Question

part e: using substitution, evaluate the following expressions with the given values for the variables.
$x = 3$ $y = 5$ $g = 2.12$ $t = 0.5$ $p = \frac{1}{4}$ $z = 8$

1. $5t^3$
2. $6 \div \frac{1}{3} \cdot (z + 2^3)$
3. $(y^2 - x) \div 2$
4. $12p - z$
5. $(x^3 \div 3) \cdot 2$
6. $8g - 5$

Explanation:

Step1: Substitute $t=0.5$

$5(0.5)^3$

Step2: Calculate power first

$5\times0.125$

Step3: Compute final product

$0.625$

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Step1: Substitute $z=8$

$6\div\frac{1}{3}\times(8 + 2^3)$

Step2: Calculate power and sum

$6\div\frac{1}{3}\times(8+8)=6\div\frac{1}{3}\times16$

Step3: Divide then multiply

$6\times3\times16=18\times16=288$

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Step1: Substitute $x=3,y=5$

$(5^2 - 3)\div2$

Step2: Calculate power and difference

$(25-3)\div2=22\div2$

Step3: Compute final quotient

$11$

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Step1: Substitute $p=\frac{1}{4}$

$12\times\frac{1}{4}-2$

Step2: Calculate product then subtract

$3-2$

Step3: Compute final difference

$1$

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Step1: Substitute $x=3,z=8$

$(3^3\div3)\times8$

Step2: Calculate power and division

$(27\div3)\times8=9\times8$

Step3: Compute final product

$72$

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Step1: Substitute $g=2.12$

$8\times2.12 - 5$

Step2: Calculate product then subtract

$16.96-5$

Step3: Compute final difference

$11.96$

Answer:

1. $0.625$
2. $288$
3. $11$
4. $1$
5. $72$
6. $11.96$