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julsineya [31]
4 years ago
10

Two years ago there was a budget cut at Denny's job because the economy was down. Unfortunately, in order to keep his job, his s

alary had to be cut by 3%. Since Denny didn't want to lose his job, he took this deal. However, since the company is doing better now, Denny's boss told him "I'd like to increase your current salary by 3% so that you will be making the same amount that you did before our budget cut". Is the statement that Denny's boss told Denny true?
Mathematics
1 answer:
erastovalidia [21]4 years ago
7 0

Answer:

Not true!

Step-by-step explanation:

Let Denny's initial salary be x.

After the cut, his salary would be 0.97x.

When increasing his salary by 3%,

1.03 x 0.97x = 0.9991 x which is not the same as x.

Hence the statement is not true.

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Answer:

1). \frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}

2). \frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}

Step-by-step explanation:

In this question we have to write the fractions in the factored form.

Rational expressions are \frac{2}{x^{2}-x-12 } and \frac{1}{x^{2}-16 }.

1). \frac{2}{x^{2}-x-12 }

Factored form of the denominator (x² - x - 12) = x² - 4x + 3x - 12

                                                                           = x(x - 4) + 3(x - 4)

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Therefore. \frac{2}{x^{2}-x-12 }=\frac{2}{(x+3)(x-4)}

2). \frac{1}{x^{2}-16 }

Factored form of the denominator (x² - 16) = (x - 4)(x + 4)

[Since (a²- b²) = (a - b)(a + b)]

Therefore, \frac{1}{x^{2}-16 }=\frac{1}{(x-4)(x+4)}

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Step-by-step explanation:

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