12 algebra questions need full explainations

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Week Number____1______ Problem Number ____2_________ 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 a membership fee of $15 plus a monthly fee of $30. a. Using variables of your choice, set-up an equation for each club’s membership cost. Make sure your variables are defined clearly. b. After how many months will the total cost at each health club be the same? c. What will be the total cost for each club from part (b)? Calculations 1 2 3 4 5 Explanations of Calculations A) B) 5th month C)165.00 Week Number____1______ Problem Number ____4_________ Solve the quadratic equation using factoring: Calculations 1 2 3 4 14x2+3x-2=0 5 7x(2x+1)-2(2x+1)=0 6 7 (2x+1)(7x-2)=0 14x2+7x-4x-2=0 2x+1=0 -1 -1 2x=-1 /2 /2 X=1/2 7x-2=0 +2 +2 7x=2 /7 /7 X=2/7 14x2 + 3x = 2 Explanations of Calculations Move all terms to one side Factor the equation Multiply 14 by -2, which is -28 Find which two numbers add up to 3 and multiply to 28, which is 7 and -4 Factor out common terms in the first two terms, then in the last two terms Factor common term 2x+1 Solve for x in each equation Final Answer x= 1/2; 2/7 Week Number_____2_____ Problem Number ______3_______ Use the graph of f to the right to determine each of the following. Where applicable, use interval notation. (Assume that at each end, there is an arrowhead) a. intervals on which f is increasing b. intervals on which f is decreasing c. any relative maxima or minima and the numbers at which they occur The graph may not be exact. Calculations 1 Explanations of Calculations Copy the problem or write out important information. 2 3 4 5 6 7 8 9 10 (Add or delete rows as needed). Week Number____2______ Problem Number _____5________ I’m thinking of a linear equation with slope equal to Determine the following: 3 7 that goes through the point (-2,5). a. Equation for the line in slope-intercept form b. What is the slope of the linear equation? Determine the y-intercept for this linear equation Calculations 1 2 3 Explanations of Calculations Copy the problem or write out important information. 4 5 6 7 8 9 10 (Add or delete rows as needed). Week Number____3______ Problem Number ______1_______ In the following functions, a basic common function, f(x), has undergone a transformation into another function. For each of the following graphs, determine the equation for g(x). a. g(x) = 𝑓(𝑥) = 𝑥 2 b. g(x) = c. g(x) = Calculations 1 Explanations of Calculations Copy the problem or write out important information. 2 3 4 5 6 7 8 9 10 (Add or delete rows as needed). Week Number____3______ Problem Number ______3_______ Given f a. b. c. (x) = – 4x + 2 and g(x) = x2 + 3x – 10, find the following: f +g f −g f •g f , find the domain g Calculations 1 2 3 4 5 6 7 8 9 10 (Add or delete rows as needed). Explanations of Calculations Copy the problem or write out important information. Week Number_____4_____ Problem Number ______1_______ Consider the parabola to the right to determine each of the following: a. Explain whether the function has a maximum value or minimum value. b. Determine the minimum or maximum value. Where does it occur? c. Identify the vertex. d. Identify the axis of symmetry. The graph may not be exact. Calculations 1 2 3 4 5 6 7 8 9 10 (Add or delete rows as needed). Explanations of Calculations Copy the problem or write out important information. Week Number____4______ Problem Number ______2_______ Considering the graph to the right, complete the following: a. Find the zeros. b. State the multiplicity of each zero. c. Write an equation, expressed as the product of factors, of a polynomial function for the graph. Use a leading coefficient of 1 or -1 and make the degree of f as small as possible. Calculations 1 2 3 4 5 6 7 8 9 10 (Add or delete rows as needed). Explanations of Calculations Copy the problem or write out important information. Week Number_____5_____ Problem Number _______1______ Suppose that you have $10,000 to invest over a 3 year period. There are two accounts to choose from: 4% compounded monthly or 3.5% compounded continuously. a. Write the formula for the first account’s compound interest for n compoundings per year. b. Write the formula for the account with continuously compounded interest. c. Use the formulas and information above to solve for the balance of each investment after 3 years. d. Which investment account offers a better return on your money? Calculations 1 Explanations of Calculations Copy the problem or write out important information. 2 3 4 5 6 7 8 9 10 (Add or delete rows as needed). Week Number_____5_____ Problem Number ______4_______ Mario decided to invest his $620 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded quarterly. Answer the following questions, assuming that Mario deposits his entire refund and does not deposit or withdraw any other amounts. a. Write an equation that models the growth of the investment. b. How many years will it take for the initial investment to double? Calculations 1 2 3 4 5 6 7 8 9 10 Explanations of Calculations Copy the problem or write out important information. Week Number____6______ Problem Number _____1_______ Solve each system of equations or indicate that it has no solution. You may use either the substitution method or the addition method. Be sure to discuss the reasoning behind your choice of method(s). 16𝑥 − 10𝑦 = 10 a. { −8𝑥 − 6𝑦 = 6 𝑦 − 4𝑥 = −19 b. { 𝑦 = −3𝑥 + 30 Calculations 1 Explanations of Calculations Copy the problem or write out important information. 2 3 4 5 6 7 8 9 10 (Add or delete rows as needed). Week Number___6_______ Problem Number ______4_______ At an auction, a lucky wealthy collector paid $7,000,000 for three paintings: a Monet, a Picasso, and a van Gogh. The Monet cost $800,000 more than the Picasso. The price of the van Gogh was $200,000 more than twice the price of the Monet. What was the price of each painting? Calculations 1 2 3 4 5 6 7 8 9 10 (Add or delete rows as needed). Explanations of Calculations Copy the problem or write out important information.
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