Elementary Algebra

Problem 1

List all of the coefficients and variable parts of the following expressions.
$$
4 x-1
$$

Emily Himsel

Numerade Educator

00:25

Problem 2

List all of the coefficients and variable parts of the following expressions.
$$
-7 x 2-2 x+1
$$

Emily Himsel

Numerade Educator

Problem 3

List all of the coefficients and variable parts of the following expressions.
$$
-x 2+5 x-3
$$

Emily Himsel

Numerade Educator

00:38

Problem 4

List all of the coefficients and variable parts of the following expressions.
$$
3 x 2 y 2-23 x y+7
$$

Emily Himsel

Numerade Educator

00:36

Problem 5

List all of the coefficients and variable parts of the following expressions.
$$
13 y 2-12 y+57
$$

Emily Himsel

Numerade Educator

Problem 6

List all of the coefficients and variable parts of the following expressions.
$$
-4 a 2 b+5 a b 2-a b+1
$$

Emily Himsel

Numerade Educator

01:08

Problem 7

List all of the coefficients and variable parts of the following expressions.
$$
2(a+b) 3-3(a+b) 5
$$

Kevin Dunn

Numerade Educator

01:06

Problem 8

List all of the coefficients and variable parts of the following expressions.
$$
5(x+2) 2-2(x+2)-7
$$

Kevin Dunn

Numerade Educator

Problem 9

List all of the coefficients and variable parts of the following expressions.
$$
m 2 n-m n 2+10 m n-27
$$

Emily Himsel

Numerade Educator

Problem 10

List all of the coefficients and variable parts of the following expressions.
$$
x 4-2 x 3-3 x 2-4 x-1
$$

Emily Himsel

Numerade Educator

Problem 11

Evaluate.
$x+3,$ where $x=-4$

Emily Himsel

Numerade Educator

Problem 12

Evaluate.
$2 x-3,$ where $x=-3$

Emily Himsel

Numerade Educator

00:23

Problem 13

Evaluate.
$-5 x+20,$ where $x=4$

Emily Himsel

Numerade Educator

00:18

Problem 14

Evaluate.
$-5 y,$ where $y=-1$

Emily Himsel

Numerade Educator

00:20

Problem 15

Evaluate.
$34 a$, where $a=32$

Emily Himsel

Numerade Educator

00:20

Problem 16

Evaluate.
$2(a-4),$ where $a=-1$

Emily Himsel

Numerade Educator

00:27

Problem 17

Evaluate.
$-10(5-z),$ where $z=14$

Emily Himsel

Numerade Educator

Problem 18

Evaluate.
$5 y-1,$ where $y=-15$

Emily Himsel

Numerade Educator

Problem 19

Evaluate.
$-2 a+1,$ where $a=-13$

Emily Himsel

Numerade Educator

Problem 20

Evaluate.
$4 x+3,$ where $x=316$

Emily Himsel

Numerade Educator

Problem 21

Evaluate.
$-x+12,$ where $x=-2$

Emily Himsel

Numerade Educator

Problem 22

Evaluate.
$23 x-12,$ where $x=-14$

Emily Himsel

Numerade Educator

00:33

Problem 23

For each problem below, evaluate $b_{2}-4 a c$, given the following values for $a, b$, and $c$.
$$
a=1, b=2, c=3
$$

Emily Himsel

Numerade Educator

Problem 24

For each problem below, evaluate $b_{2}-4 a c$, given the following values for $a, b$, and $c$.
$$
a=3, b=4, c=1
$$

Emily Himsel

Numerade Educator

Problem 25

For each problem below, evaluate $b_{2}-4 a c$, given the following values for $a, b$, and $c$.
$$
a=6, b=0, c=2
$$

Emily Himsel

Numerade Educator

Problem 26

For each problem below, evaluate $b_{2}-4 a c$, given the following values for $a, b$, and $c$.
$$
a=12, b=1, c=23
$$

Emily Himsel

Numerade Educator

Problem 27

For each problem below, evaluate $b_{2}-4 a c$, given the following values for $a, b$, and $c$.
$$
a=-3, b=-12, c=19
$$

Emily Himsel

Numerade Educator

00:30

Problem 28

For each problem below, evaluate $b_{2}-4 a c$, given the following values for $a, b$, and $c$.
$$
a=-13, b=-23, c=0
$$

