Algebra

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Chapter 1 Equations and Inequalities - all with Video Answers

Educators

Section 1

Expressions and Formulas

00:38

Problem 1

Evaluate each expression if $x=4, y=-2,$ and $z=3.5$
$z-x+y$

Zach S.

Numerade Educator

00:58

Problem 2

Evaluate each expression if $x=4, y=-2,$ and $z=3.5$
$x+(y-1)^{3}$

Zach S.

Numerade Educator

01:25

Problem 3

Evaluate each expression if $x=4, y=-2,$ and $z=3.5$
$x+[3(y+z)-y]$

Zach S.

Numerade Educator

00:50

Problem 4

Evaluate each expression if $x=4, y=-2,$ and $z=3.5$
$\frac{x^{2}-y}{z+2.5}$

Zach S.

Numerade Educator

01:16

Problem 5

Evaluate each expression if $x=4, y=-2,$ and $z=3.5$
$\frac{x+2 y^{2}}{x-z}$

Zach S.

Numerade Educator

02:12

Problem 6

Evaluate each expression if $x=4, y=-2,$ and $z=3.5$
$\frac{y^{3}+2 x z}{x^{2}-z}$

Zach S.

Numerade Educator

00:39

Use the following information.
Simple interest is calculated using the formula $I=p r t,$ where $p$ represents the principal in dollars, $r$ represents the annual interest rate, and $t$ represents the time in years. Find the simple interest I given each set of values.
$p=\$ 1800, r=6 \%, t=4$ years

Zach S.

Numerade Educator

01:24

Problem 8

Zach S.

Numerade Educator

00:29

Problem 9

Evaluate each expression if $w=6, x=0.4, y=\frac{1}{2},$ and $z=-3$.
$w+x+z$

Zach S.

Numerade Educator

00:35

Problem 10

Evaluate each expression if $w=6, x=0.4, y=\frac{1}{2},$ and $z=-3$.
$v+12 \div z$

Zach S.

Numerade Educator

00:34

Problem 11

Evaluate each expression if $w=6, x=0.4, y=\frac{1}{2},$ and $z=-3$.
$w(8-y)$

Zach S.

Numerade Educator

00:31

Problem 12

Evaluate each expression if $w=6, x=0.4, y=\frac{1}{2},$ and $z=-3$.
$z(x+1)$

Zach S.

Numerade Educator

00:50

Problem 13

Evaluate each expression if $w=6, x=0.4, y=\frac{1}{2},$ and $z=-3$.
$w-3 x+y$

Zach S.

Numerade Educator

00:25

Problem 14

Evaluate each expression if $w=6, x=0.4, y=\frac{1}{2},$ and $z=-3$.
$5 x+2 z$

Zach S.

Numerade Educator

00:45

Problem 15

Evaluate each expression if $a=3, b=0.3, c=\frac{1}{3},$ and $d=-1$.
$\frac{a-d}{b c}$

Zach S.

Numerade Educator

00:44

Problem 16

Evaluate each expression if $a=3, b=0.3, c=\frac{1}{3},$ and $d=-1$.
$\frac{a+d}{c}$

Zach S.

Numerade Educator

00:43

Problem 17

Evaluate each expression if $a=3, b=0.3, c=\frac{1}{3},$ and $d=-1$.
$\frac{a^{2} c^{2}}{d}$

Zach S.

Numerade Educator

01:00

Problem 18

Evaluate each expression if $a=3, b=0.3, c=\frac{1}{3},$ and $d=-1$.
$\frac{a-10 b}{c^{2} d^{2}}$

Zach S.

Numerade Educator

00:43

Problem 19

Evaluate each expression if $a=3, b=0.3, c=\frac{1}{3},$ and $d=-1$.
$\frac{d+4}{a^{2}+3}$

Zach S.

Numerade Educator

01:13

Problem 20

Evaluate each expression if $a=3, b=0.3, c=\frac{1}{3},$ and $d=-1$.
$\frac{1-b}{3 c-3 b}$

Zach S.

Numerade Educator

00:48

Problem 21

Determine the IV flow rate for the patient described at the beginning of the lesson by finding the value of $\frac{1500 \times 15}{12 \times 60}$.

Zach S.

Numerade Educator

01:25

Problem 22

Air pollution can be reduced by riding a bicycle rather than driving a car. To find the number of pounds of pollutants created by starting a typical car 10 times and driving it for 50 miles, find the value of the expression $\frac{(52.84 \times 10)+(5.955 \times 50)}{454}$.

Zach S.

Numerade Educator

01:17

Problem 23

The formula for the area $A$ of a circle with diameter $d$ is $A=\pi\left(\frac{d}{2}\right)^{2} .$ Write an expression to represent the area of the circle.

Zach S.

Numerade Educator

01:38

Problem 24

The formula for the volume $V$ of a right circular cone with radius $r$ and height $h$ is $V=\frac{1}{3} \pi r^{2} h .$ Write an expression for the volume of a cone with $r=3 x$ and $h=2 x$.

Zach S.

Numerade Educator

00:45

Problem 25

Evaluate each expression if $a=\frac{2}{5}, b=-3, c=0.5,$ and $d=6$.
$b^{4}-d$

Zach S.

