In a triangle, the measure of the first angle is three times the measure of the second

According to the U.S. Office of Management and Budget, the 2011 budget for defense exceeded the budget for education by $658.6 billion. If x represents the budget for education, in billions of dollars, the budget for defense can be represented by ______________.

In 2000, 31% of U.S. adults viewed a college education as essential for success. For the period from 2000 through 2010, this percentage increased by approximately 2.4 each year. The percentage of U.S. adults who viewed a college education as essential for success x years after 2000 can be represented by ______________.

A text message plan costs $4 per month plus $0.15 per text. The monthly cost for x text messages can be represented by ______________.

I purchased a computer after a 15% price reduction. If x represents the computers original price, the reduced price can be represented by ______________.

Solving a formula for a variable means rewriting the formula so that the variable is ______________.

The first step in solving IR + Ir = E for I is to obtain a single occurrence of I using the ___________________ property.

70% of what number is 224?

70% of what number is 252?

One number exceeds another by 26. The sum of the numbers is 64. What are the numbers?

One number exceeds another by 24. The sum of the numbers is 58. What are the numbers?

y1 = 13x - 4, y2 = 5x + 10, and y1 exceeds y2 by 2.

y1 = 10x + 6, y2 = 12x - 7, and y1 exceeds y2 by 3.

y1 = 10(2x - 1), y2 = 2x + 1, and y1 is 14 more than 8 times y2 .

y1 = 9(3x - 5), y2 = 3x - 1, and y1 is 51 less than 12 times y2 .

y1 = 2x + 6, y2 = x + 8, y3 = x, and the difference between 3 times y1 and 5 times y2 is 22 less than y3 .

y1 = 2.5, y2 = 2x + 1, y3 = x, and the difference between 2 times y1 and 3 times y2 is 8 less than 4 times y3 .

Whats the last word in capital punishment? An analysis of the final statements of all men and women Texas has executed since the Supreme Court reinstated the death penalty in 1976 revealed that love is by far the most frequently uttered word. The bar graph shows the number of times various words were used in final statements by Texas death-row inmates. 700 500 600 400 300 200 Number of Times Used Frequently Uttered Words in Final Statements of Death-Row Inmates Frequently Uttered Word Love Thanks Sorry Peace Guilty 100 95 7 Source: Texas Department of Criminal Justice The number of times love was used exceeded the number of times sorry was used by 419. The number of utterances of thanks exceeded the number of utterances of sorry by 32. Combined, these three words were used 1084 times. Determine the number of times each of these words was used in final statements by Texas inmates.

How many words are there? The bar graph shows the number of words in English, in thousands, compared with four other languages. 1050 750 900 600 450 300 Number of Words (thousands) Number of Words in English and Other Major Languages Language English Chinese Japanese Spanish Russian 150 225 195 Source: Global Language Monitor The number of words in English exceeds the number of words in Japanese by 767 thousand. The number of words in Chinese (various dialects) exceeds the number of words in Japanese by 268 thousand. Combined, these three languages contain 1731 thousand words. Determine the number of words, in thousands, for each of these three languages.

In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 8 less than the measure of the second angle. What is the measure of each angle?

In a triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 35 less than the measure of the second angle. What is the measure of each angle?

In a triangle, the measures of the three angles are consecutive integers. What is the measure of each angle?

In a triangle, the measures of the three angles are consecutive even integers. What is the measure of each angle?

In 2000, 31% of U.S. adults viewed a college education as essential for success. For the period 2000 through 2010, the percentage viewing a college education as essential for success increased on average by approximately 2.4 each year. If this trend continues, by which year will 67% of all American adults view a college education as essential for success?

In 2000, 45% of U.S. adults believed that most qualified students get to attend college. For the period from 2000 through 2010, the percentage who believed that a college education is available to most qualified students decreased by approximately 1.7 each year. If this trend continues, by which year will only 11% of all American adults believe that most qualified students get to attend college?

If this trend continues, by which year will corporations pay zero taxes? Round to the nearest year.

If this trend continues, by which year will the percentage of federal tax receipts coming from the corporate income tax drop to 5%? Round to the nearest year.

Each day, the number of births in the world is 92 thousand less than three times the number of deaths. a. If the population increase in a single day is 214 thousand, determine the number of births and deaths per day. b. If the population increase in a single day is 214 thousand, by how many millions of people does the worldwide population increase each year? Round to the nearest million. c. Based on your answer to part (b), approximately how many years does it take for the population of the world to increase by an amount greater than the entire U.S. population (308 million)?

