# 0.1 Cumulative review

 Page 1 / 1

Note: Answers to the Cumulative Review can be found in the Supplemental Resources. Please visit http://openstaxcollege.org to view an updated list of the Learning Resources for this title and how to access them.

No exercises.

## Chapter 2 the language of algebra

Simplify:

$1.\phantom{\rule{0.4em}{0ex}}5\left(3+2·6\right)-{8}^{2}$

Solve:

$2.\phantom{\rule{0.4em}{0ex}}17=y-13$

$3.\phantom{\rule{0.4em}{0ex}}p+14=23$

Translate into an algebraic expression.

$4.\phantom{\rule{0.4em}{0ex}}11$ less than the product of $7$ and $x.$

Translate into an algebraic equation and solve.

$5.\phantom{\rule{0.2em}{0ex}}$ Twice the difference of $y$ and $7$ gives $84.$

$6.\phantom{\rule{0.2em}{0ex}}$ Find all the factors of $72.$

$7.\phantom{\rule{0.2em}{0ex}}$ Find the prime factorization of $132.$

$8.\phantom{\rule{0.2em}{0ex}}$ Find the least common multiple of $12$ and $20.$

## Chapter 3 integers

Simplify:

$9.\phantom{\rule{0.4em}{0ex}}|8-9|-|3-8|$

$10.\phantom{\rule{0.4em}{0ex}}-2+4\left(-3+7\right)$

$11.\phantom{\rule{0.4em}{0ex}}27-\left(-4-7\right)$

$12.\phantom{\rule{0.4em}{0ex}}28÷\left(-4\right)-7$

Translate into an algebraic expression or equation.

$13.\phantom{\rule{0.2em}{0ex}}$ The sum of $-5$ and $13,$ increased by $11.$

$14.\phantom{\rule{0.2em}{0ex}}$ The product of $-11\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}8.$

$15.\phantom{\rule{0.2em}{0ex}}$ The quotient of $7$ and the sum of $-4\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}m\text{.}$

$16.\phantom{\rule{0.2em}{0ex}}$ The product of $-3$ and is $-51.$

Solve:

$17.\phantom{\rule{0.4em}{0ex}}-6r=24$

## Chapter 4 fractions

$18.\phantom{\rule{0.2em}{0ex}}$ Locate the numbers on a number line. $\frac{7}{8},\frac{5}{3},3\frac{1}{4},5.$

Simplify:

$19.\phantom{\rule{0.4em}{0ex}}\frac{21p}{57q}$

$20.\phantom{\rule{0.4em}{0ex}}\frac{3}{7}·\left(-\frac{28}{45}\right)$

$21.\phantom{\rule{0.4em}{0ex}}-6\frac{3}{4}÷\frac{9}{2}$

$22.\phantom{\rule{0.4em}{0ex}}-3\frac{3}{5}÷6$

$23.\phantom{\rule{0.4em}{0ex}}-4\frac{2}{3}\phantom{\rule{0.2em}{0ex}}\left(-\frac{6}{7}\right)$

$24.\phantom{\rule{0.4em}{0ex}}\frac{-2\frac{1}{4}}{-\frac{3}{8}}$

$25.\phantom{\rule{0.4em}{0ex}}\frac{7·8+4\left(7-12\right)}{9·6-2·9}$

$26.\phantom{\rule{0.4em}{0ex}}-\frac{23}{36}+\frac{17}{20}$

$27.\phantom{\rule{0.4em}{0ex}}\frac{\phantom{\rule{0.2em}{0ex}}\frac{1}{2}+\frac{1}{3}\phantom{\rule{0.2em}{0ex}}}{\frac{3}{4}-\frac{1}{3}}$

$28.\phantom{\rule{0.4em}{0ex}}3\frac{5}{8}-2\frac{1}{2}$

$29.\phantom{\rule{0.4em}{0ex}}-\frac{2}{3}r=24$

## Chapter 5 decimals

Simplify:

$30.\phantom{\rule{0.4em}{0ex}}24.76-7.28$

$31.\phantom{\rule{0.4em}{0ex}}12.9+15.633$

$32.\phantom{\rule{0.4em}{0ex}}\left(-5.6\right)\left(0.25\right)$

$33.\phantom{\rule{0.4em}{0ex}}6.29÷12$

$34.\phantom{\rule{0.4em}{0ex}}\frac{3}{4}\left(13.44-9.6\right)$

$35.\phantom{\rule{0.4em}{0ex}}\sqrt{64}+\sqrt{225}$

$36.\phantom{\rule{0.4em}{0ex}}\sqrt{121{x}^{2}{y}^{2}}$

$37.\phantom{\rule{0.2em}{0ex}}$ Write in order from smallest to largest: $\frac{5}{8},0.75,\frac{8}{15}$

Solve :

$38.\phantom{\rule{0.4em}{0ex}}-8.6x=34.4$

$39.\phantom{\rule{0.2em}{0ex}}$ Using $3.14$ as the estimate for pi, approximate the (a) circumference and (b) area of a circle whose radius is $8$ inches.

