Completing the Square
What value would make this expression a perfect square trinomial?
z2 + 30z
225
If there is a specific order in which the events must occur, then is the event a permutation or a combination?
Permutation
What does it mean to rationalize a denominator?
Eliminate any square roots that exist in the denominator.
Square root of 45 minus square root of 20.
Square root of 5.
What are the six main trigonometric functions?
Sine, Cosine, Tangent, Cosecant, Secant, Cotangent
Add the proper constant to the binomial so that the resulting trinomial is a perfect square. Then factor the trinomial.
n2 + 22n
121
(n + 11)2
For a segment of a radio show, a disc jockey can play 8 records. If there are 13 records to select from, in how many ways can the program for this segment be arranged?
51,891,840
Simplify the square root of one-half.
Square root of two over two
5 times the square root of 48 minus 2 times the square root of 32 plus the square root of 27.
23 times the square root of 3 minus 8 times the square root of 2.
If a right triangle has legs that are 28 inches and 21 inches long, how long is the hypotenuse?
35 inches
Solve the equation by completing the square.
x2 + 12x = -27
x = -3
x = -9
Of 17 possible books, you plan to take 3 with you on vacation. How many different collections of 3 books can you take?
680
Simplify three divided by the square root of 20x.
3 times the square root of 5x divided by 10x.
Square root of 16b3 plus the square root of 9b3 minus the square root of 25b3
2b times the square root of b.
In a right triangle, the opposite side to angle A is 3 units, the adjacent side to angle A is 4 units, and the hypotenuse is 5 units. What is the measure of the cosine of angle A?
4/5
Solve the equation by completing the square.
x2 + 10x = -23
x = -5 + square root of 2
x = -5 - square root of 2
In how many distinct ways can the digits in the number 7,552,222 be arranged?
105
Simplify 8 divided by the quantity 3 minus the square root of eleven.
-12 - 4 times the square root of eleven
5 minus 4 times the square root of y6 plus 2 times the square root of y6 plus 7
-2y3 + 12
In a right triangle, one of the angles measure 35 degrees. If the side adjacent to the angle is 130 feet, what is the length of the side opposite, to the nearest hundredth, to the angle?
91.03 feet
Solve the equation by completing the square.
9y2 - 12y + 1 = 0
y = 2 - square root of three all over 3
y = 2 + square root of three all over 3
How many sequences of three numbers can be made from the numbers 1, 3, 5, 7, and 9, if the numbers can be repeated?
125
Simplify the square root of n divided by the quantity square root of n minus the square root of p.
n + square root of np divided by (n - p)
6 times the square root of 2 divided by 7 plus 7 times the square root of 2 divided by 6.
85 times the square root of 2 divided by 42.
If f(x) = 3x2 - 7, find f(-4).
f(-4) = 41