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In a video game, each player starts the game with k points and loses 2 points each time a task is not completed. If a player who gains no additional points and fails to complete 100 tasks has a score of 200 points, what is the value of k ?
A landscaper buys a new commercial-grade lawn mover that costs $2,800. Based on past experience, he expects it to last about 8 years, and then he can sell it for scrap metal with a salvage value of about $240. Assuming the value of the lawn mower depreciates at a constant rate, which equation could be used to find its approximate value after x years, given that x < 8?
During a 40-minute session at a 220 volt charging station, the charge on an electric car battery increases from an initial charge of 50 power units to a final charge of 106 power units. If this charge increases linearly with time, which of the following best describes the charge, q, in power units, on this same battery after charging for t hours from an initial charge of 20 power units? (1 hour = 60 minutes)
Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation \(P=108-23d\), where P is the number of phones left and d is the number of days she has worked that week. What is the meaning of the value 108 in the equation?
The graph above displays the total cost C, in dollars, of renting a boat for h hours.
What does the C-intercept represent in the graph?
$$h=3a+28.6$$
A pediatrician uses the model above to estimate the height h of a boy, in inches, in terms of the boy’s age a, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy’s height each year?
\((8m^2+5)-(-3m^2-4)\)
The given expression is equivalent to \(am^2+k\), where \(a\) and \(k\) are constants. What are the values of \(a\)?
If \(\frac ab=2\), what is the value of \(\frac{4b}a\)?
$$a=1,052+1.08t$$
The speed of a sound wave in air depends on the air temperature. The formula above shows the relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit (°F).
Which of the following expresses the air temperature in terms of the speed of a sound wave?
$$I=\frac P{4\mathrm{πr}^2}$$
At a large distance r from a radio antenna, the intensity of the radio signal I is related to the power of the signal P by the formula above.
Which of the following expresses the square of the distance from the radio antenna in terms of the intensity of the radio signal and the power of the signal?
$$ax+by=12\\2x+8y=60$$
In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of \(\frac ab\)?
$$2x+5y=8\\x+3y=3$$
If \((x, y)\) is a solution to the system of equations above, what is the value of \(y^2\)?
$$-2x+5y=1\\7x-10y=-11$$
If \((x, y)\) is a solution to the system of equations above, what is the sum of x and y ?
$$\frac34x-\frac12y=12\\kx-2y=22$$
If the system of linear equations above has no solution, and k is a constant, what is the value of k?
Which of the following values satisfies the inequalities \(t-\frac34>\frac32\;and\;\frac t4-\frac13<\frac5{12}\)?
If \(0.002\leq x\leq0.2\) and \(5\leq y\leq25\), what is the maximum value of \(\frac xy\)?
Which of the following systems of inequalities could be represented by the graph shown?
Tickets for a school show cost $5 for students and $10 for visitors. If the school sold 122 tickets, and made $800 in ticket sales, how many visitor tickets were sold?
A worker uses a forklift to move boxes that weight either 40 pounds or 65 pounds each. Let x be the number of 40-pound boxes and y be the number of 65-pound boxes. The forklift can carry up to either 45 boxes or a weight of 2,400 pounds. Which of the following systems of inequalities represents this relationship?
At a lunch stand, each hamburger has 50 more calories than each order of fries. If 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?
Each winter, Captain Dan’s Ski Lodge rents both pairs of skis and snowboards to its guests for a flat daily rate per pair of skis and a flat daily rate per snowboard. Five pairs of skis and two snowboards will cost a family $370. Three pairs of skis and four snowboards will cost a family $390. During a particularly slow season, Captain Dan announces a 10% discount on all skis and snowboards. What would be the cost of renting two pairs of skis and two snowboards if they were rented during this discount period?