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Simplify each algebraic expression.
A rectangle with length $\text{\hspace{0.17em}}L\text{\hspace{0.17em}}$ and width $\text{\hspace{0.17em}}W\text{\hspace{0.17em}}$ has a perimeter $\text{\hspace{0.17em}}P\text{\hspace{0.17em}}$ given by $\text{\hspace{0.17em}}P=L+W+L+W.\text{\hspace{0.17em}}$ Simplify this expression.
If the amount $\text{\hspace{0.17em}}P\text{\hspace{0.17em}}$ is deposited into an account paying simple interest $\text{\hspace{0.17em}}r\text{\hspace{0.17em}}$ for time $\text{\hspace{0.17em}}t,$ the total value of the deposit $\text{\hspace{0.17em}}A\text{\hspace{0.17em}}$ is given by $\text{\hspace{0.17em}}A=P+Prt.\text{\hspace{0.17em}}$ Simplify the expression. (This formula will be explored in more detail later in the course.)
$A=P\left(1+rt\right)$
Access these online resources for additional instruction and practice with real numbers.
Is $\text{\hspace{0.17em}}\sqrt{2}\text{\hspace{0.17em}}$ an example of a rational terminating, rational repeating, or irrational number? Tell why it fits that category.
irrational number. The square root of two does not terminate, and it does not repeat a pattern. It cannot be written as a quotient of two integers, so it is irrational.
What is the order of operations? What acronym is used to describe the order of operations, and what does it stand for?
What do the Associative Properties allow us to do when following the order of operations? Explain your answer.
The Associative Properties state that the sum or product of multiple numbers can be grouped differently without affecting the result. This is because the same operation is performed (either addition or subtraction), so the terms can be re-ordered.
For the following exercises, simplify the given expression.
$10+2\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\left(5-3\right)$
$18+{\left(6-8\right)}^{3}$
$\mathrm{-2}\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}{\left[16\xf7{\left(8-4\right)}^{2}\right]}^{2}$
$\mathrm{-2}$
$4-6+2\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}7$
$4+6-10\xf72$
${\left(4+5\right)}^{2}\xf73$
$3-12\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}2+19$
-2
$2+8\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}7\xf74$
$9-18\xf7{3}^{2}$
$14\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}3\xf77-6$
0
$9-\left(3+11\right)\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}2$
$6+2\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}2-1$
9
$64\xf7\left(8+4\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}2\right)$
${\left(12\xf73\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}3\right)}^{2}$
$\left(15-7\right)\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\left(3-7\right)$
$2\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}4-9\left(\mathrm{-1}\right)$
17
${4}^{2}-25\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\frac{1}{5}$
For the following exercises, solve for the variable.
$8\left(x+3\right)=64$
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