

Try the first number as x and rewrite the expression.

8 * (12 - 6) = 4 * 12

Following PEMDAS (the Order of Operations), you need to solve the problem inside the parenthesis.

12 - 6 = 6

Rewrite the problem.

8 * 6 = 4 * 12

8 times 6 is 48.

4 times 12 is 48.

The variable in the expression 8 * (x - 6) = 4 * x is 12.

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<h3>Answer: 73</h3>

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Work Shown:

Check out the diagram below. Note the pair of alternate interior angles that are congruent (each 37 degrees). Then focus on triangle ABC. With the reference angle being at A, this means we use the tangent function because BC = x is the opposite side and AB = 97 is the adjacent side.

tan(angle) = opposite/adjacent

tan(A) = BC/AB

tan(37) = x/97

97*tan(37) = x

x = 97*tan(37)

x = 73.094742859971

For the last step, you'll need a calculator that can handle trig functions. Make sure the calculator is in degree mode. The result here is approximate. This rounds to 73 when rounding to the nearest whole number.