Pythagorean Theorem
A triangle has side lengths of 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle?
Yes; 72 + 242 = 49 + 576 = 625 & 252 = 625.
A __________ is a graph that shows the relationship between two variables using dots.
scatterplot
Find the volume of a cone with a radius of 3 cm and a height of 9 cm. Use the pi symbol. Round to the nearest hundredth.
Volume of a cone = 1/3 * pi * r2 * h
84.82 cm3
A sphere has a radius of 5 cm. What is its volume? Use the pi symbol. Round to the nearest hundredth.
Volume of a sphere = 4/3 * pi * r3
523.60 cm3
Triangle ABC has vertices at A(1,2), B(3,4), and C(5,6). Apply the translation that moves each vertex 3 units to the right and 2 units down.
What are the new coordinates of the translated triangle? Use the ` symbol in your final answer.
A`(4,0)
B`(6,2)
C`(8,4)
A right triangle has legs that measure 6 m and 8 m. What is the length of the hypotenuse?
c = 10 meters
If the lines in a system of equations are parallel, how many solutions does the system have when graphed?
No solution
A triangular pyramid has a base with an area of 24 cm2 and a height of 10 cm. What is the volume of the pyramid?
Volume of a pyramid = 1/3 * B * h
80 cm3
A sphere has a radius of 7 inches. What is the surface area? Use the pi symbol. Round to the nearest hundredth.
Surface area of a sphere: 4 * pi * r2
615.75 in2
Reflect quadrilateral PQRS with vertices P(2,3), Q(4,5), R(6,7), and S(8,9) across the x-axis.
What are the new coordinates of the reflected quadrilateral? Use the ` symbol in your final answer.
P`(2,-3)
Q`(4,-5)
R`(6,-7)
S`(8,-9)
A right triangle has a hypotenuse of 13 cm and one leg that measures 5 cm. What is the length of the other leg?
a (or b) = 12 cm
How many solutions does the following system of equations have?
y=3x+2
2y=6x+4
There are infinitely many solutions.
A square pyramid has a base with side length 6 meters and a height of 10 meters. Find the volume. Use the pi symbol.
Volume of a pyramid = 1/3 * B * h
120 m3
A sphere has a diameter of 12 m. What is its surface area? Use the pi symbol. Round to the nearest hundredth.
Surface area of a sphere: 4 * pi * r2
452.39 m2
Two triangles, ABC and A`B`C`, are similar.
The side lengths of ABC are: AB=12, BC=16, and AC=20.
The side lengths of A`B`C`are: A`B`=6, B`C`=8, and A`C`=10.
What is the scale factor?
scale factor = new/original = 6/12 = 8/16 = 10/20 = 1/2 = 0.5
A ladder is leaning against a wall. The base of the ladder is 9 feet away from the wall, and the ladder reaches 12 feet up the wall. How long is the ladder?
The ladder is 15 feet.
Is the ordered pair (2,4) a solution to the system? Show your work by substituting into both equations.
y=3x-2
y=-x+6
Yes, the ordered pair is a solution to the system.
Find the volume of a cone with a diameter of 10 inches and a height of 12 inches. Use the pi symbol. Round to the nearest hundredth.
Volume of a cone = 1/3 * pi * r2 * h
314.16 in3
A company is manufacturing a spherical ball for a new product. The ball has a radius of 8 cm. The company needs to cover the entire surface of the ball with a special type of paint which costs $5 per square centimeter.
What will be the total cost to cover the entire surface of one ball with paint? Use the pi symbol.
Surface area of a sphere = 4 * pi * r2
The total cost to cover the entire surface of the ball with paint is about $4,021.25.
Rectangle ABCD has vertices at A(1,2), B(3,2), C(3,4), and D(1,4). Dilate the rectangle by a scale factor of 2.
What are the coordinates of the new rectangle? Use the ` symbol in your final answer.
A`(2,4)
B`(6,4)
C`(6,8)
D`(2,8)
In a right triangle, one leg is 9 inches, and the other leg is 12 inches. Find the perimeter of the triangle.
P = 36 inches
The data shows the number of hours students studied and their corresponding test scores.
Hours studied: 1, 2, 3, 4, 5
Test scores: 65, 71, 75, 81, 87
Based on the trend, predict the test score for a student who studies for 6 hours.
A. 88%
B. 92%
C. 84%
D. 100%
B. 92%
A triangular pyramid has a base in the shape of a triangle with a base of 6 feet and a height of 10 feet. The height of the pyramid is 9 feet. Find the volume of the pyramid.
Volume of a pyramid = 1/3 * B * h
90 ft3
The volume of a sphere is 904.78 cm3. What is the radius of the sphere?
Volume of a sphere: 4/3 * pi * r3
6 cm
Rotate triangle XYZ with vertices at X(1,1), Y(2,3), and Z(3,2) 90 degrees about the origin.
What are the new coordinates of the rotated triangle? Use the ` symbol in your final answer.
X`(-1,1)
Y`(-3,2)
Z`(-2,3)