Algebra 2
What is x?
2x + 3 = 10
x = 7/2
or
x = 3.5
The two shortest sides of a right triangle have lengths of 7 cm and 24 cm. What is the length of the hypotenuse in centimeters?
25 cm
Find the solution (x, y) to the system of equations below.
x + y = 1
2x - y = -7
(-2, 3)
There are five marbles in a bag: two red and three yellow. If a marble is randomly chosen, what is the probability that it's red?
0.4 or 2/5
For the function f, f(0) = 86, and for each increase in x by 1, the value of f(x) decreases by 80%. What is the value of f(2)?
3.44 or 86/25
Expand (i - 2)(i + 2)
Note: i is the imaginary unit
-5
Find the midpoint of segment AB if A is located at (1, 1) and B is located at (5, -7).
(3, -3)
2, 2, 2, 3, 4, 4, 11
What is the median of the seven data values shown?
3
What is the volume of a cylinder with a radius of 2 and a height of 5?
20π cubic units
Triangle ABC has side lengths AB = BC = CA = 2. It is then dilated by a scale factor of 2. What is the perimeter of the resulting shape?
12
Factor x3 - 3x2 - x + 3 given that the polynomial has a zero at x = 3.
(x+1)(x-1)(x-3)
Points A and B lie on a circle with a radius of 1, and arc AB has length π/2. What fraction of the circumference of the circle is length of arc AB?
1/4
Triangle XYZ is similar to triangle RST such that X, Y, and Z correspond to R, S, and T, respectively. The measure of angle Z is 20 degrees, and 2XY = RS. What is the measure of angle T?
20 degrees
What is the end behavior of f(x) = -13x6 + 12x5 - 11x4 + 10x3 - 9x2 + 8x - 7 as x approaches ∞?
-∞
At a certain time and day, the Washington Monument in Washington, DC, casts a shadow that is 296 feet long. At the same time, a nearby cherry tree casts a shadow that is 16 feet long. Given that the Washington Monument is approximately 555 feet tall, what is the height, in feet, of the cherry tree?
30
A given that function f(x) = x2, find and simplify g(x) such that g(x) = 3f(x+1) - 5.
g(x) = 3x2 + 6x - 2
ABC is similar to triangle XYZ, with A corresponding to X and B corresponding to Y. If AB = 2 and YZ = 3BC, then what is the length of segment XY?
6
Square A has side lengths that are 166 times the side lengths of square B. The area of square A is k times the area of square B. What is the value of k?
27,556
A sample of 40 fourth-grade students were selected at random from a certain school. The 40 students completed a survey about the morning announcements, and 32 thought the announcements were helpful. True or false: the largest population to which the results can reasonably be applied is all fourth grade students at the school.
True
Triangle FGH is similar to triangle JKL, where angle F corresponds to angle J and angles G and K are right angles. If sin(F) = 308/317, what is the value of 1/cos(L)?
1/cos(L) = 317/308
What is f(100) equal to given the following?
Note: x is given in degrees.
f(x) = sin2(x) + 1/sec2(x)
1
A circle in the xy-plane is modeled by x² + y² + 6y - 72 = 0. What is the radius of the circle?
9
Joseph has a map of a building and calculated the area of the floor on paper to be 180cm2. The scale on the map shows that 1cm = 20ft. If Joseph plans to cover the entire floor, and every 400ft2 of carpet costs $2, approximately how much money will he need?
$360
Given that the following system of equations has infinite solutions, what is the value of a?
ay + x = 1
4y + 8x = 8
a = 0.5 or 1/2
Five books, each a different color, are stacked on a shelf. Then, one book is removed at random. What is the number of distinct arrangements that the could be made by this process?
120