$40.\phantom{\rule{0.2em}{0ex}}$ Find the mean of the numbers, $18,16,20,12$

$41.\phantom{\rule{0.2em}{0ex}}$ Find the median of the numbers, $24,29,27,28,30$

$42.\phantom{\rule{0.2em}{0ex}}$ Identify the mode of the numbers, $6,4,4,5,6,6,4,4,4,3,5$

$43.\phantom{\rule{0.2em}{0ex}}$ Find the unit price of one t-shirt if they are sold at $3$ for $\text{28.97}.$

## Chapter 6 percents

$44.\phantom{\rule{0.2em}{0ex}}$ Convert $\text{14.7%}$ to (a) a fraction and (b) a decimal.

Translate and solve.

$45.\phantom{\rule{0.4em}{0ex}}63$ is $35%$ of what number?

$46.\phantom{\rule{0.2em}{0ex}}$ The nutrition label on a package of granola bars says that each granola bar has $180$ calories, and $81$ calories are from fat. What percent of the total calories is from fat?

$47.\phantom{\rule{0.2em}{0ex}}$ Elliot received $\text{510}$ commission when he sold a $\text{3,400}$ painting at the art gallery where he works. What was the rate of commission?

$48.\phantom{\rule{0.2em}{0ex}}$ Nandita bought a set of towels on sale for $\text{67.50}.$ The original price of the towels was $\text{90}.$ What was the discount rate?

$49.\phantom{\rule{0.2em}{0ex}}$ Alan invested $\text{23,000}$ in a friend’s business. In $5$ years the friend paid him the $\text{23,000}$ plus $\text{9,200}$ interest. What was the rate of interest?

Solve:

$50.\phantom{\rule{0.4em}{0ex}}\frac{9}{p}=\frac{-6\phantom{\rule{0.2em}{0ex}}}{14}$

## Chapter 7 the properties of real numbers

$51.\phantom{\rule{0.2em}{0ex}}$ List the (a) whole numbers, (b) integers, (c) rational numbers, (d) irrational numbers,

(e) real numbers $-5,-2\frac{1}{4},-\sqrt{4},0.\overline{25},\frac{13}{5},4$

Simplify:

$52.\phantom{\rule{0.4em}{0ex}}\left(\frac{8}{15}+\frac{4}{7}\right)+\frac{3}{7}$

$53.\phantom{\rule{0.4em}{0ex}}3\left(y+3\right)-8\left(y-4\right)$

$54.\phantom{\rule{0.4em}{0ex}}\frac{8}{17}·49·\frac{17}{8}$

$55.\phantom{\rule{0.2em}{0ex}}$ A playground is $55$ feet wide. Convert the width to yards.

$56.\phantom{\rule{0.2em}{0ex}}$ Every day last week Amit recorded the number of minutes he spent reading. The recorded number of minutes he read each day was $48,26,81,54,43,62,106.$ How many hours did Amit spend reading last week?

$57.\phantom{\rule{0.2em}{0ex}}$ June walked $2.8$ kilometers. Convert this length to miles knowing $1$ mile is $1.61$ kilometer.

## Chapter 8 solve linear equations

Solve:

$58.\phantom{\rule{0.4em}{0ex}}y+13=-8$

$59.\phantom{\rule{0.4em}{0ex}}p+\frac{2}{5}=\frac{8}{5}$

$60.\phantom{\rule{0.4em}{0ex}}48=\frac{2}{3}x$

$61.\phantom{\rule{0.4em}{0ex}}4\left(a-3\right)-6a=-18$

$62.\phantom{\rule{0.4em}{0ex}}7q+14=-35$

$63.\phantom{\rule{0.4em}{0ex}}4v-27=7v$

$64.\phantom{\rule{0.4em}{0ex}}\frac{7}{8}y-6=\frac{3}{8}y-8$

$65.\phantom{\rule{0.4em}{0ex}}26-4\left(z-2\right)=6$

$66.\phantom{\rule{0.4em}{0ex}}\frac{3}{4}\phantom{\rule{0.2em}{0ex}}x-\frac{2}{3}=\frac{1}{2}x-\frac{5}{6}$

$67.\phantom{\rule{0.4em}{0ex}}0.7y+4.8=0.84y-5.3$

Translate and solve.

$68.\phantom{\rule{0.2em}{0ex}}$ Four less than $n$ is $13.$

## Chapter 9 math models and geometry

$69.\phantom{\rule{0.2em}{0ex}}$ One number is $8$ less than another. Their sum is negative twenty-two. Find the numbers.

