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# Algebra

### Algebra: inverse of a function

Consider the following function f: R --> R defined by f(x) = x3 - 5 . (a) Use the contrapositive to explain (no proof necessary) that f is a one-to-one function. (b) Find f -1. (c) Compute f o f.

### Calculate remaining minutes on phone card.

1. The credit remaining on a phone card(in dollars)is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of -0.15. There is 29.35 in credit remaining on the card after 29 minutes of calls. How much credit will there be after 41 minutes of calls? 2.

### Calculate greatest number of strawberry-banana shakes possible

Please show all steps and computation. This morning, Mr. Singh will make strawberry-banana shakes using 300 strawberries and 60 bananas. Mr. Singh knows that he will use more strawberries than bananas in each shake , and he does not want to have any leftovers fruit. He wants all of the shakes to have equalnumbers of whole b

### Various Equations

See the attached file. Solve each system by the substitution method: 1. x = 9 - 2y x + 2y = 13 2. 6x + 2y = 7 y = 2 - 3x 3. y = 3x -5 21x - 35 = 7y 4. 9x - 3y = 12 y = 3x - 4 5. 3x - 2y = -5 4x + y = 8 6. 2x + 5y = -4 3x - y = 11.

### Solve by Substitution Method

Solve each system by the substitution method only. Show step-by-step solutions. 1) 4x + 3y = 15 2x - 5y = 1 2) 3x - 7y = 13 6x + 5y =7 3) 3x - 4y = 11 2x + 3y = -4 4) 2x + 3y = -16 5x - 10y = 30 5) 3x = 4y + 1 3y = 1 - 4x 6) 5x = 6y + 40 2y = 8 - 3x.

### Commuting students word problem

Commuting students. At a well-known university, 1/4 of the undergraduate students commute, and 1/3 of the graduate students commute. One-tenth of the undergraduate students drive more than 40 miles daily, and 1/6 of the graduate students drive more than 40 miles daily. If there are twice as many undergraduate students as there a

### Filling a tank word problem

Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?

### Upstream, downstream. word problem

Upstream, downstream. Junior's boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current?

### Algebra study guide

Week 3 Study guide Which numbers cannot be used in place of the variable in each rational expression? 44. Section 6.2 Perform the indicated operation. 70. Section 6.4 Addition and Subtraction of Rational Expressions 28. Perform the indicated operation. Reduce each answer to lowest terms. 40. 5

### Divergent Sequence

(x_n tends to plus infinity if and only if for each M belonging to real numbers there exists an N belonging to natural numbers such that: n>=N implies x_>M. x_n is said diverge yo minus infinity if and only if for each M belonging to natural numbers such that: n>=N implies x_n <M.) Prove by above definition that each of

### Rewriting a Formula and Finding N: Example Problem

In a study of workers at Wong laboratories, it was found that the number of components assembled per hour by the average worker t hours. After starting work could be modeled by the formula: N(t) = -3t^3+23t^2+8t a) Re-write the formula by factoring the right-hand side completely b) Use the factor

### Amount of an investment of P dollars for t years at simple interest rate r is given by A = P+Prt. a) Re-write this formula by factoring out the greatest common factor on the right hand side b) Find A if \$ 8300 is invested for 3 years at a simple interest rate of 15%

Amount of an investment of P dollars for t years at simple interest rate r is given by A = P+Prt. a) Re-write this formula by factoring out the greatest common factor on the right hand side b) Find A if \$ 8300 is invested for 3 years at a simple interest rate of 15%

### Solve by Factorization & Square Root Property

See the attached file. Show your work step by step. Solve each equation by factoring. 1. x^2 = -11x - 10 2. 4x^2 - 13x = -3 3. 16x(x-2) = 8x - 25 Show your work. Solve each equation by the square root property 4. 5x^2=45 5. 2x^2 - 7 = -15 6. 3(x+4)^2 = 21 7. (x+2)^2 = -7 8. (8x-3)^

### Equations using the substitution method

Show work. Solve using the substitution method 1. 5x + 12y + z = 10 2x + 5y + 2z = -1 x + 2y - 3z = 5 2. 2x - 4y + z =3 X - 3y + z= 5 3x-7y+2z=12 3. 5x + 8y - 6z=14 3x+ 4y -2z=8 x+2y-2z=3 4. 5x-11y+6z=12 -x+3y-2z=-4 3x-5y+2z=4 5. 3x+4y+2z=3 4x-2y-8z=-4 x+y-z=3 6. 2x-y-z=0 x+2y+z=3 3x+4y+2

### Pick a country of your choice that is experiencing population growth. Using the Library, web resources, and/or other materials to find the most recent population count of the country you have chosen and the population growth rate of that country.

