Question 1

Logarithms are sometimes needed to solve linear equations.

Accepted Answer

Logarithms are used to solve exponential equations, not linear equations. Linear equations involve variables raised to the first power and do not require logarithms for their solutions.

Question 2

One rental company charges $58.32 in fees for a television plus $23.76 per week.A second rental company charges $39.14 in fees plus $26.49 per week.How many weeks would make the total cost of renting a television the same for both companies? You can be charged for part of a week, so you should report your answer correct to two decimal places. ​
A) 7.03 weeks
B) 58.32 weeks
C) 9.03 weeks
D) It never happens

Accepted Answer

The total cost of renting a television from the first company is $58.32 + $23.76 per week. The total cost of renting a television from the second company is $39.14 + $26.49 per week. The total cost of renting a television from both companies will be the same when $58.32 + $23.76 per week = $39.14 + $26.49 per week. Solving for the number of weeks, we get $23.76 per week - $26.49 per week = $39.14 - $58.32, which simplifies to -$2.73 per week = -$19.18. Dividing both sides by -$2.73, we get 7.03 weeks.

Question 3

A rental car charges $55.09 for insurance and other fees plus a flat rate of $26.97 per day.Write a formula that gives the cost C, in dollars, of renting a car for t days. ​
A) 
B) ​ 
C) ​ 
D) ​

Accepted Answer

A

Question 4

Techniques for solving linear equations can sometimes be used to reverse the roles of variables in equations.

Accepted Answer

Techniques such as substitution and elimination can be used to manipulate linear equations, allowing for the roles of variables to be reversed or redefined in terms of each other. This is often done to solve for one variable in terms of another.

Question 5

Solve the equation  . ​
A) There is no solution.
B) 
C) 
D)

Accepted Answer

The answer of Solve the equation  . ​
A) There...

Question 6

As you drive up a hill, your elevation E, in feet, increases with each mile m that you drive.The relationship is  . Express the miles you drive as a function of elevation.
​
A) 
B) ​ 
C) ​ 
D) ​

Accepted Answer

The answer of As you drive up a hill, your...

Question 7

The amount M, in billions of dollars, collected by the Internal Revenue Service t years after 2003 is given by  . ​
According to this model, in what year would IRS collections reach 3,554 billion dollars?
A) 2014
B) 2012
C) 2010
D) It never happens

Accepted Answer

The answer of The amount M, in billions of dollars,...

Question 8

If you wish to have an item you ordered delivered quickly, you must pay extra for shipping, and the amount you pay depends on the weight w, in pounds, of the item.The shipping cost S, in dollars, is given by  . You have $32.39 to spend on shipping costs.How large an item can you have shipped?
A) 12.42 pounds
B) 21.41 pounds
C) 11.98 pounds
D) 11.31 pounds

Accepted Answer

The answer of If you wish to have an item...

Question 9

The speed S, in meters per second, of sound in the ocean depends on the depth D, in kilometers.(It depends on other quantities as well, but those will be ignored for this problem.) The relationship is  . At what depth is the speed of sound 1,604.04 meters per second?
​
A) 4.18 kilometers
B) 5.24 kilometers
C) 28,802.68 kilometers
D) 4.12 kilometers

Accepted Answer

The answer of The speed S, in meters per second,...

Question 10

To say that an equation is linear means that it is a straight line.

Accepted Answer

The answer of To say that an equation is linear...

Question 11

An iPad costs $498 at your local computer store.The cable company charges $22 per month for a DSL Internet connection.Write a formula that gives the cost C, in dollars, of buying an iPad and paying for t months of Internet service. ​
A) 
B) ​ 
C) ​ 
D) ​

Accepted Answer

The answer of An iPad costs $498 at your local...

Question 12

You start making regular deposits to your piggy bank.The amount P, in dollars, in your piggy bank after t weeks is given by ​  .
The price of the computer you want to buy is decreasing.The price C, in dollars, t weeks after you started saving money is given by  .
​
When will there be enough money in your piggy bank to buy the computer? Report your answer as a whole number.
​
A) After 8 weeks
B) After 7 weeks
C) After 10 weeks
D) There will never be enough.

Accepted Answer

The answer of You start making regular deposits to your...

