Deck 1: Equations and Inequalities

Question 1

Solve the rational equation.

Answer 1

D

Question 2

A equation is an equation in which each term contains a rational expression.

Answer 2

rational

Question 3

Determine whether the equation is a conditional equation, an identity, or a contradiction.

A) Conditional
B) Identity
C) Contradiction

Answer 3

A

Question 4

The solution to an equation is the set of all solutions to the equation.

Question 5

A is an equation that is false for all values of the variable.

Question 6

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.

Question 7

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
In the mid-nineteenth century, explorers used the boiling point of water to estimate altitude. The boiling temperature of water T (in °F) can be approximated by the model T = -1.83a + 212, where a
Is the altitude in thousands of feet. Two campers hiking in Colorado boil water for tea. If the water
Boils at 196°F, approximate the altitude of the campers. Give the result to the nearest hundred feet.

A) 8,900 ft
B) 8,700 ft
C) 1,600 ft
D) 2,900 ft

Question 8

The property of equality indicates that if provided tha

Question 9

An is an equation that is true for all values of the variable for which the expressions in
the equation are defined.

Question 10

A linear equation is also called a -degree equation because the degree of the variable is 1.

Question 11

A to an equation is the value of the variable that makes the equation a true statement.

Question 12

A equation is one that is true for some values of the variable and false for others.

Question 13

The property of equality indicates that adding the same real number to both sides of an
equation results in an equivalent equation.

Question 14

Determine whether the equation is a conditional equation, an identity, or a contradiction.

A) Conditional
B) Identity
C) Contradiction

Question 15

Two equations are equations if they have the same solution set.

Question 16

Determine whether the equation is a conditional equation, an identity, or a contradiction.

Question 17

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
In the mid-nineteenth century, explorers used the boiling point of water to estimate altitude. The boiling temperature of water be approximated by the model T = -1.83a + 212, where a
Is the altitude in thousands of feet. Determine the temperature at which water boils at an altitude of
9,000 ft. Round to the nearest degree.

A) 214 °F
B) 228 °F
C) 196 °F
D) 210 °F

Question 18

If an equation has no solution, then the solution set is the set and is denoted by
.

Question 19

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
A train ride is $2.85 per ride. A commuter can purchase an unlimited-ride card for $45 per month. How many rides are required for a commuter to save money by buying the card?

A) 16 rides
B) 22 rides
C) 20 rides
D) 18 rides

Question 20

An equation that can be written in the form where a and b are real numbers and is
called a equation in one variable.

Question 21

Determine the restrictions on x.

Question 22

Solve for the indicated variable.

Question 23

Solve the rational equation.

Question 24

Solve the rational equation.

Question 25

Solve for the indicated variable.

Question 26

Solve for the indicated variable.

Question 27

Solve for the indicated variable.

Question 28

Solve for the indicated variable.

Question 29

Solve the equation.

Question 30

Solve for the indicated variable.

Question 31

Solve the rational equation.

Question 32

Solve for the indicated variable.

Question 33

Solve for the indicated variable.

Question 34

Solve the rational equation.

Question 35

Solve the equation.

Question 36

Solve for the indicated variable.

Question 37

Solve the rational equation.

Question 38

Solve the problem.
Dema's truck gets 32 mpg on the highway and 18 mpg in the city. The amount of gas he uses A (in gal) is given by , where c is the number of city miles driven and h is the number of
Highway miles driven. If Dema drove 45 mi in the city and used 8 gal of gas, how many highway
Miles did he drive?

A) 176 miles
B) 192 miles
C) 200 miles
D) 160 miles

Question 39

Solve for the indicated variable.

Question 40

Solve the rational equation.

Question 41

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The sum of the measures of the angles inscribed inside a triangle is .

Question 42

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
If $13,000 is borrowed at 5.8% simple interest for 10 years, how much interest will be paid for the loan?

A) $9,845.47
B) $20,540.00
C) $7,540.00
D) $22,845.47

Question 43

Write the word or phrase that best completes each statement or answers the question.
A boat can travel 42 miles upstream against the current in the same amount of time it can travel 63
miles downstream with the current. If the boat's average speed in still water is 20 miles per hour,
find the speed of the current.

Question 44

Find the value of a so that the equation has the given solution set.

Question 45

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Suppose that 8% of a solution is fertilizer by volume and the remaining 92% is water. How much
fertilizer is there in a 2 L bucket of solution?

Question 46

Choose the one alternative that best completes the statement or answers the question.
The perimeter of a rectangular lot of land is 436 ft. This includes an easement of x feet of uniform width inside the lot on which no building can be done. If the buildable area is 122 ft by 60 ft,
Determine the width of the easement.

A) 4.5 feet
B) 18 feet
C) 7 feet
D) 9 feet

Question 47

Choose the one alternative that best completes the statement or answers the question.
The property tax on a $160,000.00 house is $2,400.00. At this rate, what is the property tax on a house that is $280,000.00?

A) $4,620.00
B) $5,040.00
C) $3,780.00
D) $4,200.00

Question 48

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
Two cars are 261 miles apart and travel toward each other on the same road. They meet in 3 hours. One car travels 3 mph faster than the other. What is the average speed of each car?

