Name: ______Date: ______Period: _____
Solving Equations Practice
Directions: Solve the equations below on separate paper. Then find the solution at the bottom of this page, and write the letter that’s paired with the solution on the line above the problem number to solve the riddle. Make sure you number each problem on the separate paper and show your work. At the end of class, you will hand in this page, as well as your “work” pages.
RIDDLE: Why did the relation need a math tutor?
______
6 10 2 22 26 3 7 21 25 1 5
______!
14 13 17 4 20 11 23 16 8 27 12 24 18 15 9 19
Problems:
1.√x – 6 = 110. x2 – 49 = 019.√(x + 3) – 1 = 7
2.│-6x│ = 3011.√(3x) – 1 = 520.│5x│ + 5 = 45
3.√(5x) + 3 = 712.3(x – 5)2 = 1221.√(3x + 7) – 5 = 0
4.(x + 3)2 = 2513.√x + 7 = 1122.(x – 4)2 = 16
5. x2 = 8114.│x + 8│ - 5 = 223.4x2 – 200 = -20
6.√(4x) = 1015.7x2 = 8424.│-2x + 6│ = 6
7.│x/3│ = 216.√(6x) = 1225.√(6x + 1) + 9 = 16
8.x2 + 1 = 217.│-2x - 1│ = 1126.7x2 – 6 = 57
9.-5│3 + 4x│ = -11518.x2 + 7 = 627.-6√(x + 4) = -12
Solutions:
D (x = 6) / C (x = 12) / I (x = 25) / E (x = ±3)H (x = 49) / T (x = ±7) / T (x = 61) / I (x = 0)
N (x = 3 or 7) / E (x = ±9) / F (x = ±5) / L (x = 3.2)
T (no solution) / V (x = -1 or -15) / E (x = 16) / S (x = 5 or -6.5)
A (x = ±3√5) / R (x = -6 or 5) / I (x = ±8) / A (x = 8 or 0)
E (x = 0 or 6) / L (x = 24) / E (x = ±2√3) / L (x = ±1)
T (x = 2 or -8) / E (x = ±6) / T (x = 8)
Name: ______Date: ______Period: ___
Writing and Solving Equations – Word Problems
Directions: Solve each word problem by writing an equation (either absolute value, quadratic or square root). Make sure you answer in complete sentences with labels.
1.A machine fills Quaker Oatmeal containers with 32 ounces of oatmeal. After the containers are filled, another machine weighs them. If the container’s weight differs from the desired 32 ounce weight by more than 0.5 ounces, the container is rejected. What are the heaviest and lightest acceptable weights for the Quaker Oatmeal container?
2) The speed that a tsunami (tidal wave) can travel is modeled by the equation
whereSis the speed in kilometers per hour anddis the average depth of the water in kilometers.
a. What is the speed of the tsunami when the average water depth is 0.512 kilometers?(round to nearest tenth)
b.Solve the equation ford.
c.A tsunami is found to be traveling at 120 kilometers per hour. What is the average depth of the water?(round to three decimal places)
When an object is dropped, its speed continually increases, and therefore its height above the ground decreases at a faster and faster rate. The height h (in feet) of the object t seconds after it is dropped can be modeled by the function h = -16t2 + h0where h0 is the object’s initial height. This model assumes that the force of air resistance on the object is negligible. Also, the model works only on Earth. For planets with stronger or weaker gravity, different models are used.
Use the equation from the paragraph above, to answer the following questions:
3) A stunt man working on the set of a movie is to fall out of a window 100 feet abovethe ground. For the stunt man’s safety, an air cushion 26 feet wide by 30 feet long by 9 feet high is positioned on the ground below the window.
a. For how many seconds will the stunt man fall before he reaches the cushion?
b. A movie camera operating at a speed of 24 frames per second records the stuntman’s fall. How many frames of film show the stunt man falling?
4)A woman at the top of a cliff that is 225 feet tall drops her hairpin. How long will it take for the hairpin to reach the ground? Round your answer to the nearest tenth of a second.