Emily Himsel

Numerade Educator

00:32

Problem 29

Evaluate.
$-4 x y 2,$ where $x=-3$ and $y=2$

Emily Himsel

Numerade Educator

Problem 30

Evaluate.
$58 x 2 y,$ where $x=-1$ and $y=16$

Emily Himsel

Numerade Educator

00:20

Problem 31

Evaluate.
$a_{2}-b_{2},$ where $a=2$ and $b=3$

Emily Himsel

Numerade Educator

00:46

Problem 32

Evaluate.
$a_{2}-b_{2},$ where $a=-1$ and $b=-2$

Emily Himsel

Numerade Educator

00:21

Problem 33

Evaluate.
$x 2-y_{2},$ where $x=12$ and $y=-12$

Emily Himsel

Numerade Educator

Problem 34

Evaluate.
$3 x_{2}-5 x+1,$ where $x=-3$

Emily Himsel

Numerade Educator

00:18

Problem 35

Evaluate.
$y_{2}-y-6,$ where $y=0$

Emily Himsel

Numerade Educator

Problem 36

Evaluate.
$1-y_{2},$ where $y=-12$

Emily Himsel

Numerade Educator

Problem 37

Evaluate.
$(x+3)(x-2),$ where $x=-4$

Cory Kuzinski

Numerade Educator

Problem 38

Evaluate.
$(y-5)(y+6),$ where $y=5$

Emily Himsel

Numerade Educator

Problem 39

Evaluate.
$3(\alpha-\beta)+4,$ where $\alpha=-1$ and $\beta=6$

Emily Himsel

Numerade Educator

Problem 40

Evaluate.
$3 \alpha_{2}-\beta_{2},$ where $\alpha=2$ and $\beta=-3$

Emily Himsel

Numerade Educator

00:39

Problem 41

Evaluate $4(x+h),$ given $x=5$ and $h=0.01$.

Emily Himsel

Numerade Educator

00:36

Problem 42

Evaluate $-2(x+h)+3,$ given $x=3$ and $h=0.1$

Emily Himsel

Numerade Educator

00:45

Problem 43

Evaluate $2(x+h) 2-5(x+h)+3,$ given $x=2$ and $h=0.1$

Emily Himsel

Numerade Educator

00:44

Problem 44

Evaluate $3(x+h) 2+2(x+h)-1,$ given $x=1$ and $h=0.01$.

Emily Himsel

Numerade Educator

00:37

Problem 45

Convert the following temperatures to degrees Celsius given $C=59(F-32),$ where F represents degrees Fahrenheit.
$$
86^{\circ} \mathrm{F}
$$

Emily Himsel

Numerade Educator

Problem 46

Convert the following temperatures to degrees Celsius given $C=59(F-32),$ where F represents degrees Fahrenheit.
$$
95^{\circ} \mathrm{F}
$$

Emily Himsel

Numerade Educator

00:37

Problem 47

Convert the following temperatures to degrees Celsius given $C=59(F-32),$ where F represents degrees Fahrenheit.
$$
-13^{\circ} \mathrm{F}
$$

Emily Himsel

Numerade Educator

Problem 48

Convert the following temperatures to degrees Celsius given $C=59(F-32),$ where F represents degrees Fahrenheit.
$$
14^{\circ} \mathrm{F}
$$

Emily Himsel

Numerade Educator

Problem 49

Convert the following temperatures to degrees Celsius given $C=59(F-32),$ where F represents degrees Fahrenheit.
$$
32^{\circ} \mathrm{F}
$$

Emily Himsel

Numerade Educator

00:42

Problem 50

Convert the following temperatures to degrees Celsius given $C=59(F-32),$ where F represents degrees Fahrenheit.
$$
0^{\circ} \mathrm{F}
$$

Emily Himsel

Numerade Educator

Problem 51

Given the base and height of a triangle, calculate the area. $(A=12 b h)$
$b=25$ centimeters and $h=10$ centimeters

Emily Himsel

Numerade Educator

Problem 52

Given the base and height of a triangle, calculate the area. $(A=12 b h)$
$b=40$ inches and $h=6$ inches

Emily Himsel

Numerade Educator

Problem 53

Given the base and height of a triangle, calculate the area. $(A=12 b h)$
$b=12$ foot and $h=2$ feet

Emily Himsel

Numerade Educator

00:46

Problem 54

Given the base and height of a triangle, calculate the area. $(A=12 b h)$
$b=34$ inches and $h=58$ inches

Emily Himsel

Numerade Educator

00:50

A certain cellular phone plan charges $\$ 23.00$ per month plus $\$ 0.09$ for each minute of usage. The monthly charge is given by the formula monthly charge $=0.09 x+23,$ where $x$ represents the number of minutes of usage per month. What is the charge for a month with 5 hours of usage?

Emily Himsel

Numerade Educator

00:39

Problem 56

A taxi service charges $\$ 3.75$ plus $\$ 1.15$ per mile given by the formula charge $=1.15 x+3.75,$ where $x$ represents the number of miles driven. What is the charge for a 17 -mile ride?

Emily Himsel

Numerade Educator

01:03

Problem 57

If a calculator is sold for $\$ 14.95,$ then the revenue in dollars, $R,$ generated by this item is given by the formula $R=14.95 q$, where $q$ represents the number of calculators sold. Use the formula to determine the revenue generated by this item if 35 calculators are sold.

