HOAY
Rewrite 4x + 12y = 36 in slope intercept form.
y = -3x + 3
If 1/3 of a number is 4 less than 1/2 of the number, the number is
24. Let x represent the unknown number. Since 1/3 of x is 4 less than 1/2 of x, x/3 = x/2 - 4. So, 2x = 3x - 24, giving x = 24.
Mariah is recreating the blueprints of a home that has a base width of 40.75 and a length of 25. The reproduction will be ¼ of the original size. What is the length of the reproduction?
6.25
In how many different ways can five students be seated in three chairs?
60. 5x4x3=60
Jenny’s birthday cake is circular and has a 30 cm radius. Her slice creates an arc with a central angle of 120°. What is the arc length of Jenny’s slice of cake? Give your answer in terms of π.
20pi
Find the value of f(3) - f(4) in the function f(x) = 9x2 + 5x + 10.
-68
5(p+2) + 7(p-2) = 10p
2
Ryan earned a 75% on a test that he studied 4 hours for. Assuming the relationship is proportional, what should he expect to get if he studies for 5 hours? Round to the nearest whole percent.
94
What is the arc length of a circle with a radius of 9 and a degree of 120?
6pi
What is the remainder when is divided by
(2x3 - 5x2 - x + 3) is divided by (x-3)?
-93
A culture of 5000 bacteria triples every 15 minutes. What is the size of the bacteria population after 2 hours have elapsed?
32,805,000
If 3(c + d) = 12, what is the value of c+d?
Simplify (4a-3)(4b-2)
16ab-8a-12b+6
Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads?
1/8
The attendance at a surprise “pop-up” concert at North Avenue Beach can be modeled by the equation where A is the number of people currently at the show and m is the number of minutes the show has been going on. What does the 57 represent in this equation?
Number of people who strted at the concert.
In y=kx, y = 24 when x = 96. Find y when x = 144.
36
Jars A, B, and C each contain 8 marbles. What is the minimum number of marbles that must be transferred among the jars so that the ratio of the number of marbles in jar A to the number in jar B to the number in jar C is 1:2:3?
4. Since jars A, B, and C each contain 8 marbles, there are 24 marbles in the three jars. Let x, 2x, and 3x represent the new numbers of marbles in jars A, B, and C, respectively. Hence, x + 2x + 3x = 24 or 6x = 24, so x=4.
Michael is a fitness instructor who gets paid based on the number of people who take his class, along with a flat fee. He receives a base pay of $80 and charges each person In his class $30. In his most recent class, he made no more than $275. What is the maximum number of people who could have taken his class?
6
What are the solutions to the equation:
4x2 - 8x - 12 = 0
3 and -1
x = y - 20
y = 4x + 8
Find x + y.
28
5(p+2) + 7(p-2) = 10p
Find p.
2
Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit are needed to make a dessert that serves 18 people, what is the cost of the fruit needed to make enough of the same dessert to serve 24 people?
$8.00. If 5 pounds of fruit serve 18 people, then 5/18 pound serves one person, so 24 x 5/18 = 20/3 pounds. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 24 people is 20/3 x $1.20 = $8.00.
The mean test score of Mr. Neely’s first period, which has 25 students in it, is an 87. When the highest score is removed, the mean falls to an 86.5. What did the highest scorer earn?
99
x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?
32. x=70, y=38. 70-38=32.