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Chapter 5: Problem 110

Use the order of operations to find the value of each expression. \(\frac{-3 \cdot 5^{2}+89}{(5-6)^{2}-2|3-7|}\)

Short Answer

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Step by step solution

01

Exponents

Calculate the value of any exponent in the expression first. Here, the expression contains \(5^{2}\) in the numerator and \(5-6)^{2}\) in the denominator. Thus, these calculations become \(5^{2} = 25\) and \((5-6)^{2} = (-1)^{2} = 1\). The expression now becomes: \(-3 \cdot 25 + 89 / (1 - 2|3 - 7|)\)
02

Absolute Value

Now, calculate the absolute value of any number in the expression. The expression here contains \(|3 - 7|\), which equals \(-4\). The absolute value of -4 is 4. The expression now becomes: \(\frac{-3 \cdot 25 + 89}{1 - 2*4}\)
03

Multiplication, Division, Addition, and Subtraction

Next, perform the remaining operations according to the order of operations - multiplication and division, followed by addition and subtraction. This results in \( -75 + 89\) in the numerator and \(1 - 8\) in the denominator. The expression now becomes: \(\frac{14}{-7}\)
04

Final Division

Finally, perform the division: \(14 / -7 = -2\)

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Most popular questions from this chapter

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0004,-0.004,0.04,-0.4, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=3000, r=-1\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{100}\), when \(a_{1}=50, r=1\).

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=1000, r=1\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-2, r=-3\)
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