Question 13

The length L, in feet, of a baby blue whale depends on its age T, in months.The relationship is  . How old is a baby wale that is 47 feet long?
​
A) 5.43 months
B) 17.78 months
C) 6.83 months
D) A baby whale is never that long.

Accepted Answer

The answer of The length L, in feet, of a...

Question 14

Solve the equation  .Round your answer to two decimal places. ​
A) There is no solution.
B) 
C) ​ 
D) ​

Accepted Answer

The answer of Solve the equation  .Round your answer...

Question 15

Linear equations are always difficult to solve.

Accepted Answer

Linear equations are often straightforward to solve, especially when they involve only one variable, as they can typically be solved by simple algebraic manipulations.

Question 16

For connection to the system and water usage w, in hundreds of gallons, a water company charges  dollars. ​
Solve this equation for w to express water consumption as a function of the charges.
​
A) There is no solution.
B) 
C) 
D)

Accepted Answer

The answer of For connection to the system and water...

Question 17

You got a birthday gift of $34.94, which you choose to spend on music.You pay $12.50 for an iPad app that lets you download songs for $1.02 each.How many songs can you download before your birthday money is used up? ​
A) 29 songs
B) 19 songs
C) 22 songs
D) 24 songs

Accepted Answer

The answer of You got a birthday gift of $34.94,...

Question 18

The life expectancy E, in years, for a child born t years after 2000 is given by  . In what birth year would a child have a life expectancy of 78.06 years?
​
A) 2010
B) 2008
C) 2006
D) That life expectancy never occurs.

Accepted Answer

The answer of The life expectancy E, in years, for...

Question 19

For connection to the system and water usage w, in hundreds of gallons, water company A charges  . ​
For connection to the system and water usage w, in hundreds of gallons, water company B charges  .
Both A and B are in dollars.How many hundreds of gallons of water will result in the same charge from water company A and water company B? Round your answer to two decimal places.
​
A) The charge will never be the same.
B) 424.00 hundred gallons
C) 191.15 hundred gallons
D) 423.53 hundred gallons

Accepted Answer

The answer of For connection to the system and water...

Question 20

The long jump record L, in meters, for the nth Olympics after 1900 is given approximately by the formula  . When did the long jump record reach 8.60 meters?
​
A) In the 10th Olympics after 1900
B) In the 7th Olympics after 1900
C) In the 12th Olympics after 1900
D) The record never reached 8.60 meters.

Accepted Answer

The answer of The long jump record L, in meters,...

Quiz 7: Solving Linear Equations

Logarithms are sometimes needed to solve linear equations.

A rental car charges $55.09 for insurance and other fees plus a flat rate of $26.97 per day.Write a formula that gives the cost C, in dollars, of renting a car for t days.

Techniques for solving linear equations can sometimes be used to reverse the roles of variables in equations.

Solve the equation .

As you drive up a hill, your elevation E, in feet, increases with each mile m that you drive.The relationship is . Express the miles you drive as a function of elevation.

The amount M, in billions of dollars, collected by the Internal Revenue Service t years after 2003 is given by . According to this model, in what year would IRS collections reach 3,554 billion dollars?

If you wish to have an item you ordered delivered quickly, you must pay extra for shipping, and the amount you pay depends on the weight w, in pounds, of the item.The shipping cost S, in dollars, is given by . You have $32.39 to spend on shipping costs.How large an item can you have shipped?

The speed S, in meters per second, of sound in the ocean depends on the depth D, in kilometers.(It depends on other quantities as well, but those will be ignored for this problem.) The relationship is . At what depth is the speed of sound 1,604.04 meters per second?

To say that an equation is linear means that it is a straight line.

An iPad costs $498 at your local computer store.The cable company charges $22 per month for a DSL Internet connection.Write a formula that gives the cost C, in dollars, of buying an iPad and paying for t months of Internet service.

The length L, in feet, of a baby blue whale depends on its age T, in months.The relationship is . How old is a baby wale that is 47 feet long?

Solve the equation .Round your answer to two decimal places.

Linear equations are always difficult to solve.

For connection to the system and water usage w, in hundreds of gallons, a water company charges dollars. Solve this equation for w to express water consumption as a function of the charges.

