Question

19 evaluate. use paper to record your work.
\\(\frac{24 - 2^3}{2 + 2(5 - 2)}\\)

20 evaluate the expression when \\(x = -8\\). use paper to record your work.
\\(x^2 - 5x + 1\\)

21 evaluate the function when \\(f(39)\\). use paper to record your work.
\\(f(x) = \sqrt{x - 3} + 1\\)

22 simplify. your answer should contain only positive exponents.
\\((xy^3)(x^2y)\\)

23 simplify. your answer should contain only positive exponents.

Explanation:

Question 19

Step1: Calculate exponent and parentheses

First, calculate \(2^3 = 8\) and \(5 - 2 = 3\). The expression becomes \(\frac{24 - 8}{2 + 2\times3}\).

Step2: Simplify numerator and denominator

Simplify numerator: \(24 - 8 = 16\). Simplify denominator: \(2 + 2\times3 = 2 + 6 = 8\).

Step3: Divide numerator by denominator

Now, divide \(16\) by \(8\): \(\frac{16}{8} = 2\).

Step1: Substitute \(x = -8\) into the expression

Substitute \(x = -8\) into \(x^2 - 5x + 1\). So we have \((-8)^2 - 5\times(-8) + 1\).

Step2: Calculate each term

Calculate \((-8)^2 = 64\), \( -5\times(-8) = 40\).

Step3: Sum the terms

Now, sum the terms: \(64 + 40 + 1 = 105\).

Step1: Substitute \(x = 39\) into the function

Substitute \(x = 39\) into \(f(x)=\sqrt{x - 3}+1\). So we have \(\sqrt{39 - 3}+1\).

Step2: Simplify the square root

Simplify \(39 - 3 = 36\), so \(\sqrt{36}=6\).

Step3: Add 1

Now, add \(1\) to \(6\): \(6 + 1 = 7\).

Answer:

\(2\)

Question 20