Nick Johnson

Numerade Educator

00:47

Problem 58

Yearly subscriptions to a tutoring website can be sold for $\$ 49.95$. The revenue in dollars, $R$, generated by subscription sales is given by the formula $R=49.95 q,$ where $q$ represents the number of yearly subscriptions sold. Use the formula to calculate the revenue generated by selling 250 subscriptions.

Emily Himsel

Numerade Educator

00:36

Problem 59

The cost of producing pens with the company logo printed on them consists of a onetime setup fee of $\$ 175$ plus $\$ 0.85$ for each pen produced. This cost can be calculated using the formula $C=175+0.85 q,$ where $q$ represents the number of pens produced. Use the formula to calculate the cost of producing 2,000 pens.

Emily Himsel

Numerade Educator

00:54

Problem 60

The cost of producing a subscription website consists of an initial programming and setup fee of $\$ 4,500$ plus a monthly Web hosting fee of $\$ 29.95$. The cost of creating and hosting the website can be calculated using the formula $C=4500+29.95 n$, where $n$ represents the number of months the website is hosted. How much will it cost to set up and host the website for 1 year?

Emily Himsel

Numerade Educator

00:42

Problem 61

The perimeter of a rectangle is given by the formula $P=2 l+2 w$, where $/$ represents the length and $w$ represents the width. What is the perimeter of a fenced-in rectangular yard measuring 70 feet by 100 feet?

Emily Himsel

Numerade Educator

Problem 62

Calculate the perimeter of an 8 -by-10-inch picture.

Emily Himsel

Numerade Educator

00:38

Problem 63

Calculate the perimeter of a room that measures 12 feet by 18 feet.

Emily Himsel

Numerade Educator

00:44

Problem 64

A computer monitor measures 57.3 centimeters in length and 40.9 centimeters high. Calculate the perimeter.

Emily Himsel

Numerade Educator

00:33

Problem 65

The formula for the area of a rectangle in square units is given by $A=l \cdot w,$ where $/$ represents the length and $w$ represents the width. Use this formula to calculate the area of a rectangle with length 12 centimeters and width 3 centimeters.

Emily Himsel

Numerade Educator

Problem 66

Calculate the area of an 8 -by-12-inch picture.

Emily Himsel

Numerade Educator

Problem 67

Calculate the area of a room that measures 12 feet by 18 feet.

Emily Himsel

Numerade Educator

00:58

Problem 68

A computer monitor measures 57.3 centimeters in length and 40.9 centimeters in height. Calculate the total area of the screen.

Breanna Ollech

Numerade Educator

00:55

Problem 69

A concrete slab is poured in the shape of a rectangle for a shed measuring 8 feet by 10 feet. Determine the area and perimeter of the slab.

Emily Himsel

Numerade Educator

00:54

Problem 70

Each side of a square deck measures 8 feet. Determine the area and perimeter of the deck.

Emily Himsel

Numerade Educator

Problem 71

The volume of a rectangular solid is given by $V=l w h,$ where $/$ represents the length, w represents the width, and $h$ is the height of the solid. Find the volume of a rectangular solid if the length is 2 inches, the width is 3 inches, and the height is 4 inches.

Emily Himsel

Numerade Educator

01:37

Problem 72

If a trunk measures 3 feet by 2 feet and is $2 \%$ feet tall, then what is the volume of the trunk?

Kevin Dunn

Numerade Educator

Problem 73

The interior of an industrial freezer measures 3 feet wide by 3 feet deep and 4 feet high. What is the volume of the freezer?

Emily Himsel

Numerade Educator

02:09

Problem 74

A laptop case measures 1 feet 2 inches by 10 inches by 2 inches. What is the volume of the case?

Kevin Dunn

Numerade Educator

01:38

Problem 75

If the trip from Fresno to Sacramento can be made by car in $21 / 2$ hours at an average speed of 67 miles per hour, then how far is Sacramento from Fresno?

Kevin Dunn

Numerade Educator

Problem 76

A high-speed train averages 170 miles per hour. How far can it travel in $11 / 2$ hours?

Emily Himsel

Numerade Educator

Problem 77

A jumbo jet can cruises at an average speed of 550 miles per hour. How far can it travel in 4 hours?

Emily Himsel

Numerade Educator

Problem 78

A fighter jet reaches a top speed of 1,316 miles per hour. How far will the jet travel if it can sustain this speed for 15 minutes?

Emily Himsel

Numerade Educator

00:45

Problem 79

The Hubble Space Telescope is in low earth orbit traveling at an average speed of 16,950 miles per hour. What distance does it travel in $11 / 2$ hours?

Emily Himsel

Numerade Educator