A triangle has side lengths 10, 15, and 7. Is the triangle acute, obtuse, or right? Show your work and explain.
A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 5 miles. To the nearest hundredth of a mile, how high does the highway rise in this 5-mile section? Show the stems you use to find the distance.
A forest ranger spots a fire from a 28-foot tower. The angle of depression from the tower to the fire is 11. To the nearest foot, how far is the fire from the base of the tower? Show the steps you use to find the solution.
State whether the transformation appears to be a rigid motion. Explain.
How can you verify Euler’s formula for this net of a cube?
Jason designed an arch made of wrought iron for the top of a mall entrance. The 11 segments between the two concentric circles are each 1.25 m long. Find the total length of wrought iron used to make the structure. Round the answer to the nearest meter. Show your work.
Consider the prism shown below.
Janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimeters. The vase had a height of 50 centimeters. Find the radius of the vase. Explain the method you would use to find the radius.
A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm of air. How much air does the balloon hold when the design is 10 cm wide? Explain the method you use to find the amount of air.
In circle O, and are tangents. (The figure is not drawn to scale.)
Prove that .
Find mBOD for mAOP = 64. Explain your reasoning.
Determine whether a tangent line to circle O is shown in the diagram, for AB = 7.75, OB = 4, and AO = 8.75. Explain your reasoning. (The figure is not drawn to scale.)
scale.) Show your work.
In circle O, CD = 44, OM = 20, ON = 19, , (The figure is not drawn to
a. Find the radius. If your answer is not an integer, express it in radical form.
b. Find FN. If your answer is not an integer, express it in radical form.
is tangent to the circle at B. mA = 14 and (The figure is not drawn to scale.) Show your work.
a. Find x
b. Find y
At a track meet, 50 people ran the 100-meter dash. 2 people finished in 11 seconds, 5 people finished in 12 seconds, 8 people finished in 13 seconds, 10 people finished in 14 seconds, 21 people finished in 15 seconds, 2 people finished in 16 seconds, and 2 people finished in 17 seconds. What is the probability distribution for the finish times?
Is there a similarity transformation that maps to ? If so, identify the similarity transformation and write a similarity statement. Explain your answer.
Janine wants to paint just the sides of a cylindrical pottery vase that has a height of 45 cm and a diameter of 14 cm. To the nearest whole number, find the number of square centimeters she will need to paint. Explain the method you would use to find the lateral area.
Determine whether a tangent line is shown in the diagram, for AB = 7, OB = 3.75, and AO = 8. Explain your reasoning. (The figure is not drawn to scale.)
The equation (x + 5) + (y + 3) = 169 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals.
An hourglass, composed of two identical cones, is 12 cm tall. The radius of each cone is 3 cm. If you want to fill the bottom half of the hourglass full of salt, how much salt will you need? Explain the method you would use to find the amount of salt.
Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm.
a. What is the volume of the cylinder? Explain your method for finding the volume.
b. What is the total volume of the three balls? Explain your method for finding the total volume.
c. What percent of the volume of the container is occupied by the three balls? Explain how you would find the percent.
2. In , is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. Show your work.
3. Please show your work to find the mean and standard deviation of the data. Round to the nearest tenth.
20, 16, 18, 14, 9, 20, 16
4. What are the points of discontinuity? Are they all removable? Please show your work.
5. A sound wave is modeled with the equation .
a. Find the period. Explain your method.
b. Find the amplitude. Explain your method.
c. What is the equation of the midline? What does it represent?
6. Paula spots a glider located at an angle of elevation of 42°. The distance between the glider and Paula is 3280 feet. To the nearest foot, what is the height of the glider h from the ground? Show your work.
7. What is the product in simplest form? State any restrictions on the variable. Please show your work.
Verify the identity. Justify each step.
9. Verify the identity .
10. Find the values of the 30th and 90th percentiles of the data. Please show your work.
129, 113, 200, 100, 105, 132, 100, 176, 146, 152
11. What is the quotient in simplified form? State any restrictions on the variable. Show Work.
12. Vance is designing a garden in the shape of an isosceles triangle. The base of the garden is 36 feet long. The function models the height of the triangular garden.
a. What is the height of the triangle when
b. What is the height of the triangle when
c. Vance is considering using either or for his garden. Compare the areas of the two possible gardens. Explain how you found the areas.
13. Verify the identity. Justify each step.
14. Compare the graphs of the inverse variations. Please provide at least 3 comparisons
15. Use a graphing calculator to solve the equation in the interval from . Round to the nearest hundredth.
16. The equation models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released.
a. Solve the equation for t.
b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.
c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.
Consider the graph of the cosine function shown below.
a. Find the period and amplitude of the cosine function.
b. At what values of for do the maximum value(s), minimum values(s), and zeros occur?
Use the graph of the sine function shown below.
a. How many cycles occur in the graph?
b. Find the period of the graph.
c. Find the amplitude of the graph.
19. Verify the Pythagorean Identity.
Howard is flying a kite and wants to find its angle of elevation. The string on the kite is 32 meters long and the kite is level with the top of a building that he knows is 28 meters high.
To the nearest tenth of a degree, find the angle of elevation. Show your work.