Each day, the number of births in the world exceeds twice the number of deaths by 61 thousand. a. If the population increase in a single day is 214 thousand, determine the number of births and deaths per day. b. If the population increase in a single day is 214 thousand, by how many millions of people does the worldwide population increase each year? Round to the nearest million. c. Based on your answer to part (b), approximately how many years does it take for the population of the world to increase by an amount greater than the entire U.S. population (308 million)?

You are choosing between two health clubs. Club A offers membership for a fee of $40 plus a monthly fee of $25. Club B offers membership for a fee of $15 plus a monthly fee of $30. After how many months will the total cost at each health club be the same? What will be the total cost for each club?

Video Store A charges $9 to rent a video game for one week. Althoughonly members canrentfrom the store, membership is free. Video Store B charges only $4 to rent a video game for one week. Only members can rent from the store and membership is $50 per year. After how many video-game rentals will the total amount spent at each store be the same? What will be the total amount spent at each store?

The bus fare in a city is $1.25. People who use the bus have the option of purchasing a monthly discount pass for $15.00. With the discount pass, the fare is reduced to $0.75. Determine the number of times in a month the bus must be used so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass.

A discount pass for a bridge costs $30 per month. The toll for the bridge is normally $5.00, but it is reduced to $3.50 for people who have purchased the discount pass. Determine the number of times in a month the bridge must be crossed so that the total monthly cost without the discount pass is the same as the total monthly cost with the discount pass.

In 2008, there were 13,300 students at college A, with a projected enrollment increase of 1000 students per year. In the same year, there were 26,800 students at college B, with a projected enrollment decline of 500 students per year. a. According to these projections, when will the colleges have the same enrollment? What will be the enrollment in each college at that time? b. Use the following table to numerically check your work in part (a). What equations were entered for y1 and y2 to obtain this table?

In 2000, the population of Greece was 10,600,000, with projections of a population decrease of 28,000 people per year. In the same year, the population of Belgium was 10,200,000, with projections of a population decrease of 12,000 people per year. (Source: United Nations) According to these projections, when will the two countries have the same population? What will be the population at that time?

After a 20% reduction, you purchase a television for $336. What was the televisions price before the reduction?

After a 30% reduction, you purchase a dictionary for $30.80. What was the dictionarys price before the reduction?

Including 8% sales tax, an inn charges $162 per night. Find the inns nightly cost before the tax is added.

Including 5% sales tax, an inn charges $252 per night. Find the inns nightly cost before the tax is added.

The selling price of a refrigerator is $584. If the markup is 25% of the dealers cost, what is the dealers cost of the refrigerator?

The selling price of a scientific calculator is $15. If the markup is 25% of the dealers cost, what is the dealers cost of the calculator?

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the courts perimeter is 228 feet, what are the courts dimensions?

The length of a rectangular pool is 6 meters less than twice the width. If the pools perimeter is 126 meters, what are its dimensions?

The rectangular painting in the figure shown measures 12 inches by 16 inches and contains a frame of uniform width around the four edges. The perimeter of the rectangle formed by the painting and its frame is 72 inches. Determine the width of the frame.

The rectangular swimming pool in the figure shown measures 40 feet by 60 feet and contains a path of uniform width around the four edges. The perimeter of the rectangle formed by the pool and the surrounding path is 248 feet Determine the width of the path.

For an international telephone call, a telephone company charges $0.43 for the first minute, $0.32 for each additional minute, and a $2.10 service charge. If the cost of a call is $5.73, how long did the person talk?

A job pays an annual salary of $33,150, which includes a holiday bonus of $750. If paychecks are issued twice a month, what is the gross amount for each paycheck?

A = lw for l (geometry)

A = lw for w (geometry)

A = 1 2 bh for b (geometry)

A = 1 2 bh for h (geometry)

I = Prt for P (finance)

I = Prt for t (finance)

T = D + pm for p (finance)

P = C + MC for M (finance)

A = 1 2 h(a + b) for a (geometry)

A = 1 2 h(a + b) for b (geometry)

V = 1 3 pr2 h for h (geometry)

V = 1 3 pr2 h for r 2 (geometry)

y - y1 = m(x - x1) for m (algebra)

y2 - y1 = m(x2 - x1) for m (algebra)

V = d1 - d2 t for d1 (physics)

z = x - u s for x (statistics)

Ax + By = C for x (algebra)

Ax + By = C for y (algebra)

s = 1 2 at 2 + vt for v (physics)

s = 1 2 at 2 + vt for a (physics)

L = a + (n - 1)d for n (algebra)

L = a + (n - 1)d for d (algebra)

A = 2lw + 2lh + 2wh for l (geometry)

A = 2lw + 2lh + 2wh for h (geometry)

IR + Ir = E for I (physics)

A = x1 + x2 + x3 n for n (statistics)

In your own words, describe a step-by-step approach for solving algebraic word problems.

