Chapter 1.2, Problem 13WE

a.

To determine

To Evaluate: The expression $xy+z$ if $t=6$ , $x=3$ , $y=4$ , and $z=5$

Answer to Problem 13WE

The value of the expression $xy+z$ is $xy+z=17$

Explanation of Solution

Given information:

The expression $xy+z$ and the values $t=6$ , $x=3$ , $y=4$ , and $z=5$

Concept Used:

The value of an expression at the given values of the unknowns is calculated by substituting the given values of the unknowns into the expression and simplifying it.

Calculation:

Given the expression $xy+z$

Evaluating the expression $xy+z$ at $x=3$ , $y=4$ , and $z=5$ , we have

  $\begin{array}{c}xy+z=\left(3\right)\left(4\right)+5\text{ Substituting } x=3\text{, }y=4\text{, }z=5\\ =12+5\text{ Multiplying}\\ =17\text{ Adding}\end{array}$

Therefore, $xy+z=17$

Conclusion:

The value of the expression $xy+z$ is $xy+z=17$

b.

To determine

To Evaluate: The expression $x\left(y+z\right)$ if $t=6$ , $x=3$ , $y=4$ , and $z=5$

Answer to Problem 13WE

The value of the expression $x\left(y+z\right)$ is $x\left(y+z\right)=27$

Explanation of Solution

Given information:

The expression $x\left(y+z\right)$ and the values $t=6$ , $x=3$ , $y=4$ , and $z=5$

Concept Used:

The value of an expression at the given values of the unknowns is calculated by substituting the given values of the unknowns into the expression and simplifying it.

Calculation:

Given the expression $x\left(y+z\right)$

Evaluating the expression $x\left(y+z\right)$ at $x=3$ , $y=4$ , and $z=5$ , we have

  $\begin{array}{c}x\left(y+z\right)=3\left(4+5\right)\text{ Substituting } x=3\text{, }y=4\text{, }z=5\\ =3\left(9\right)\text{ Adding}\\ =27\text{ Multiplying}\end{array}$

Therefore, $x\left(y+z\right)=27$

Conclusion:

The value of the expression $x\left(y+z\right)$ is $x\left(y+z\right)=27$