Chapter 7, Problem 1P

Evaluate formulas and literal expressions.

If x = 2, y = 3, a = 5, b = 6, find the value of

1. (a) $2x+y$ _____
2. (b) $\frac{1+x^2+2a}{y}$ _____
3. (c) $A=x^{2}y$ A = _____
4. (d) $T=\frac{2\left(a+b+1\right)}{3x}$ T = _____
5. (e) $P=ab{x}^2$ P = _____

To determine

To evaluate: The given expression for the given values.

Answer to Problem 1P

The value of the given expression is $\underset{\_}{7}$.

Explanation of Solution

Given:

The expression is $2x+y$.

The values are $x=2\text{ and }y=3$.

Procedure used:

The order of operations for arithmetic calculations used while evaluating formulas:

“1. First, do any operations inside the parentheses.

2. Second, find all powers and roots.

3. Next, do all multiplications or divisions left to right.

4. Finally, do all additions or subtractions left to right”.

Calculation:

Compute the value of the given expression as follows.

Substitute $x=2\text{ and }y=3$ in $2x+y$.

$\begin{array}{c}2\left(2\right)+3=4+3\left[\text{Multiply from left to right}\right]\\ =7\left[\text{Add from left to right}\right]\end{array}$

That is, the value of the given expression is 7.

Use calculator and compute the value of the given expression as follows.

$2\boxed{\times }2\boxed{+}3\boxed{=}$

The output will display in the calculator as follows.

From the above screenshot, it is observed that the value of the given expression is 7.

Thus, the value of the of the given expression is $\underset{\_}{7}$.

To determine

To evaluate: The given expression for the given values.

Answer to Problem 1P

The value of the given expression is $\underset{\_}{5}$.

Explanation of Solution

Given:

The expression is $\frac{1+x^2+2a}{y}$.

The values are $x=2\text{, }y=3\text{ and }a=5$.

Calculation:

Compute the value of the given expression as follows.

Substitute $x=2\text{, }y=3\text{ and }a=5$ in $\frac{1+x^2+2a}{y}$.

$\begin{array}{c}\frac{1+{\left(2\right)}^2+2\left(5\right)}{3}=\frac{1+4+2\left(5\right)}{3}\left[\text{Evaluate the value of the exponent}\right]\\ =\frac{1+4+10}{3}\left[\text{Multiply from left to right}\right]\\ =\frac{15}{3}\left[\text{Add from left to right}\right]\\ =5\left[\text{Divide }15\text{ by }3\right]\end{array}$

That is, the value of the given expression is 5.

Use calculator and compute the value of the given expression as follows.

$\boxed{(}1\boxed{+}2\boxed{^}2\boxed{+}2\boxed{\times }5\boxed{)}\boxed{÷}3\boxed{=}$

The output will display in the calculator as follows.

From the above screenshot, it is observed that the value of the given expression is 5.

Thus, the value of the of the given expression is $\underset{\_}{5}$.

To determine

The value of A.

Answer to Problem 1P

The value of A is $\underset{\_}{12}$.

Explanation of Solution

Given:

The formula is $A=x^{2}y$.

The values are $x=2\text{ and }y=3$.

Calculation:

Compute the value of A as follows.

Substitute $x=2\text{ and }y=3$ in $A=x^{2}y$.

$\begin{array}{c}A={\left(2\right)}^2\left(3\right)\\ =\text{4}\left(3\right)\left[\text{Evaluate the value of the exponent}\right]\\ =12\left[\text{Multiply from left to right}\right]\end{array}$

That is, the value of A is 12.

Use calculator and compute the value of A as follows.

$\boxed{(}2\boxed{^}2\boxed{)}\boxed{\times }3\boxed{=}$

The output will display in the calculator as follows.

From the above screenshot, it is observed that the value of A is 12.

Thus, the value of the of A is $\underset{\_}{12}$.

To determine

The value of T.

Answer to Problem 1P

The value of T is $\underset{\_}{4}$.

Explanation of Solution

Given:

The formula is $T=\frac{2\left(a+b+1\right)}{3x}$.

The values are $x=2,a=\text{5 and }b=6$.

Calculation:

Compute the value of T as follows.

Substitute $x=2,a=\text{5 and }b=6$ in $T=\frac{2\left(a+b+1\right)}{3x}$.

$\begin{array}{c}T=\frac{2\left(5+6+1\right)}{3\left(2\right)}\\ =\frac{2\left(12\right)}{3\left(2\right)}\left[\text{Evaluate inside the parentheses}\right]\\ =\frac{24}{6}\left[\text{Multiply from left to right}\right]\\ =4\left[\text{Divide 24 by 6}\right]\end{array}$

That is, the value of T is 4.

Use calculator and compute the value of T as follows.

$\boxed{(}2\boxed{(}5\boxed{+}6\boxed{+}1\boxed{)}\boxed{)}\boxed{÷}\boxed{(}3\boxed{\times }2\boxed{)}\boxed{=}$

The output will display in the calculator as follows.

From the above screenshot, it is observed that the value of T is 4.

Thus, the value of T is $\underset{\_}{4}$.

To determine

The value of P.

Answer to Problem 1P

The value of P is $\underset{\_}{120}$.

Explanation of Solution

Given:

The formula is $P=ab{x}^2$.

The values are $x=2,a=\text{5 and }b=6$.

Calculation:

Compute the value of P as follows.

Substitute $x=2,a=\text{5 and }b=6$ in $P=ab{x}^2$.

$\begin{array}{c}P=\left(5\right)\left(6\right){\left(2\right)}^2\\ =\left(5\right)\left(6\right)\left(4\right)\left[\text{Evaluate the value of the exponent}\right]\\ =120\left[\text{Multiply from left to right}\right]\end{array}$

That is, the value of P is 120.

Use calculator and compute the value of P as follows.

$5\boxed{\times }6\boxed{\times }2\boxed{^}2\boxed{=}$

The output will display in the calculator as follows.

From the above screenshot, it is observed that the value of P is 120.

Thus, the value of P is $\underset{\_}{120}$.