Pick a country of your choice that is experiencing population growth. Using the Library, web resources, and/or other materials to find the most recent population count of the country you have chosen and the population growth rate of that country. Use that growth rate to approximate the population in the year 2012. Solve the prob

### Swimming space: The length of a rectangular swimming pool is 2x-1 meters

Swimming space: The length of a rectangular swimming pool is 2x-1 meters , and the width is x+2 meters. Write a polynomial A(x) that represents the area. Find A(5)

### equations with variables in denominators

#28 contain linear equations with constants in denominators. Solve the equation. #50 Contain rational equations with variables in denominators. Write the value or values of the variable tht make a denominator zero. These are the restrictions on the variable. Keeping the restrictions in mind, solve the equation.

### Word Problem

#1) Ziggys Famous Yogurt blends regular yogurt that is 3% fat with its no-fat yogurt to obtain low-fat yogurt that is 1% fat. How many pounds of regular yogurt and how many pounds of no-fat should be mixed to obtain 60 pounds of low fat yogurt.

### Word Prob-Other

#1 Find slope given the following points: (2,5) and (2,1) #2. Find slope given the following points: (-3,-1) and (-2,4) #3. Write the point-slope form of the line using the requirements below, then use the point slope form of the equation to write the slope intercept form. Slope = 6 passing through (-4,7) #4)

### Supply and Demand Curves Explanation

The equations S=5000 + 200x and D=9500-100x express the supply S and the demand D respectively, for the popular compact disc brand in terms of its price x (in dollars). a) Graph the equation on the same coordinate system. b) What happens to the supply as the price increases? c) What happens to the demand as the price i

### system as independent, inconsistent, or dependent

Solve by graphing, indicate whether each system is independent, inconsistent, or dependent. 1. x + y = 5 x - y = -1 2. y = -x y = -x + 3 Solve by substitution, indicate whether each system is independent, inconsistent, or dependent. 3. x - y = 3 3x - 2y = 3 4. 2x - y = 3 6x - 9 = 3y Solve by the addition metho

### A small publishing company is planning to publish a new book.

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will amount to \$37,146 . The variable costs will be \$8.50 per book. The publisher will sell the finished product to bookstores at a

### Direct and Inverse Proportional Relationship among Variables

1. Write formula that expresses relationship described by each statement. Use k for the constant in each case. a) m varies directly as p. b) u varies inversely as n. 2. Find variation constant and write a formula that expresses the indicated variation for: c varies inversely as d, and c=5 when d=2. 3. Solve vari

To earn an A- in a course, you must have a final average of at least 90%. On the first four exams, you have the grades of 86%, 88%, 92%, and 84%. If the final exam counts for two grades, what must you get on the final in order to get an A- in the course?

### A Word Problem: Determining Net Worth

Melanies' house is worth \$125,000, but she still owes \$78,422 on her mortgage. She has \$21,236 in a savings account and has \$9477 in credit card debt. She owes \$6131 to the credit union and figures that her cars and other household items are worth a total of \$15,000. What is Melanies' net worth.

### Divide and Simplify Functions

Please see attached for full details of the problem. #1 Multiply. (3y - 7) A. B. C. D. #2 Divide and simplify. A. 3u/v B. 3v/u C. -3v/u D. #3 Simplify. A. B. C. D. #4 Factor completely. A. (h - 9s)(h - s) B. (h

### Tournament Expenses and Teams

The star youth soccer club helps to support its 20 boys and girls teams financially, primarily through the payment of coaches. The club puts on a tournament each fall to help pay its expenses. The cost of putting on the tournament is \$8,000 mainly for development, printing and mailing the tournament brochures. The tournament ent

### Problem Solving Using Polya's 4 step model

This is the Problem: Public relations. Memorial Hospital is planning an advertising campaign. It costs the hospital \$3000 each time a television ad is aired and \$2000 each time a radio ad is aired. The administrator wants to air 60 more television ads than radio ads. If the total cost of airing the ads is \$580,000, the

### Substitution and value of the variables

Please show work. 8. Solve by substitution. 52. Unknown numbers. Find two numbers whose ratio is 4 to 3 and are such that the sum of their square is 100. 4. Find the value of each determinant. 2. Find the values of the variables for which each statement is true. =

### parabola open upward or downward

Solve the 2 problems. Show your work. 1. y = x ^2 - 4x -12 a) What is the vertex? b) What are the intercepts? c) Does the parabola open upward or downward? 2. y = -x^2 + 2x +3 a) What is the vertex? b) What are the intercepts? c) Does the parabola open upward or downward?