Numerade Educator

00:54

Problem 26

Evaluate each expression if $a=\frac{2}{5}, b=-3, c=0.5,$ and $d=6$.
$(5-d)^{2}+a$

Zach S.

Numerade Educator

01:03

Problem 27

Evaluate each expression if $a=\frac{2}{5}, b=-3, c=0.5,$ and $d=6$.
$\frac{5 a d}{b}$

Zach S.

Numerade Educator

01:24

Problem 28

Evaluate each expression if $a=\frac{2}{5}, b=-3, c=0.5,$ and $d=6$.
$\frac{2 b-15 a}{3 c}$

Zach S.

Numerade Educator

01:34

Problem 29

Evaluate each expression if $a=\frac{2}{5}, b=-3, c=0.5,$ and $d=6$.
$(a-c)^{2}-2 b d$

Zach S.

Numerade Educator

00:41

Problem 30

Evaluate each expression if $a=\frac{2}{5}, b=-3, c=0.5,$ and $d=6$.
$\frac{1}{c}+\frac{1}{d}$

Zach S.

Numerade Educator

01:12

Problem 31

Find the value of $a b^{n}$ if $n=3, a=2000,$ and $b=-\frac{1}{5}$

Zach S.

Numerade Educator

00:43

Problem 32

Suppose you are about a mile from a fireworks display. You count 5 seconds between seeing the light and hearing the sound of the fireworks display. You estimate the viewing angle is about $4^{\circ} .$ Using the information at the left, estimate the width of the firework display.

Zach S.

Numerade Educator

01:31

Problem 33

In $1960,$ the average price of a car was about $\$ 2500 .$ This may sound inexpensive, but the average income in 1960 was much less than it is now. To compare dollar amounts over time, use the formula $V=\frac{A}{S} C$, where $A$ is the old dollar amount, $S$ is the starting year's Consumer Price Index (CPI), $C$ is the converting year's CPI, and $V$ is the current value of the old dollar amount. Buying a car for $\$ 2500$ in 1960 was like buying a car for how much money in 2004$?$

Zach S.

Numerade Educator

02:20

Problem 34

A patient must take blood pressure medication that is dispensed in 125-milligram tablets. The dosage is 15 milligrams per kilogram of body weight and is given every 8 hours. If the patient weighs 25 kilograms, how many tablets would be needed for a 30-day supply? Use the formula $n=[15 b \div(125 \times 8)] \times 24 d,$ where $n$ is the number of tablets, $d$ is the number of days the supply should last, and $b$ is body weight in kilograms.

Zach S.

Numerade Educator

03:06

Problem 35

The formula for quarterback efficiency rating in the National Football League is $\left(\frac{\frac{C}{A}-0.3}{0.2}+\frac{\frac{Y}{A}-3}{4}+\frac{\frac{T}{A}}{0.05}+\frac{0.095-\frac{I}{A}}{0.04}\right) \times \frac{100}{6},$ where $C$ is the number of passes completed, A is the number of passes attempted, Y is passing yardage, T is the number of touchdown passes, and I is the number of interceptions. In 2005, Ben Roethlisberger of the Pittsburgh Steelers completed 168 of the 268 passes he attempted for 2385 yards. He threw 17 touchdowns and 9 interceptions. Find his efficiency rating for 2005.

Dharmendra J.

Numerade Educator

00:32

Problem 36

Write an algebraic expression in which subtraction is performed before division, and the symbols ( ), [ ], or { } are not used.

Zach S.

Numerade Educator

03:56

Problem 37

Write expressions having values from one to ten using exactly four 4 $\mathrm{s}$ . You may use any combination of the operation symbols $+,-, \mathrm{x}, \div,$ and / or grouping symbols, but no other digits are allowed. An example of such an expression with a value of zero is $(4+4)-(4+4) .$

Dharmendra J.

Numerade Educator

00:43

Problem 38

How to evaluate $a+b[(c+d) \div e],$ if you were given the values for $a, b, c, d,$ and $e .$

Zach S.

Numerade Educator

00:49

Problem 39

Use the information about IV flow rates on page 6 to explain how formulas are used by nurses. Explain why a formula for the flow rate of an IV is more useful than a table of specific IV flow rates and describe the impact of using a formula, such as the one for IV flow rate, incorrectly.

Zach S.

Numerade Educator

01:20

Problem 40

The following are the dimensions of four rectangles. Which rectangle has the same area as the triangle at the right?
A. 1.6 $\mathrm{ft}$ by 25 $\mathrm{ft}$
B. 5 $\mathrm{ft}$ by 16 $\mathrm{ft}$
C. 3.5 $\mathrm{ft}$ by 4 $\mathrm{ft}$
D. 0.4 $\mathrm{ft}$ by 50 $\mathrm{ft}$

Zach S.

Numerade Educator

01:07

Problem 41

How many cubes that are 3 inches on each edge can be placed completely inside a box that is 9 inches long, 6 inches wide, and 27 inches tall?
F. 12
G. 54
H. 36
J. 72

Zach S.

Numerade Educator

00:20