Heart of Algebra
If 4x - 2y = 12 and x+ y = 9, what is the value of x(y)?
A) 4 B) 20 C) 5 D) 40
What is B?
If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5 ?
What is 20?
what is the sum (7 + 3i) + (−8 + 9i) ?
What is -1+12i?
If (x− 1)/3=k and k = 3, what is the value of x ?
What is 10?
If (ax + 2)(bx + 7) = 15x^2 + cx + 14 for all values of x, and a + b = 8, what are the two possible values for c ?
A) 3 and 5 B) 6 and 35 C) 10 and 21 D) 31 and 41
What is D?
Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p ?
What is p/( .8 * 1.08)?
In a right triangle, one angle measures x°, where sin x° =4/5. What is cos(90° − x°) ?
What is 4/5?
On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?
What is 5m+4p?
h = − 4.9t^2 + 25t The equation above expresses the approximate height h, in meters, of a ball t seconds after it is launched vertically upward from the ground with an initial velocity of 25 meters per second. After approximately how many seconds will the ball hit the ground?
What is 5.1?
Katarina is a botanist studying the production of pears by two types of pear trees. She noticed that Type A trees produced 20 percent more pears than Type B trees did. Based on Katarina’s observation, if the Type A trees produced 144 pears, how many pears did the Type B trees produce?
What is 120?
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 this equation?
What is Kathy will start each week with 108 phones to fix?
Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the expression $100(x)^t to find the value of the account after t years. What is the value of x in the expression?
What is1.02
In a graph that displays the total cost C, in dollars, of renting a boat for h hours. What does the C-intercept represent in the graph?
A) The initial cost of renting the boat B) The total number of boats rented C) The total number of hours the boat is rented D) The increase in cost to rent the boat for each additional hour
What is A?
A dairy farmer uses a storage silo that is in the shape of the right circular cylinder with height 8. If the volume of the silo is 72(pi) cubic yards, what is the diameter of the base of the cylinder, in yards?
V = pi (r^2) h
What is 6?
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?
What is 3?
y<-x+a, y>x+b In the xy-plane, if (0, 0) is a solution to the system of inequalities above, which of the following relationships between a and b must be true?
A) a<b B) a=b C) a>b D) 2a > b
What is C) a>b
g(x) = ax^2 + 24 For the function g defined above, a is a constant and g(4) = 8. What is the value of g(−4) ?
What is 8?