Write an original word problem that can be solved using a linear equation. Then solve the problem.

Explain what it means to solve a formula for a variable.

Did you have difficulties solving some of the problems that were assigned in this Exercise Set? Discuss what you did if this happened to you. Did your course of action enhance your ability to solve algebraic word problems?

The bar graph in Figure 1.23 on page 55 indicates a gender gap in pay at all levels of education. What explanations can you offer for this phenomenon?

Use a graphing utility to numerically or graphically verify your work in any one exercise from Exercises 2932. For assistance on how to do this, refer to the Using Technology box on page 59.

The formula y = 31 + 2.4x models the percentage of U.S. adults, y, viewing a college education as essential for success x years after 2000. Graph the formula in a [0, 20, 1] by [0, 100, 10] viewing rectangle. Then use the TRACE or ZOOM feature to verify your answer in Exercise 23.

In Exercises 2526, we saw that in 1960, 23% of U.S. taxes came from corporate income tax, decreasing by approximately 0.28% per year. a. Write a formula that models the percentage of U.S. taxes from corporations, y, x years after 1960. b. Enter the formula from part (a) as y1 in your graphing utility. Then use either a table for y1 or a graph of y1 to numerically or graphically verify your answer to Exercise 25 or Exercise 26.

I solved the formula for one of its variables, so now I have a numerical value for that variable.

Reasoning through a word problem often increases problem-solving skills in general.

The hardest part in solving a word problem is writing the equation that models the verbal conditions.

When traveling in Europe, the most useful form of the two Celsius-Fahrenheit conversion formulas is the formula used to convert from Fahrenheit to Celsius.

If I = prt, then t = I - pr

If y = kx z , then z = kx y .

It is not necessary to use the distributive property to solve P = C + MC for C.

An items price, x, reduced by 1 3 is modeled by x - 1 3 .

The price of a dress is reduced by 40%. When the dress still does not sell, it is reduced by 40% of the reduced price. If the price of the dress after both reductions is $72, what was the original price?

Suppose that we agree to pay you 8 for every problem in this chapter that you solve correctly and fine you 5 for every problem done incorrectly. If at the end of 26 problems we do not owe each other any money, how many problems did you solve correctly?

It was wartime when the Ricardos found out Mrs. Ricardo was pregnant. Ricky Ricardo was drafted and made out a will, deciding that $14,000 in a savings account was to be divided between his wife and his child-to-be. Rather strangely, and certainly with gender bias, Ricky stipulated that if the child were a boy, he would get twice the amount of the mothers portion. If it were a girl, the mother would get twice the amount the girl was to receive. Well never know what Ricky was thinking, for (as fate would have it) he did not return from war. Mrs. Ricardo gave birth to twinsa boy and a girl. How was the money divided?

A thief steals a number of rare plants from a nursery. On the way out, the thief meets three security guards, one after another. To each security guard, the thief is forced to give one-half the plants that he still has, plus 2 more. Finally, the thief leaves the nursery with 1 lone palm. How many plants were originally stolen?

Solve for C: V = C - C - S L N.

Express in set-builder notation and graph: (-4, 0]. (Section 1.1, Example 7)

Simplify: (2 + 4) 2 + (-1) 5 12 , 2 # 3 - 3 . (Section 1.2, Example 8)

Solve: 2x 3 - 8 3 = x. (Section 1.4, Example 4)

In parts (a) and (b), complete each statement. a. b4 # b3 = (b # b # b # b)(b # b # b) = b? b. b5 # b5 = (b # b # b # b # b)(b # b # b # b # b) = b? c. Generalizing from parts (a) and (b), what should be done with the exponents when multiplying exponential expressions with the same base?

In parts (a) and (b), complete each statement. a. b7 b3 = b # b # b # b # b # b # b b # b # b = b? b. b8 b2 = b # b # b # b # b # b # b # b b # b = b? c. Generalizing from parts (a) and (b), what should be done with the exponents when dividing exponential expressions with the same base?

Simplify: 1 a- 1 2 b 3 .