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College Algebra with Corequisite Support

Jay Abramson

Chapter 1

Prerequisites - all with Video Answers

Educators

Section 1

Real Numbers: Algebra Essentials

00:27

Problem 1

Is $\sqrt{2}$ an example of a rational terminating, rational repeating, or irrational number? Tell why it fits that category.

Patil Kaptanian
Patil Kaptanian
Numerade Educator
01:02

Problem 2

What is the order of operations? What acronym is used to describe the order of operations, and what does it stand for?

K B
K B
Numerade Educator
01:55

Problem 3

What do the Associative Properties allow us to do when following the order of operations? Explain your answer.

Patil Kaptanian
Patil Kaptanian
Numerade Educator
00:36

Problem 4

For the following exercises, simplify the given expression.
$10+2 \times(5-3)$

K B
K B
Numerade Educator
02:50

Problem 5

For the following exercises, simplify the given expression.
$6 \div 2-\left(81 \div 3^{2}\right)$

Patil Kaptanian
Patil Kaptanian
Numerade Educator
00:36

Problem 6

For the following exercises, simplify the given expression.
$18+(6-8)^{3}$

K B
K B
Numerade Educator
02:26

Problem 7

For the following exercises, simplify the given expression.
$-2 \times\left[16 \div(8-4)^{2}\right]^{2}$

Patil Kaptanian
Patil Kaptanian
Numerade Educator
01:23

Problem 8

For the following exercises, simplify the given expression.
$4-6+2 \times 7$

Breanna Ollech
Breanna Ollech
Numerade Educator
00:49

Problem 9

For the following exercises, simplify the given expression.
$3(5-8)$

Patil Kaptanian
Patil Kaptanian
Numerade Educator
00:29

Problem 10

For the following exercises, simplify the given expression.
$4+6-10 \div 2$

K B
K B
Numerade Educator
01:12

Problem 11

For the following exercises, simplify the given expression.
$12 \div(36 \div 9)+6$

Patil Kaptanian
Patil Kaptanian
Numerade Educator
00:32

Problem 12

For the following exercises, simplify the given expression.
$(4+5)^{2} \div 3$

K B
K B
Numerade Educator
01:11

Problem 13

For the following exercises, simplify the given expression.
$3-12 \times 2+19$

Patil Kaptanian
Patil Kaptanian
Numerade Educator
00:37

Problem 14

For the following exercises, simplify the given expression.
$2+8 \times 7 \div 4$

K B
K B
Numerade Educator
01:34

Problem 15

For the following exercises, simplify the given expression.
$5+(6+4)-11$

Patil Kaptanian
Patil Kaptanian
Numerade Educator
00:30

Problem 16

For the following exercises, simplify the given expression.
$9-18 \div 3^{2}$

K B
K B
Numerade Educator
01:09

Problem 17

For the following exercises, simplify the given expression.
$14 \times 3 \div 7-6$

Patil Kaptanian
Patil Kaptanian
Numerade Educator
00:31

Problem 18

For the following exercises, simplify the given expression.
$9-(3+11) \times 2$

K B
K B
Numerade Educator
00:39

Problem 19

For the following exercises, simplify the given expression.
$6+2 \times 2-1$

James Leslie
James Leslie
Numerade Educator
00:34

Problem 20

For the following exercises, simplify the given expression.
$64 \div(8+4 \times 2)$

K B
K B
Numerade Educator
00:43

Problem 21

For the following exercises, simplify the given expression.
$9+4\left(2^{2}\right)$

James Leslie
James Leslie
Numerade Educator
00:34

Problem 22

For the following exercises, simplify the given expression.
$(12 \div 3 \times 3)^{2}$

K B
K B
Numerade Educator
01:03

Problem 23

For the following exercises, simplify the given expression.
$25 \div 5^{2}-7$

James Leslie
James Leslie
Numerade Educator
00:25

Problem 24

For the following exercises, simplify the given expression.
$(15-7) \times(3-7)$

K B
K B
Numerade Educator
01:07

Problem 25

For the following exercises, simplify the given expression.
$2 \times 4-9(-1)$

James Leslie
James Leslie
Numerade Educator
00:33

Problem 26

For the following exercises, simplify the given expression.
$4^{2}-25 \times \frac{1}{5}$

