5.1.1: Exercises
- Page ID
- 169538
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)For the following exercises, translate from algebra to words.
\(50-15\)
(10) \((x)\)
\(2 a-b\)
\(100 \div 33\)
\(3 x+5\)
For the following exercises, translate from words to algebra.
15 divided by 3 .
The sum of 13 and 13.
120 minus 12 .
The product of 5 and 4.
The sum of double \(x\) and 5 .
For the following exercises, translate from an English phrase to an expression.
Three times \(y\) minus 7 .
\(a\) divided by 2 ; then add 4.
\(x\) squared minus 3 .
A rental car company charges \(\$ 0.15\) per mile \(m\), plus a \(\$ 40\) flat fee for the rental.
A parking garage in New York City charges \(\$ 20\) for the first hour, then \(\$ 5\) per hour \(h\).
For the following exercises, use parentheses to make the statements true.
\(16 \div 4 \bullet 2+5=13\)
\(2^2-5+3 \bullet 2=5\)
\(x-3 \bullet x-2=x^2-5 x+6\)
\(20 x \div 5-1-5 x=0\)
\(5 x+3 x \div 3-7 x+1 \bullet x=0\)
For the following exercises, evaluate and simplify the expression.
\(x^2\) when \(x=9\)
\(2 x+5\) when \(x=3\)
\((3 x+1)(4 x-6)\) when \(x=2\)
\(x^2+3 x+8\) when \(x=3\)
\(\left(x^2+5 x-4\right)(2 x)\) when \(x=4\)
\(4 a+5-2 a-8\) when \(a=6\)
\(8 a^2+4 a+9-a^2-1\) when \(a=5\)
Yasenia is 3 years older than Xavier. How old is Yasenia when Xavier is 18 years old?
A rental car company charges \(\$ 0.15\) per mile \(m\), plus a \(\$ 40\) flat fee for the rental. What is the cost of the car rental if one drives 100 miles?
A parking garage in New York City charges \(\$ 20\) for the first hour, then \(\$ 5\) per hour \(h\). What is the cost of parking for 10 hours?
For the following exercises, perform the indicated operation for the expressions.
Add \((4 x-9)+(x+12)\).
Add \(\left(3 x^2+2 x+1\right)+\left(x^2-2 x+2\right)\).
Subtract \((4 x-9)-(-x+2)\).
Subtract \(\left(3 x^2+5 x\right)-\left(x^2-3 x+11\right)\).
Multiply \(4(x+2)\).
Multiply \(2\left(3 x^2-2 x+1\right)\).
Multiply \((3 x)(x-1)\).
Multiply \((2 x-1)(x+3)\).
\(\left(125 x^2+35 x-5\right) \div(5)\).
\(\left(9 x^2+18 x-27\right) \div(3 x)\).