Mathematics for Machine Technology

John C. Peterson, Robert D. Smith

Chapter 45 Solution of Equations by the Multiplication, Root, and Power Principles of Equality - all with Video Answers

Educators

Chapter Questions

01:23

Problem 1

Solve $A-\frac{3}{4}=-2 \frac{1}{8}$ using the addition principle of equality.

Teresa Fuston

Numerade Educator

01:25

Problem 2

Solve the equation $4 x-5 x+7 x=54$ for the unknown value $x$.

Emily Himsel

Numerade Educator

03:06

Problem 3

Write 0.0000275 in scientific notation.

Ruby P

Numerade Educator

00:30

Problem 4

Use the proper order of operations to solve $\left|3^2+\sqrt[3]{-125}-5(-2)^5\right|$.

Maria Konopke

Numerade Educator

Problem 5

Read the setting in Figure 45-7 of the metric micrometer scale graduated in $0.01 \mathrm{~mm}$.

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Problem 6

Read the customary height gage measurement for this setting in Figure 45-8.

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01:47

Problem 7

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{P}{5}=6$

Melissa Lupinacci

Numerade Educator

00:39

Problem 8

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{M}{12}=5$

Heather Zimmers

Numerade Educator

01:23

Problem 9

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$D \div 9=7$

Joseph Lentino

Numerade Educator

00:51

Problem 10

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$3=L \div 8$

Sherrie Fenner

Numerade Educator

01:32

Problem 11

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$3=W \div 9$

Brandon Fox

Numerade Educator

00:39

Problem 12

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{N}{12}=-2$

Melissa Stefan

Numerade Educator

01:06

Problem 13

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{C}{14}=0$

Melissa Stefan

Numerade Educator

01:59

Problem 14

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{x}{-10}=9$

Elicia Davenport

Numerade Educator

01:12

Problem 15

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{F}{4.3}=5$

Cory Kuzinski

Numerade Educator

00:53

Problem 16

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{A}{-0.5}=24$

Raushan Kumar

Numerade Educator

00:15

Problem 17

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$5 \div(7.8)=3$

Robert Leedy

Numerade Educator

01:35

Problem 18

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$x \div(-0.3)=16$

Anas Venkitta

Numerade Educator

00:40

Problem 19

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$-20=\frac{y}{0.3}$

Brandon Fox

Numerade Educator

01:31

Problem 20

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{T}{-1.8}=2.4$

Casey Evans

Numerade Educator

00:46

Problem 21

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$0=H \div(-3.8)$

Brandon Fox

Numerade Educator

01:00

Problem 22

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$M \div 9.5=-12$

Palitha Reddy

Numerade Educator

00:35

Problem 23

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$1.04=\frac{H}{0.06}$

Patrick Burns

Numerade Educator

04:52

Problem 24

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{B}{\frac{1}{2}}=7$

Catt Huth

Numerade Educator

00:21

Problem 25

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$V \div 1 \frac{1}{4}=3$

Heather Zimmers

Numerade Educator

View

Problem 26

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{x}{\frac{3}{8}}=-\frac{1}{4}$

Trinity Steen

Numerade Educator

00:43

Problem 27

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$D \div\left(-\frac{1}{16}\right)=-32$

Ashley Volpe

Numerade Educator

00:38

Problem 28

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$4=y \div\left(-\frac{7}{8}\right)$

Jonathan Zhang

Numerade Educator

02:05

Problem 29

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$\frac{1}{2}=\frac{T}{1 \frac{1}{2}}$

Cory Kuzinski

Numerade Educator

00:46

Problem 30

Solve each of the following equations using the multiplication principle of equality. Check each answer.
$H \div(-2)=7 \frac{9}{16}$

Brandon Fox

Numerade Educator

Problem 31

All dimensions are in millimeters.
Find $x$. $\qquad$ $x=$ $\qquad$

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01:00

Problem 32

Find $x$. $\qquad$ $x=$ $\qquad$

Sarah Lewites

Numerade Educator

Problem 33

A 10 -inch sine plate is tilted at an angle of $45^{\circ}$ as shown. The gage block height divided by 10 equals 0.70711 inch. Compute the height of the gage blocks. All dimensions are in inches.

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01:44

Problem 34

The width of a rectangular sheet of metal shown is equal to the area of the sheet divided by its length. Compute the area of a sheet that is $3 \frac{1}{4}$ feet wide and $5 \frac{1}{2}$ feet long.

Lucas Finney

Numerade Educator

The depth of an American Standard thread shown divided by 0.6495 is equal to the pitch. Compute the depth of a thread with a 0.0500 -inch pitch. All dimensions are in inches. Round the answer to 3 decimal places.

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04:04

Problem 36

In mechanical energy applications, force $(F)$ in pounds equals work $(W)$ in foot-pounds divided by distance $(D)$ in feet, $F=\frac{W}{D}$. Determine $W$ when $F=150.0$ pounds and $D=7.500$ feet.

Shaza Hammoud

Numerade Educator

00:47

Problem 37

The diameter $(D)$ of a circle equals the circle circumference $(C)$ divided by $3.1416, D=\frac{C}{3.1416}$. Determine $C$ when $D=52.14$ millimeters. Round the answer to 1 decimal place.

Nicole Smina

Numerade Educator

Problem 38

The pitch $(P)$ of a spur gear equals the number of gear teeth $(N)$ divided by the pitch diameter $(D), P=\frac{N}{D}$. Determine $N$ when $P=5$ teeth per inch and $D=5.6000$ inches.

