Algebra
3/2
Convert 5π/6 radians to degrees
150°
If x + y = 12 x + y = 12 and xy=35, find x2 + y2
74
What comes next? 1,4,9,16,...
25
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.
Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x2. If m is a positive number such that f(7) = g(m) + g(2), what is the value of m?
4
What is the exact value of tan(-π/4)
-1
How many real solutions does x2 = |x| have?
3
Identify the pattern: 2, 6, 18, 54,…
Geometric, multiply by 3
A rectangle has a perimeter of 54 units. Its length is 3 units more than twice its width.
Find the dimensions.
Length of 19 units and a width of 8 units
A culture of 5000 bacteria doubles every hour. What is the size of the bacteria population after 2 hours have elapsed?
20,000
Solve sin(x) = √3/2 on [0,2π]
π/3, 5π/3
In how many different ways can five students be seated in three chairs?
60. 5x4x3=60
Three fair coins are tossed at the same time. What is the probability that all three coins will come up heads OR all will come up tails?
1/4. 1/8 (all heads) + 1/8 (all tails) = 1/4.
A boat moored in Chesapeake Bay has a ladder that hangs down from the deck of the boat and touches the flat sea surface. The rungs are 1 foot apart. At low tide, ten rungs of the ladder are exposed. At high tide, the water level rises 6 feet. How many of the rungs will remain exposed?
5 rungs. This number of rungs will be exposed. As the tide comes in, the boat will rise up.
What is the equation of the graph obtained by shifting the graph of y=x2 horizontally to the left 4 units and vertically down 3 units?
f(x) = (x+4)2 - 3
If the integer lengths of the three sides of a triangle are 4, x, and 9, what is the least possible perimeter of the triangle?
19. In the given triangle, 4+9>x, 4+x>9
Solve x2 -5x+6 ≤ 0
2≤x≤3
What's the next term in the sequence: 1, 2, 3, 5, 8, ...
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.
Working alone, Bill takes three times the amount of time to paint a fence that Mike takes. If Bill and Mike work together, they can paint the fence in 2 hours. If Mike works at the same rate as when he worked with Bill, how long would it take Mike working alone to paint the same fence?
2 hours and 40 minutes. If x represents the number of hours it takes Mike working alone to paint the fence, then 3x is the number of hours it takes Bill working alone to paint the fence. So 2(1/x) + 2(1/3x) = 1 gives x=8/3 hours.
What is the number of sides of a polygon in which the sum of the degree measures of the interior angles is 4 times the sum of the degree measures of the exterior angles?
10. Sum of the degree measures of exterior angles is 360. S = (n-2)180 = 4 x 360, where n=number of sides. Solving for (n-2) = 8 or n=10.
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.
A geometric sequence has a1 = 5, r = 2.
Find the smallest n such that an > 500
n = 8 (sequence: 5, 10, 20, 40, 80, 160, 320, 640)
Toppings for a pizza costs $1.20 a pound. If 5 pounds of toppings are needed to make enough pizza to serve 18 people, what is the cost of the toppings needed to make enough of the same type of pizza 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.