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# Basic Algebra

### Equations

The problems below follow closely the examples shown in the background materials. Complete these problems showing your work and turn them in by the end of the Module. 1. Convert the following equations into logarithmic form: a. 2 = 6x b. 7 = 6y c. 9 = 3y d. X = 8y 2. Convert the followi

### Algebra: Scientific Notation

Question: Find an example from daily life that represents an extremely large or small number. An example of a very large number is 1 light year = 9.4605284 x 1012 kilometers or 9460528400000 kilometers. Write it in scientific notation format as well as regular format. In addition, explain any other advantages of using scientific

### Algebra: Quadratic Equations and Word Problems

Apply the quadratic formula to find the roots of the given function, and then graph the function. 1. f(x) = x^2 - 4 2. g(x) = x^2 - x - 12 Factor the quadratic expression completely, and find the roots of the expression. 3. 20x^2 + 13x + 2 4. 49x^2 - 14x - 3 Complete the square, and find the

### Algebra: Addition, Subtraction, Multiplication & Division

1. Find all the numbers for which the rational expression is undefined. 7/v-3= 2. Solve s/10 - 10/s =0 The solutions are______ 3. Y^2 - 49 y - 7 ------------ divide sign ------ = _______ 64y + 448 56 4. 5/x-9 divide sign 16/(x-9)^2 = _____ 5. Add 7/v+1 + 7/5v =____

### Assistance with an Exponential Equation

Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph. Show your wok and state if the equation of the line is asymptotic to the graph (if any). y = 3-x Evaluate the exponential equation for three positive v

### exponential growth function types

Solve the problem. Randy invested his inheritance in an account that paid 6.1% interest, compounded continuously. After 5 years, he found that he now had \$51,426.94. What was the original amount of his inheritance? Solve the problem. In 1998, the population of a given country was 37 million, and the exponential growth r

### Exponential and Logaithmic Equations

1. Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph. State the equation of the line asymptotic to the graph (if any). y = 3x - 4 2. Evaluate the logarithmic equation for three values of x that

### Basic Algebra Example Problems

1. Simplify the following algebraic expressions: 2. Perform the indicated operations (Multiply/Divide) on the given algebraic expressions: 3. Factor the algebraic expressions completely: 4. Simplify the rational expressions: 5. Classify the given numbers as real and rational, real and irrational, or complex: [

### Measuring Liquid in Cups, Tablespoon & Teaspoon

1. Recipe calls for 800 mL of sour cream a. How many cups is that? b. How many teaspoons is that? c. How many tablespoons is that? 2. Cleaning solution is made by mixing 1/3 teaspoon baking soda, 2 tablespoon of dishwashing liquid and 2 cups lukewarm water. a. How many mL of dishwashing liquid is that? b. How many

### Manipulating an expression and solving an equation

How does solving an equation differ from manipulating an expression? How are they alike? Very few situations in the real world fit a linear pattern or even a non-linear pattern perfectly. How can we tell if the algebraic model we are using fits the situation "good enough?"

### Please provide the cost in millions of dollars

I am having trouble completing a math problem I will list one example. Please explain step by step on how to complete this problem. Thanks in advance. The cost, in millions of dollars, to remove x% of pollution in a lake modeled by C= 6,000 200-2x (the problem is suppose to read 6,000

### Equilibrium Expressions

What are the equilibrium expressions for: [Co(H2O)₆]²⁺(aq)+4Cl⁻(aq) <--> [CoCl4]2⁻(aq)+6H2O(l) 10. 2Ag⁺(aq)+CO3²⁻(aq) <--> Ag2CO3(s) 11. CO3²⁻(aq)+2H⁺(aq) <--> H2O(l)+CO2(g) 12. 2Ag⁺(aq)+Cl⁻(aq) <--> AgCl(s) Ag+(aq)+2NH3(aq) <--> [Ag(NH3)2⁺(aq) NH3(aq)+ H⁺(aq) <--> NH4⁺(aq)

### Quadratic perimeter and rectangular equations

1. Solve and show your work The perimeter of a rectangular building is 234 feet. The width is 25 feet shorter than the length. What are the dimensions? (Let W represent the width and L represent the length.) 2. Solve and show your work (x+7)^2=20

### Quadratic and Trinomial Squares Factored

1. Complete the square. Then write the trinomial square in factored form x^2+2/3 x 2. Solve M 1/2 +6=5m1/4 The answers to this equation is given as 16, 81. Can you explain how they were obtained? 3. For this quadratic function (a) find the vertex and the axis of symmetry (b) graph the function F(x) = -3x^2+6x+2

### Algebra: Solve, Simplify & Factorize

1. If an expression has two terms, check to see whether the problem type is the -------- of two squares, the sum of two ------ , or the ----------- of two cubes. 2. If an expression has four or more terms, try factoring it by--------------. 3. Factor the polynomial. bc + b + cd + d 4. Factor the polynomial. 64x9 -

1.Bill can row 3 mph in still water. It takes him 3 hours 36 minutes to go 3 miles upstream and return. Find the speed of the current. Show your work. 2.Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one r

1. Use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to graph the function. Show your work. F(x) = 7x^2 - 28x + 28 2. Use the discriminate to determine whether the following equations have solutions t

### Cost per ounce

Find the cost per ounce of each of the following sets of products, and tell which one is the better buy for each pair. You must show your work for both parts. a. 6 ounce tube of toothpaste for \$2.30 or a 12 ounce tube of toothpaste for \$4.10. b. 4 ounce can of spray for \$2.99 or a 6 ounce can of spray for \$4.99. c.