K B
K B
Numerade Educator
01:42

Problem 27

For the following exercises, simplify the given expression.
$12(3-1) \div 6$

James Leslie
James Leslie
Numerade Educator
00:36

Problem 28

For the following exercises, solve for the variable.
$8(x+3)-64$ for $x=2$

K B
K B
Numerade Educator
01:17

Problem 29

For the following exercises, solve for the variable.
$4 y+8-2 y$ for $y=3$

James Leslie
James Leslie
Numerade Educator
00:41

Problem 30

For the following exercises, solve for the variable.
$(11 a+3)-18 a+4$ for $a=-2$

K B
K B
Numerade Educator
01:38

Problem 31

For the following exercises, solve for the variable.
$4 z-2 z(1+4)-36$ for $z=5$

James Leslie
James Leslie
Numerade Educator
00:53

Problem 32

For the following exercises, solve for the variable.
$4 y(7-2)^{2}+200$ for $y=-2$

K B
K B
Numerade Educator
01:04

Problem 33

For the following exercises, solve for the variable.
$-(2 x)^{2}+1+3$ for $x=2$

James Leslie
James Leslie
Numerade Educator
00:40

Problem 34

For the following exercises, solve for the variable.
For the $8(2+4)-15 b+b$ for

K B
K B
Numerade Educator
01:26

Problem 35

For the following exercises, solve for the variable.
$2(11 c-4)-36$ for $c=0$

James Leslie
James Leslie
Numerade Educator
00:27

Problem 36

For the following exercises, solve for the variable.
$4(3-1) x-4$ for $x=10$ $b=-3$

K B
K B
Numerade Educator
01:39

Problem 37

For the following exercises, solve for the variable.
$\frac{1}{4}\left(8 w-4^{2}\right)$ for $w=1$

James Leslie
James Leslie
Numerade Educator
00:37

Problem 38

For the following exercises, simplify the expression.
$4 x+x(13-7)$

K B
K B
Numerade Educator
01:01

Problem 39

For the following exercises, simplify the expression.
$2 y-(4)^{2} y-11$

James Leslie
James Leslie
Numerade Educator
00:47

Problem 40

For the following exercises, simplify the expression.
$\frac{a}{2^{3}}(64)-12 a \div 6$

K B
K B
Numerade Educator
01:32

Problem 41

For the following exercises, simplify the expression.
$8 b-4 b(3)+1$

James Leslie
James Leslie
Numerade Educator
01:12

Problem 42

For the following exercises, simplify the expression.
$5 l \div 3 l \times(9-6)$

Mukesh Devi
Mukesh Devi
Numerade Educator
01:17

Problem 43

For the following exercises, simplify the expression.
$7 z-3+z \times 6^{2}$

James Leslie
James Leslie
Numerade Educator
00:40

Problem 44

For the following exercises, simplify the expression.
$4 \times 3+18 x \div 9-12$

K B
K B
Numerade Educator
02:37

Problem 45

For the following exercises, simplify the expression.
$9(y+8)-27$

James Leslie
James Leslie
Numerade Educator
00:41

Problem 46

For the following exercises, simplify the expression.
$\left(\frac{9}{6} t-4\right) 2$

K B
K B
Numerade Educator
01:34

Problem 47

For the following exercises, simplify the expression.
$6+12 b-3 \times 6 b$

James Leslie
James Leslie
Numerade Educator
00:31

Problem 48

For the following exercises, simplify the expression.
$18 y-2(1+7 y)$

K B
K B
Numerade Educator
05:12

Problem 49

For the following exercises, simplify the expression.
$\left(\frac{4}{9}\right)^{2} \times 27 x$