$70.\phantom{\rule{0.2em}{0ex}}$ The sum of two consecutive integers is $-95.$ Find the numbers.

$71.\phantom{\rule{0.2em}{0ex}}$ Wilma has $\text{3.65}$ in dimes and quarters. The number of dimes is $2$ less than the number of quarters. How many of each coin does she have?

$72.\phantom{\rule{0.2em}{0ex}}$ Two angles are supplementary. The larger angle is $24\text{°}$ more than the smaller angle. Find the measurements of both angles.

$73.\phantom{\rule{0.2em}{0ex}}$ One angle of a triangle is $20\text{°}$ more than the smallest angle. The largest angle is the sum of the other angles. Find the measurements of all three angles.

$74.\phantom{\rule{0.2em}{0ex}}$ Erik needs to attach a wire to hold the antenna to the roof of his house, as shown in the figure. The antenna is $12$ feet tall and Erik has $15$ feet of wire. How far from the base of the antenna can he attach the wire?

$75.\phantom{\rule{0.2em}{0ex}}$ The width of a rectangle is $4$ less than the length. The perimeter is $96$ inches. Find the length and the width.

$76.\phantom{\rule{0.2em}{0ex}}$ Find the (a) volume and (b) surface area of a rectangular carton with length $24$ inches, width $18$ inches, and height $6$ inches.

## Chapter 10 polynomials

Simplify:

$77.\phantom{\rule{0.4em}{0ex}}\left(8{m}^{2}+12m-5\right)-\left(2{m}^{2}-7m-1\right)$

$78.\phantom{\rule{0.4em}{0ex}}{p}^{3}·{p}^{10}$

$79.\phantom{\rule{0.4em}{0ex}}{\left({y}^{4}\right)}^{3}$

$80.\phantom{\rule{0.4em}{0ex}}{\left(3{a}^{5}\right)}^{3}$

$81.\phantom{\rule{0.4em}{0ex}}{\left({x}^{3}\right)}^{5}{\left({x}^{2}\right)}^{3}$

$82.\phantom{\rule{0.4em}{0ex}}\left(\frac{2}{3}{m}^{3}{n}^{6}\right)\left(\frac{1}{6}{m}^{4}{n}^{4}\right)$

$83.\phantom{\rule{0.4em}{0ex}}\left(y-4\right)\left(y+12\right)$

$84.\phantom{\rule{0.4em}{0ex}}\left(3c+1\right)\left(9c-4\right)$

$85.\phantom{\rule{0.4em}{0ex}}\left(x-1\right)\left({x}^{2}-3x-2\right)$

$86.\phantom{\rule{0.4em}{0ex}}{\left(8x\right)}^{0}$

$87.\phantom{\rule{0.4em}{0ex}}\frac{{\left({x}^{3}\right)}^{5}}{{\left({x}^{2}\right)}^{4}}$

$88.\phantom{\rule{0.4em}{0ex}}\frac{32{a}^{7}{b}^{2}}{12{a}^{3}{b}^{6}}$

$89.\phantom{\rule{0.4em}{0ex}}\left(a{b}^{-3}\right)\left({a}^{-3}{b}^{6}\right)$

$90.\phantom{\rule{0.2em}{0ex}}$ Write in scientific notation: $\text{(a)}\phantom{\rule{0.2em}{0ex}}4,800,000\phantom{\rule{0.5em}{0ex}}\text{(b)}\phantom{\rule{0.2em}{0ex}}0.00637$

Factor the greatest common factor from the polynomial.

$91.\phantom{\rule{0.4em}{0ex}}3{x}^{4}-6{x}^{3}-18{x}^{2}$

## Chapter 11 graphs

Graph:

$92.\phantom{\rule{0.4em}{0ex}}y=4x-3$

$93.\phantom{\rule{0.4em}{0ex}}y=-3x$

$94.\phantom{\rule{0.4em}{0ex}}y=\frac{1}{2}x+3$

$95.\phantom{\rule{0.4em}{0ex}}x-y=6$

$96.\phantom{\rule{0.4em}{0ex}}y=-2$

$97.\phantom{\rule{0.2em}{0ex}}$ Find the intercepts. $2x+3y=12$

Graph using the intercepts.

$98.\phantom{\rule{0.4em}{0ex}}2x-4y=8$

$99.\phantom{\rule{0.2em}{0ex}}$ Find slope.

$100.\phantom{\rule{0.2em}{0ex}}$ Use the slope formula to find the slope of the line between the points $\left(-5,-2\right),\left(3,2\right).$

$101.\phantom{\rule{0.2em}{0ex}}$ Graph the line passing through the point $\left(-3,4\right)$ and with slope $m=-\frac{1}{3}.$

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?