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The weekly summary answers and explanations will be posted in the Announcement section by Friday of each week. Please try to work each problem without pasting and copying or you will defeat your purpose of learning. Credit will only be given for “original” work. Please feel free to study the explanations, learn the problem, and create your own step-by-step explanation for bonus points. You may post your explanations throughout the term (please remind your instructor in the General Questions thread to grade your problems if you have posted after Sunday).
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Find the vertex of the parabola f(x) = x2 – 16x 63.
Find the x- and y-intercepts of the cubic function f(x) = (x 4)(2x-1)(x-1).
If f(x) = x2-2x-24 and g(x) = x2-x-30, find (f-g)(x).
If f(x) = x 4 and g(x) = 2×2-x-1, evaluate the composition (g o f)(2).
If f(x) = x 4 and g(x) = 2×2-x-1, find the composition (f o g)(x).
Write the following sentence as an equation: y varies directly as x.
Write the following sentence as an equation: x is directly proportional to y and is inversely proportional to the cube of z.
What are the zeros of the parabola: f(x) = x2 – 7x 10 (that is, what are the x-intercepts or the points where the graph crosses the x-axis)?
What is the vertical asymptote of the rational function f(x) = 3x / (2x – 1)?
What is the horizontal asymptote of the rational function f(x) = 3x / (2x – 1)?
If f(x) = 8x 16, then find f -1(x).
Determine if the following functions are inverses of each other:f(x) = 7x 14g(x) = (1/7)x – 2
Write the exponential equation y = 5x in logarithmic form.
Write the logarithmic equation log7x = y in exponential form.
Use the change-of-base formula to convert x=log390 to common logarithms. Then use a calculator to round the value of x to the nearest thousandth.
Find the amount of money accumulated if you invest $10,000 at 3% interest compounded quarterly for 2 years. Round your answer to the nearest cent.
Find the amount of money accumulated if you invest $10,000 at 3% interest compounded continuously for 2 years. Round your answer to the nearest cent.
Solve the following exponential equation:5x = 2Round your solution to the nearest hundredth.
Solve the following exponential equation:ex = 10Round your solution to the nearest hundredth.
Solve the following logarithmic equation:log7x log7(3x-2) = 0Be sure to check all of your solutions in the original equation.
Solve the following equation for n:n/4 – 5/6 = 5/12
Solve the following equation for x:2x/3 – 4x/5 = 1/15
Solve the following equation for x:9/(4x) 1/3 = 5/(2x)
Solve the following equation for x:|5x-7| = 14Hint: This absolute value equation will turn into 2 linear equations, so there will be two solutions!
Solve the following system of linear equations: 2x 3y = -5
-2x y = 9
6. Solve for (x, y, z), if there is a solution to the given system of linear equations:
– x 2y 3z = 0
3x – 2y – 2z = 5
4x y – 3z = -9
7. Solve: x2 – 4x 5 = 0.
8, Add the complex numbers: (5 – 2i) (1 6i)
9. Subtract the complex numbers: (4 3i) – (6 i).
10. Multiply the complex numbers (4 3i) (6 i)
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