Clear answer | Algebra homework help

part1

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1. Find the vertex of the parabola f(x) = x2 – 16x + 63.
2. Find the x- and y-intercepts of the cubic function f(x) = (x+4)(2x-1)(x-1).
3. If f(x) = x2-2x-24 and g(x) = x2-x-30, find (f-g)(x).
4. If f(x) = x+4 and g(x) = 2×2-x-1, evaluate the composition (g o f)(2).
5. If f(x) = x+4 and g(x) = 2×2-x-1, find the composition (f o g)(x).
6. Write the following sentence as an equation: y varies directly as x.
7. Write the following sentence as an equation: x is directly proportional to y and is inversely proportional to the cube of z.
8. 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)?
9. What is the vertical asymptote of the rational function f(x) = 3x / (2x – 1)?
10. What is the horizontal asymptote of the rational function f(x) = 3x / (2x – 1)?

PART2:

1. If f(x) = 8x + 16, then find f -1(x).
2. Determine if the following functions are inverses of each other:
   f(x) = 7x + 14
   g(x) = (1/7)x – 2
3. Write the exponential equation y = 5x in logarithmic form.
4. Write the logarithmic equation log7x = y in exponential form.
5. 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.
6. 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.
7. 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.
8. Solve the following exponential equation:
   5x = 2
   Round your solution to the nearest hundredth.
9. Solve the following exponential equation:
   ex = 10
   Round your solution to the nearest hundredth.
10. Solve the following logarithmic equation:
    log7x + log7(3x-2) = 0
    Be sure to check all of your solutions in the original equation.

part3:

1. Solve the following equation for n:
   n/4 – 5/6 = 5/12
2. Solve the following equation for x:
   2x/3 – 4x/5 = 1/15
3. Solve the following equation for x:
   9/(4x) + 1/3 = 5/(2x)
4. Solve the following equation for x:
   |5x-7| = 14
   Hint: This absolute value equation will turn into 2 linear equations, so there will be two solutions!
5. 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)