You got a birthday gift of $34.94, which you choose to spend on music.You pay $12.50 for an iPad app that lets you download songs for $1.02 each.How many songs can you download before your birthday money is used up?

The life expectancy E, in years, for a child born t years after 2000 is given by . In what birth year would a child have a life expectancy of 78.06 years?

The long jump record L, in meters, for the nth Olympics after 1900 is given approximately by the formula . When did the long jump record reach 8.60 meters?

Quiz 7: Solving Linear Equations

Logarithms are sometimes needed to solve linear equations.

A rental car charges $55.09 for insurance and other fees plus a flat rate of $26.97 per day.Write a formula that gives the cost C, in dollars, of renting a car for t days. ​

Techniques for solving linear equations can sometimes be used to reverse the roles of variables in equations.

Solve the equation . ​

As you drive up a hill, your elevation E, in feet, increases with each mile m that you drive.The relationship is . Express the miles you drive as a function of elevation. ​

The amount M, in billions of dollars, collected by the Internal Revenue Service t years after 2003 is given by . ​ According to this model, in what year would IRS collections reach 3,554 billion dollars?

If you wish to have an item you ordered delivered quickly, you must pay extra for shipping, and the amount you pay depends on the weight w, in pounds, of the item.The shipping cost S, in dollars, is given by . You have $32.39 to spend on shipping costs.How large an item can you have shipped?

The speed S, in meters per second, of sound in the ocean depends on the depth D, in kilometers.(It depends on other quantities as well, but those will be ignored for this problem.) The relationship is . At what depth is the speed of sound 1,604.04 meters per second? ​

To say that an equation is linear means that it is a straight line.

An iPad costs $498 at your local computer store.The cable company charges $22 per month for a DSL Internet connection.Write a formula that gives the cost C, in dollars, of buying an iPad and paying for t months of Internet service. ​

The length L, in feet, of a baby blue whale depends on its age T, in months.The relationship is . How old is a baby wale that is 47 feet long? ​

Solve the equation .Round your answer to two decimal places. ​

Linear equations are always difficult to solve.

For connection to the system and water usage w, in hundreds of gallons, a water company charges dollars. ​ Solve this equation for w to express water consumption as a function of the charges. ​

You got a birthday gift of $34.94, which you choose to spend on music.You pay $12.50 for an iPad app that lets you download songs for $1.02 each.How many songs can you download before your birthday money is used up? ​

The life expectancy E, in years, for a child born t years after 2000 is given by . In what birth year would a child have a life expectancy of 78.06 years? ​

The long jump record L, in meters, for the nth Olympics after 1900 is given approximately by the formula . When did the long jump record reach 8.60 meters? ​

A rental car charges $55.09 for insurance and other fees plus a flat rate of $26.97 per day.Write a formula that gives the cost C, in dollars, of renting a car for t days.

Solve the equation .

As you drive up a hill, your elevation E, in feet, increases with each mile m that you drive.The relationship is . Express the miles you drive as a function of elevation.

The amount M, in billions of dollars, collected by the Internal Revenue Service t years after 2003 is given by . According to this model, in what year would IRS collections reach 3,554 billion dollars?

The speed S, in meters per second, of sound in the ocean depends on the depth D, in kilometers.(It depends on other quantities as well, but those will be ignored for this problem.) The relationship is . At what depth is the speed of sound 1,604.04 meters per second?

An iPad costs $498 at your local computer store.The cable company charges $22 per month for a DSL Internet connection.Write a formula that gives the cost C, in dollars, of buying an iPad and paying for t months of Internet service.

The length L, in feet, of a baby blue whale depends on its age T, in months.The relationship is . How old is a baby wale that is 47 feet long?

Solve the equation .Round your answer to two decimal places.

For connection to the system and water usage w, in hundreds of gallons, a water company charges dollars. Solve this equation for w to express water consumption as a function of the charges.

You got a birthday gift of $34.94, which you choose to spend on music.You pay $12.50 for an iPad app that lets you download songs for $1.02 each.How many songs can you download before your birthday money is used up?

The life expectancy E, in years, for a child born t years after 2000 is given by . In what birth year would a child have a life expectancy of 78.06 years?

The long jump record L, in meters, for the nth Olympics after 1900 is given approximately by the formula . When did the long jump record reach 8.60 meters?