Given the functions f(x) = (2x)/(x-5) and g(x) = 10/x, find g^(-1)(-10).
What is -1?
100
(25^(-1/2) + 49^(-1/2))^(-2).
What is 1225/144?
100
Log8(1/16).
What is -4/3?
100
This is the difference between the definition of a linear pair and the Linear Pair Postulate.
What are supplementary angles?
100
Find the first four terms and state whether the sequence is arithmetic, geometric, or neither: An = 60(1.05)^(n).
What is 63, 66.15, 69.4575, 72.930375 and geometric?
200
Given the functions f(x) = 1/(x+2) and g(x) = x^(2) + x, find g(f(x)).
What is (x+3)/(x+2)^(2)?
200
Simplify and write your final answer in exponential form: the fourth root of: (-4x^(-1)y^(5/2))^(2) / (x^(2)y^(9)).
What is 2/(xy)?
200
This number is the average of the numbers Log14(2), Log14(2), and Log14(49).
What is 14/3?
200
This postulate states that if point B is on Line(AB) and between points A and C, then AB + BC = AC.
What is the Segment Addition Postulate?
200
This number is the seventh term in the geometric sequence: A1 = 24 and A4 = 81.
What is 2187/8 or 273.375?
300
Given the function 3x^(2)-2x+7, restrict the domain of this function so that it will be a one-to-one function.
What is x>=1/3 or x<=1/3?
300
(3^(2n))^(3) = (3^(n))^(2) x 3^(n+9).
What is 3?
300
Given the function f(x) = 3 x 5^(x-2), write an equation for the inverse.
What is (log(x/3) / log(5)) + 2?
300
Given two lines that are cut by a transversal forming congruent alternate interior angles, this postulate proves that the lines are parallel.
What is the Converse of Corresponding Angles Postulate?
300
Find the value of a car after 7 years if its sticker price was $28,000 and it depreciates by 20% each year.
What is $5,976.88?
400
Decide if each of the following is even, odd, or neither: f(x) = x^(4)-3x^(2), g(x) = 5/x^(5), h(x) = 3^(x), j(x) = (4x+5)^(1/2).
What is even, odd, neither, even, respectively?
400
4^(2x+1) = 8^(3x-4).
What is 14/5?
400
The answer to this equation: 6/(3 + 5.5^(-x)) is rounded to the nearest 0.001.
What is -0.944?
400
Given Line(DZ) and Line(AN) intersect at I, prove that vertical angles are congruent.
What is?:
1. Line(DZ) and Line(AN) intersect at I. [Given]
2. Angle(AID) and Angle(DIN) are a linear pair. Angle(NIZ) and Angle(DIN) are a linear pair. [Definition of Linear Pair]
3. Angle(AID) and Angle(DIN) are supplementary. Angle(NIZ) and Angle(DIN) are supplementary. [Linear Pair Postulate]
4. mAngle(AID) + mAngle(DIN) = 180°. mAngle(NIZ) + mAngle(DIN) = 180°. [Definition of Supplementary Angles]
5. mAngle(AID) + mAngle(DIN) = mAngle(NIZ) +mAngle(DIN). [Substitution Property of Equality]
6. mAngle(AID) = mAngle(NIZ). [Subtraction Property of Equality]
7. Angle(AID) is congruent to Angle(NIZ). [Definition of Congruence]
400
This equation represents the fifth term of a geometric sequence with first two terms x and y.
The answer to this equation: 3^(x-5) = 7^(5x+2) is rounded to the nearest 0.001.
What is -1.087?
500
A right triangle with two acute angles, an equiangular triangle, and two triangles with similar angles all contribute to these three corollaries.
What is?:
Corollary 1: In a right triangle, the acute angles are complementary.
Corollary 2: If a triangle is equiangular, then each angle measures 60°.
Corollary 3: If two angles of one triangle are congruent to angles of another triangle, then the third pair of angles must be congruent.
500
A sample of radioactive material has been decaying for six years. Two years ago, there were 8.00 g of material left. Now, 7.20 g are left. The number of grams of the original sample is rounded to the nearest 0.1.