A) 40 mph; 43 mph
B) 41 mph; 44 mph
C) 39 mph; 42 mph
D) 42 mph; 45 mph

Question 49

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.

Question 50

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The formula for the perimeter P of a rectangle with length l and width w is given by .

Question 51

Choose the one alternative that best completes the statement or answers the question.
A consultant traveled 255 miles to attend a meeting, traveling 45 mph hours for the first part of the trip, then increasing to a speed of 60 mph for the second part. If the entire trip took 5 hours, how far
Did the consultant travel at the faster speed?

A) 127.5 mi
B) 120 mi
C) 135 mi
D) 180 mi

Question 52

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
A nurse mixes 90 cc of a 45% saline solution with a 10% saline solution to produce a 20% saline solution. How much of the 10% solution should he use?

A) 18 cc
B) 180 cc
C) 225 cc
D) 202.5 cc

Question 53

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
If $6000 is borrowed at 7.5% simple interest for 2 yr, then the amount of interest is .

Question 54

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
How many gallons of gasoline that is 5% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 3% ethanol?

A) 4,115
B) 6,000
C) 3,000
D) 1,800

Question 55

Choose the one alternative that best completes the statement or answers the question.
It takes Terrell 69 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 49 minutes. How long would it take them working together? Round to the nearest tenth of
A minute.

A) 28.7 minutes
B) 24.5 minutes
C) 34.5 minutes
D) 29.5 minutes

Question 56

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
If

Question 57

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
Aaron invested a total of $4,100, some in an account earning 8% simple interest, and the rest in an account earning 5% simple interest. How much did he invest in each account if after one year he
Earned $211 in interest?

A) $3,200 at 8%, $900 at 5%
B) $3,900 at 8%, $200 at 5%
C) $900 at 8%, $3,200 at 5%
D) $200 at 8%, $3,900 at 5%

Question 58

Choose the one alternative that best completes the statement or answers the question.
The JUST-SAY-MOW lawn mowing company consists of two people: Marsha and Bob. If Marsha cuts the lawn by herself, she can do it in 3 hours. If Bob cuts the same lawn himself, it takes him an
Hour longer than Marsha. How long would it take them if they worked together? Round to the
Nearest hundredth of an hour.

A) 4.00 hours
B) 1.71 hours
C) 3.50 hours
D) 1.00 hour

Question 59

Choose the one alternative that best completes the statement or answers the question.
To estimate the number of bass in a lake, a biologist catches and tags 32 bass. Several weeks later, the biologist catches a new sample of 55 bass and finds that 5 are tagged. How many bass are in the
Lake?

A) 275 bass
B) 1,760 bass
C) 160 bass
D) 352 bass

Question 60

Choose the one alternative that best completes the statement or answers the question.
The plans for a rectangular deck call for the width to be 4 feet less than the length. Sam wants the deck to have an overall perimeter of 52 feet. What should the length of the deck be?

A) 4 feet
B) 28 feet
C) 19 feet
D) 15 feet

Question 61

Choose the one alternative that best completes the statement or answers the question.
Simplify the expression in terms of i:

Question 62

Choose the one alternative that best completes the statement or answers the question.
Aliyah earned an $6,000 bonus from her sales job for exceeding her sales goals. After paying taxes at a 30% rate, she invested the remaining money in two stocks. One stock returned the equivalent of
10% simple interest after 1 yr, and the other returned 4% at the end of 1 yr. If her investments
Returned $240.00 (excluding commissions) how much did she invest in each stock

A) $2,750 at 4% and $1,450 at 10%
B) $3,000 at 4% and $1,200 at 10%
C) $1,200 at 4% and $3,000 at 10%
D) $1,450 at 4% and $2,750 at 10%

Question 63

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Given a complex number a + bi, the expression a - bi is called the complex .

Question 64

Choose the one alternative that best completes the statement or answers the question.
Suppose that a merchant buys a patio set from the wholesaler for $260. At what price should the merchant mark the patio set so that it may be offered at a discount of 25% but still give the merchant
A 20% profit on his $260 investment?

A) $325
B) $416
C) $377
D) $312

Question 65

Simplify the expression.

Question 66

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The imaginary number i is defined so that .

Question 67

Simplify and write the result in standard form, a + bi.

Question 68

Choose the one alternative that best completes the statement or answers the question.
One number is 33 more than another number. The quotient of the larger number and smaller number is 5 and the remainder is 1. Find the numbers.

A) 10 and 43
B) 8 and 41
C) 5 and 38
D) 11 and 44

Question 69

Simplify the expression.

Question 70

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
Given a complex number a + bi, the value of a is called the part and the value of b is
called the part.

Question 71

Simplify and write the result in standard form, a + bi.

Question 72

Identify the real and imaginary parts of the complex number.

Question 73

Simplify the expression.

Question 74

Simplify and write the result in standard form, a + bi.

Question 75

Simplify.

Question 76

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
For a positive real number, b, the value .

Question 77

Simplify and write the result in standard form, a + bi.

Question 78

Simplify.

Question 79

Identify the real and imaginary parts of the complex number.

Question 80

Choose the one alternative that best completes the statement or answers the question.
Simplify the expression in terms of i: