Algebra Test 4

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What is the value of f(18) from the given table?

6

What is the input value when the output is 12 from the given table?

3

What is the domain of the function g(x) from the given graph?

[-4, -3] U [-2, 3]

What is the value of x when G(x) = 20, given the function G(x) = 2x + 8?

6 Signup and view all the answers

What is the value of g(-2), given the function g(x) = √(3x + 10)?

4 Signup and view all the answers

What is the meaning of the statement H(8) = 40 in the context of the story?

8 years after 1990, there were 40 ducks in the lake. Signup and view all the answers

What is the relationship between the speed of a car and the length of its skid marks on a dry asphalt road?

The speed of the car, S(L), is related to the length of the skid marks, L, by the function S(L) = √(20L). Signup and view all the answers

If the skid marks of a car measure 100 feet, what was the speed of the car?

44.72 mph Signup and view all the answers

What is the concentration of a drug in a patient's bloodstream 3 hours after injection?

2.8 Signup and view all the answers

At what time(s) does the concentration of the drug reach 2?

2 hours and 10 hours Signup and view all the answers

What is the height of the ball 2 seconds after it is thrown from the roof of a building?

200 feet Signup and view all the answers

What is the maximum height of the ball?

It depends on the calculations, but it can be found by finding the vertex of the parabola represented by the function h(t). Signup and view all the answers

What is the profit function that represents the profit from selling x toys, and what is the number of toys that should be sold to break even?

P(x) = 2x - 80; 40 toys Signup and view all the answers

Find the slope-intercept form of the equation of the line that passes through the points (1,2) and (3,6).

y = 2x + (-2) Signup and view all the answers

What is the meaning of the slope in the equation E = 4500 - 70t, which represents Terry's elevation in feet after t seconds?

The elevation is going down 70 feet per second. Signup and view all the answers

What is the meaning of the y-intercept in the equation E = 4500 - 70t, which represents Terry's elevation in feet after t seconds?

For every steep hill, Terry starts at an elevation of 4500 feet. Signup and view all the answers

What is the total cost, C, to produce n toys, if it costs $400 to develop the toy and $10 to manufacture each toy?

C = 10n + 400 Signup and view all the answers

With a total budget of $2000, how many toys can be produced, if it costs $400 to develop the toy and $10 to manufacture each toy?

160 toys Signup and view all the answers

Solve for x: $5(3.4)x = 90$

X-2.362 Signup and view all the answers

Solve for x: In(x) = 3

x=20.1 Signup and view all the answers

A sum of $30,000 is invested in an account with an annual interest rate of 4%, compounded quarterly. What is the balance, in the account, in two years and nine months?

4842.23 Signup and view all the answers

Tracy wants to have $100,000, in ten years, as a down payment for the purchase of a house. She found a bank that pays 6% annual interest rate, compounded continuously. How much money should she invest now to reach her goal?

54,881.2 Signup and view all the answers

The value of a new car, after t years, is modeled by the function V(t) = 36000(0.92)^t. What is the price of the car after two years?

36000(0.92)^2 Signup and view all the answers

How long will it take for the value of the car to reach $30,000?

t ≈ 2.2 yrs Signup and view all the answers

What is the value of $x$ when $5(3.4x - 2.362) = 90$?

Divide both sides by 5, then add 2.362 to both sides, and finally divide both sides by 3.4. Signup and view all the answers

What is the value of $x$ when $2log_3(x+4) - 2log_3(x) = 2$?

Use the quotient rule of logarithms, then take the antilogarithm of both sides, and finally solve for x. Signup and view all the answers

What is the value of $log₂(3)$?

Use the change of base formula, or a calculator, to find the value of log₂(3). Signup and view all the answers

What is the value of $V(0)$, given the function $V(t) = 36000(0.92)^t$?

36000, since $V(0) = 36000(0.92)^0 = 36000$. Signup and view all the answers