James Leslie
James Leslie
Numerade Educator
00:32

Problem 50

For the following exercises, simplify the expression.
$8(3-m)+1(-8)$

K B
K B
Numerade Educator
01:47

Problem 51

For the following exercises, simplify the expression.
$9 x+4 x(2+3)-4(2 x+3 x)$

James Leslie
James Leslie
Numerade Educator
00:23

Problem 52

For the following exercises, simplify the expression.
$5^{2}-4(3 x)$

K B
K B
Numerade Educator
02:29

Problem 53

For the following exercises, consider this scenario: Fred earns $$\$ 40$$ mowing lawns. He spends $$\$ 10$$ on $\mathrm{mp} 3 \mathrm{~s}$, puts half of what is left in a savings account, and gets another $$\$ 5$$ for washing his neighbor's car.
Write the expression that represents the number of dollars Fred keeps (and does not put in his savings account). Remember the order of operations.

James Leslie
James Leslie
Numerade Educator
00:47

Problem 54

For the following exercises, consider this scenario: Fred earns $$\$ 40$$ mowing lawns. He spends $$\$ 10$$ on $\mathrm{mp} 3 \mathrm{~s}$, puts half of what is left in a savings account, and gets another $$\$ 5$$ for washing his neighbor's car.
How much money does Fred keep?

K B
K B
Numerade Educator
03:34

Problem 55

According to the U.S. Mint, the diameter of a quarter is 0.955 inches. The circumference of the quarter would be the diameter multiplied by $\pi$. Is the circumference of a quarter a whole number, a rational number, or an irrational number?

James Leslie
James Leslie
Numerade Educator
00:45

Problem 56

Jessica and her roommate, Adriana, have decided to share a change jar for joint expenses. Jessica put her loose change in the jar first, and then Adriana put her change in the jar. We know that it does not matter in which order the change was added to the jar. What property of addition describes this fact?

K B
K B
Numerade Educator
View

Problem 57

For the following exercises, consider this scenario: There is a mound of g pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel.
Write the equation that describes the situation.

Marie Lucie Gauthe
Marie Lucie Gauthe
Numerade Educator
00:54

Problem 58

For the following exercises, consider this scenario: There is a mound of g pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel.
Solve for g.

K B
K B
Numerade Educator
01:17

Problem 59

Ramon runs the marketing department at his company. His department gets a budget every year, and every year, he must spend the entire budget without going over. If he spends less than the budget, then his department gets a smaller budget the following year. At the beginning of this year, Ramon got $\$ 2.5$ million for the annual marketing budget. He must spend the budget such that $2,500,000-x=0 .$ What property of addition tells us what the value of $x$ must be?

Lynn Larson
Lynn Larson
Numerade Educator
01:37

Problem 60

For the following exercises, use a graphing calculator to solve for $x$. Round the answers to the nearest hundredth.
$0.5(12.3)^{2}-48 x=\frac{3}{5}$

K B
K B
Numerade Educator
01:19

Problem 61

For the following exercises, use a graphing calculator to solve for $x$. Round the answers to the nearest hundredth.
$(0.25-0.75)^{2} x-7.2=9.9$

Julie Silva
Julie Silva
Numerade Educator
00:43

Problem 62

If a whole number is not a natural number, what must the number be?

K B
K B
Numerade Educator
01:21

Problem 63

Determine whether the statement is true or false: The multiplicative inverse of a rational number is also rational.

Stephen Hobbs
Stephen Hobbs
Numerade Educator
00:32

Problem 64

Determine whether the statement is true or false: The product of a rational and irrational number is always irrational.

K B
K B
Numerade Educator
View

Problem 65

Determine whether the simplified expression is rational or irrational:
$\sqrt{-18-4(5)(-1)}$

Amatullah Ahmed
Amatullah Ahmed
Numerade Educator
00:39

Problem 66

Determine whether the simplified expression is rational or irrational: $\sqrt{-16+4(5)+5} .$

K B
K B
Numerade Educator
00:35

Problem 67

The division of two whole numbers will always result in what type of number?

Julie Silva
Julie Silva
Numerade Educator
00:27

Problem 68

What property of real numbers would simplify the following expression: $4+7(x-1) ?$

K B
K B
Numerade Educator