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00:15

Problem 39

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$S^2=16$

Jake Zanazzi

Numerade Educator

00:59

Problem 40

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$P^2=81$

Amy Jiang

Numerade Educator

00:56

Problem 41

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$81=M^2$

Grace Muhihu

Numerade Educator

00:42

Problem 42

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$49=B^2$

Ashley High

Numerade Educator

00:55

Problem 43

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$D^3=64$

Brandon Fox

Numerade Educator

02:14

Problem 44

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$x^3=-64$

Erika Bustos

Numerade Educator

01:01

Problem 45

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$144=F^2$

Julie Silva

Numerade Educator

01:03

Problem 46

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$-64=y^3$

Julie Silva

Numerade Educator

01:11

Problem 47

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$10,000=L^2$

Matt Gibson

Numerade Educator

01:59

Problem 48

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$-125=x^3$

Amy Jiang

Numerade Educator

01:30

Problem 49

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$\frac{9}{25}=W^2$

Teresa Liang

Numerade Educator

01:56

Problem 50

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$C^2=\frac{1}{16}$

Christine Anacker

Numerade Educator

00:31

Problem 51

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$P^2=\frac{16}{49}$

Teresa Liang

Numerade Educator

03:43

Problem 52

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$M^3=\frac{1}{64}$

Andrija Isakov

Numerade Educator

00:20

Problem 53

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$-\frac{1}{8}=y^3$

Lily An

Numerade Educator

00:55

Problem 54

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$D^3=\frac{64}{27}$

Brandon Fox

Numerade Educator

00:34

Problem 55

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$E^2=0.04$

K B

Numerade Educator

01:06

Problem 56

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$0.64=H^2$

Brandon Fox

Numerade Educator

01:30

Problem 57

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$W^2=2.753$

Teresa Liang

Numerade Educator

01:39

Problem 58

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$0.0017=R^2$

Cory Kuzinski

Numerade Educator

03:42

Problem 59

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$N^3=0.123$

Eva R

Numerade Educator

01:10

Problem 60

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$-0.123=x^3$

Julie Silva

Numerade Educator

00:38

Problem 61

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$7.843=F^4$

Lily An

Numerade Educator

01:05

Problem 62

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal places where necessary.
$T^2=7.056$

Carson Merrill

Numerade Educator

01:14

Problem 63

The area of a square equals the length of a side squared, $A=s^2$. For each area of a square given, compute the length of a side. Round the answers to 3 decimal places where necessary.
a. 36 square inches
$$
s=
$$
$\qquad$
b. $\frac{25}{64}$ square foot
$$
s=
$$
$\qquad$
c. 1.44 square meters
$$
s=
$$
$\qquad$
d. 64.700 square meters
$$
s=
$$
$\qquad$
e. 0.049 square foot
$$
s=
$$
$\qquad$

Erika Bustos

Numerade Educator

01:47

Problem 64

The volume of a cube equals the length of a side cubed, $V=s^3$. For each volume of a cube given, compute the length of a side. Round the answers to 3 decimal places where necessary.
a. 125 cubic inches
$$
s=
$$
$\qquad$
b. $\frac{27}{216}$ cubic foot
$$
s=
$$
$\qquad$
c. 0.642 cubic meter
$$
s=
$$
$\qquad$
d. 92.76 cubic millimeters
$$
s=
$$
$\qquad$
e. 0.026 cubic foot
$$
s=
$$
$\qquad$

Erika Bustos

Numerade Educator

00:39

Problem 65

Solve each of the following equations using the power principle of equality. Check all answers. Round the answers to 3 decimal places where necessary.
$\sqrt{C}=6$

Ernest Castorena

Numerade Educator

00:56

Problem 66

Solve each of the following equations using the power principle of equality. Check all answers. Round the answers to 3 decimal places where necessary.
$\sqrt{T}=12$

Linh Vu

Numerade Educator

00:30

Problem 67

Solve each of the following equations using the power principle of equality. Check all answers. Round the answers to 3 decimal places where necessary.
$\sqrt{P}=1.2$

Victor Salazar

Numerade Educator

00:56

Problem 68

Solve each of the following equations using the power principle of equality. Check all answers. Round the answers to 3 decimal places where necessary.
$0.8=\sqrt{M}$

Grace Muhihu

Numerade Educator

01:15

Problem 69

Solve each of the following equations using the power principle of equality. Check all answers. Round the answers to 3 decimal places where necessary.
$0.82=\sqrt{F}$

Amy Jiang

Numerade Educator

01:37

Problem 70

Solve each of the following equations using the power principle of equality. Check all answers. Round the answers to 3 decimal places where necessary.
$\sqrt[3]{V}=3$

Luke P

Numerade Educator

01:06

Problem 71

Solve each of the following equations using the power principle of equality. Check all answers. Round the answers to 3 decimal places where necessary.
$\sqrt[3]{H}=1.7$

Brandon Fox

Numerade Educator

00:29

Problem 72

Solve each of the following equations using the power principle of equality. Check all answers. Round the answers to 3 decimal places where necessary.
$\sqrt[3]{x}=-4$

Victor Salazar

Numerade Educator

01:04

Problem 73

Solve each of the following equations using the power principle of equality. Check all answers. Round the answers to 3 decimal places where necessary.
$\sqrt{A}=0$

Breanna Ollech

Numerade Educator