Chapter 39, Problem 21A

To determine

(a)

The value of $2xy+7$.

Answer to Problem 21A

The value of $2xy+7$ is $151$.

Explanation of Solution

Given:

The value of $x$ is $12$ and $y$ is $6$.

Calculation:

The algebraic expression is given below:

  $2xy+7$  ... (1)

Substitute $12$ for $x$ and $6$ for $y$ in equation (1) as follows:

  $\begin{array}{c}2xy+7=2\left(12\times 6\right)+7\\ =2\times 72+7\\ =144+7\\ =151\end{array}$

Thus, the value of $2xy+7$ is $151$.

Conclusion:

The value of $2xy+7$ is $151$.

To determine

(b)

The value of $3x-2y+xy$.

Answer to Problem 21A

The value of $3x-2y+xy$ is $96$.

Explanation of Solution

Given:

The value of $x$ is $12$ and $y$ is $6$.

Calculation:

The algebraic expression is given below:

  $3x-2y+xy$  ... (1)

Substitute $12$ for $x$ and $6$ for $y$ in equation (1) as follows:

  $\begin{array}{c}3x-2y+xy=\left(3\times 12\right)-\left(2\times 6\right)+\left(12\times 6\right)\\ =36-12+72\\ =24+72\\ =96\end{array}$

Thus, the value of $3x-2y+xy$ is $96$.

Conclusion:

The value of $3x-2y+xy$ is $96$.

To determine

(c)

The value of $\frac{5xy-2y}{8x-xy}$.

Answer to Problem 21A

The value of $\frac{5xy-2y}{8x-xy}$ is $14.5$.

Explanation of Solution

Given:

The value of $x$ is $12$ and $y$ is $6$.

Calculation:

The algebraic expression is given below:

  $\frac{5xy-2y}{8x-xy}$  ... (1)

Substitute $12$ for $x$ and $6$ for $y$ in equation (1) as follows:

  $\begin{array}{c}\frac{5xy-2y}{8x-xy}=\frac{\left(5\times 12\times 6\right)-\left(2\times 6\right)}{\left(8\times 12\right)-\left(12\times 6\right)}\\ =\frac{360-12}{96-72}\\ =\frac{348}{24}\\ =14.5\end{array}$

Thus, the value of $\frac{5xy-2y}{8x-xy}$ is $14.5$.

Conclusion:

The value of $\frac{5xy-2y}{8x-xy}$ is $14.5$.

To determine

(d)

The value of $\frac{4x-4y}{3}$.

Answer to Problem 21A

The value of $\frac{4x-4y}{3}$ is $8$.

Explanation of Solution

Given:

The value of $x$ is $12$ and $y$ is $6$.

Calculation:

The algebraic expression is given below:

  $2xy+7$  ... (1)

Substitute $12$ for $x$ and $6$ for $y$ in equation (1) as follows:

  $\begin{array}{c}\frac{4x-4y}{3}=\frac{\left(4\times 12\right)-\left(4\times 6\right)}{3}\\ =\frac{48-24}{3}\\ =\frac{24}{3}\\ =8\end{array}$

Thus, the value of $\frac{4x-4y}{3}$ is $8$.

Conclusion:

The value of $\frac{4x-4y}{3}$ is $8$.

To determine

(e)

The value of $6x-3y+xy$.

Answer to Problem 21A

The value of $6x-3y+xy$ is $126$.

Explanation of Solution

Given:

The value of $x$ is $12$ and $y$ is $6$.

Calculation:

The algebraic expression is given below:

  $6x-3y+xy$  ... (1)

Substitute $12$ for $x$ and $6$ for $y$ in equation (1) as follows:

  $\begin{array}{c}6x-3y+xy=\left(6\times 12\right)-\left(3\times 6\right)+\left(12\times 6\right)\\ =72-18+72\\ =144-18\\ =126\end{array}$

Thus, the value of $6x-3y+xy$ is $126$.

Conclusion:

The value of $6x-3y+xy$ is $126$.

To determine

(f)

The value of $x^2-y^2$.

Answer to Problem 21A

The value of $x^2-y^2$ is $108$.

Explanation of Solution

Given:

The value of $x$ is $12$ and $y$ is $6$.

Calculation:

The algebraic expression is given below:

  $x^2-y^2$  ... (1)

Substitute $12$ for $x$ and $6$ for $y$ in equation (1) as follows:

  $\begin{array}{c}{x}^2-y^2={12}^2-6^2\\ =\left(12\times 12\right)-\left(6\times 6\right)\\ =144-36\\ =108\end{array}$

Thus, the value of $x^2-y^2$ is $108$.

Conclusion:

The value of $x^2-y^2$ is $108$.