### Distance and measurements still have me stumped

1.Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable and please show your work. A plane flies 400 miles with the wind and 300 miles against the wind in the same length of time. If the speed of the wi

### MTH - 209, 21 questions !!! Algebra Questions 1. Using the x, y graph plot the point 2. Give an ordered pair of numbers that satisfy the following equation: 3. For each point in the table below, decide whether it is on Line 1, Line 2, both, or neither. Line 1: Line 2: (x, y) Line 1 Line 2 Both Lines Neither Line (-6, 7) (-2, 4) (0, -4) 4. Graph the line whose y-intercept is 3 and whose x-intercept is 2. 5. Graph the line. 6. Graph the line. 7. Graph the line with slope passing through the point . 8. Find the slope of the line graphed below (-3, 7) and (2, -6) 9. Graph the line 10. Graph the inequality below on the number line. 11. Find the y -intercept of the line whose equation is 12. Find the x-intercept and y-intercept of the line given by the equation 13. Find the slope of the line 14. A line passes through the point and has a slope of 3 Write an equation for this line. 15. Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 35 liters per minute. There are 700 liters in the pond to start. Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes that water has been added. Write an equation relating W to T, and then graph your equation using the axes below. 16. Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, HCF). When graphed, the function gives a line with a slope of 1.75. If the monthly bill for 15 HCF is \$24.01, what is the monthly bill for 11 HCF? 17. The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes), as shown in the figure below. The monthly cost for 47 minutes of calls is \$14.97 and the monthly cost for 100 minutes is \$21.86. What is the monthly cost for 57 minutes of calls? 18. Find an equation of the line that is parallel to the line and that passes through the point . 19. The sum of two numbers is 63. The larger number is 5 more than the smaller number. What are the large number and the small number? 20. In a family there are two cars. The sum of the average miles per gallon obtained by the two cars in a particular week is 65. The first car has consumed 56 gallons during that week, and the second has consumed 25 gallons, for a total of 1325 miles driven by the two cars combined. What was the average gas mileage obtained by each of the two cars in that week? 21. A motorboat travels 595 mi in 7 hours going upstream and 484 mi in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Algebra Questions 1. Using the x, y graph plot the point 2. Give an ordered pair of numbers that satisfy the following equation: 3. For each point in the table below, decide whether it is on Line 1, Line 2, both, or neither. Line 1: Line 2: (x, y) Line 1 Line 2 Both Lines Neither Line (-6, 7) (-2,

### Exponential and Logarithmic Functions

Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in months, is graphed on a rectangular coordinate system where time is on the horizontal axis. Further suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C= p * a t (C=p*a^t) where p is the number of

### Algebra

1. Multiply (2-5x&#8311;)² =_____ 2. The base of a triangle is 4 cm greater than the height. The area is 30 cm². Find the height and length of the base. Height is ________cm Base is _________cm 3. (y²-7) (6y²-3y+5) =_______ 4. Find the greatest common factor (GCF) of 12x and 14x³ The GCF is_____________

### Evaluating Expressions: Example Problems

Evaluate the expressions when x=3 and y=8 we must show all. Three answers were given directly without any extra steps or explanation, essay. a. x + 2y b. -4(y - x) c. x - y d. 2x + 3y e. y - 2(x+y)

### Algebra: Solving Equations

1. Solve this equation The polynomial 0.041h - 0.018A - 2.69 can be used to estimate the lung capacity, in liters, of a female with height h cm and age A years. Find the lung capacity of a 30-year-old woman who is 180 cm tall. Round to the nearest liter. Show your solving steps in the answer. 2. Solve this equation A l

### Receivables Turnover Firms

The company with sales of\$1,034,550 has recievables of \$267700 and the industry's average collection period of 65 days. Calculate the firms average collection period, and compare it to the industry average. If the firms receivables turned over as fast as the industry average, how much would the company's receivable be reduced, a

### Maximum Pulse Rate

If A is your age, the maximum pulse rate you should maintain during aerobic activities is 0.88(220-A). What is the maximum pulse rate you should maintain if you are 15 years old? 35 years old? 40 years old

### Fibonacci sequence: Example problem

Using Fn+3 = Fn+2 + Fn+1 show that Fn+3 + Fn = 2Fn + 2 and Fn + 3 - Fn = 2Fn + 1 It seems intuitive at first but would appreciate a detailed explanation - how does one identify the terms to be used? Thank you

### Problem Solving

Guess how much money is in the sugar bowl. There are 7 nickels, but that's not all. There is less than a dollar. I can separate it into 6 piles with the same amount in each pile. I cannot make 7 piles with the same amount in each pile. I could trade my money for dimes and have nothing left over. If I had one more dime, I

### MCQ on Loan Amortization: Example Problem

Loan amortization, which refers to determining equal annual loan payments, can be implemented by which of the following? a. Adding the loan amount by the interest factor for the present value of an annuity for the appropriate discount rate and number of years. b. Subtracting the loan amount by the interest factor for the

### Compounded Annuity Solving for Rate using Logarithms

If it takes 9 years for a one-time deposit in a savings account that receives interest compounded quarterly to triple, then what is the interest rate to the nearest tenth of a percent? To answer this question, you will need to utilize the following relationship: If ln(x) = N, where N is some number, then x = eN (if