POST ASSESSMENT FOR COLLEGE ALGEBRA

The price of a home theater system has been discounted 18%. The sale price is $289. Find the original price of the system.

$352.44

An investment is expected to pay 11% per year compounded continuously. If you want the value of the investment to be $900,000 after 25 years, how much should you invest initially? Round to the nearest dollar. Select one:

$57,535

Find g ∘ f. f(x) = x - 7 g(x) = x2

(g ∘ f)(x) = x2 -14x + 49

Decide whether the function is even, odd, or neither. g(x) = x3 - 5x

Odd

Consider the graph of f(x) = x3. Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of f is shifted three units to the left.

y = (x + 3)3

The population y (in millions of people) of North America from 1980 to 2050 can be modeled by y = 5.3x + 483, -40 ≤≤ x ≤≤ 30 where x represents the year, with x = 30 corresponding to 2050. Find the y-intercept of the graph of the model. What does it represent in the given situation?

(0, 483); It represents the population (in millions of people in North America in 2020.

Solve the absolute value equation for m. |4m+20|=32

-13, 3

Simplify and write the following complex number in standard form. (-3 - 10i) + (4 - 5i) Select one:

1 - 15i

Evaluate (f + g)(-9) where f(x) = x2 + x -20 and g(x) = 4x + 2.

18

Given p(x) = 5x2 - 1, find p(-2).

19

The height, in feet, of a projectile with an initial velocity of 96 feet per second and an initial height of 75 feet is a function of time t, in seconds, given by h(t) = -16t2 + 96t + 75 Find the maximum height of the projectile. Select one:

219 ft

The sum of two consecutive numbers is 245. Write an equation to model this situation.

2n + 1 = 245

The height, h, in feet, of a baseball above the ground t seconds after it is hit is given by h = -16t2 + 48t + 4.5. Use this equation to determine the number of seconds, to the nearest tenth of a second, from the time the ball is hit until the ball hits the ground.

3.1s

Evaluate the logarithm using the change of base formula. Round to 3 decimal places. log6345

3.261

The demand equation for a product is p = 30 - 0.005x, where p is the price per unit and x is the number of units sold. The total revenue R for selling x units is given by R = xp = x(30 - 0.005x) How many units must be sold to produce a revenue of $45,000?

3000 units

Use synthetic division to divide. (4x3 - 11x2 - 43x - 10) ÷ (x - 5)

4x2 + 9x + 2

Approximately the solution to ln 4x = 3.2. Round to 3 decimal places.

6.133

Use the graph of ƒ to determine whether the function has an inverse function. y=f(x)

Yes, ƒ has an inverse function.

The distance between two points is

d=√((x^2-x^1)²+(y^2-y^1)²)

Using the factors (x + 2) and (x - 3), find the remaining factor(s) of f(x) = x3 - 2x2 - 5x + 6 and write the polynomial in fully factored form.

f(x) = (x + 2)(x - 3)(x - 1)

Write the exponential equation 53 = 125 in its logarithmic form.

log5 125 = 3

Find the real zeros of the polynomial function f(x) = x5 - 6x4 + 9x3 and determine the multiplicity of each.

x = 0, multiplicity 3; x = 3, multiplicity 2

x2 - 6x + 5 = 0

x = 1, 5

Solve the quadratic equation. x2 - 10x = -16

x = 2, 8

√x−12 =3

x = 21

x/11−x2=7+7x22

x = −77/8

Find the inverse function of the function ƒ given by the set of ordered pairs. {(1,4),(2,5),(3,6),(4,7)}

ƒ-1 = {(4,1),(5,2),(6,3),(7,4)}