Question

1. one meaning of the word evaluate is to find the value of an expression. to evaluate, replace a variable with a number and calculate the result. for example, when you are asked to evaluate the expression 4x - 2 when x = -7, you would put -7 in place of the variable and calculate 4·(-7) - 2 = - 30 evaluate the expressions below for the given values of x and y a. $\frac{6}{x}+9$ if $x = 3$ b. $8x - 3 + y$ if $x = 2$ and $y = 1$ c. $2xy$ if $x = 5$ and $y = -3$ d. $2x^{2}-y$ if $x = 3$ and $y = 8$

Explanation:

Step1: Substitute x value for a

Substitute \(x = 3\) into \(\frac{6}{x}+9\).
\(\frac{6}{3}+9\)

Step2: Calculate a

\(\frac{6}{3}+9=2 + 9=11\)

Step3: Substitute x and y values for b

Substitute \(x = 2\) and \(y = 1\) into \(8x-3 + y\).
\(8\times2-3 + 1\)

Step4: Calculate b

\(8\times2-3 + 1=16-3 + 1=14\)

Step5: Substitute x and y values for c

Substitute \(x = 5\) and \(y=-3\) into \(2xy\).
\(2\times5\times(-3)\)

Step6: Calculate c

\(2\times5\times(-3)=10\times(-3)=-30\)

Step7: Substitute x and y values for d

Substitute \(x = 3\) and \(y = 8\) into \(2x^{2}-y\).
\(2\times3^{2}-8\)

Step8: Calculate d

First, calculate \(3^{2}=9\), then \(2\times9-8=18 - 8=10\)

Answer:

a. 11
b. 14
c. -30
d. 10