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In the following exercises, check whether the given values are solutions.

For the equation x + 12 = x :
Is x = 4 a solution?
Is x = −3 a solution?

yes no

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For the equation y + 20 = y :
Is y = 4 a solution?
Is y = −5 a solution?

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For the equation t + 6 = t :
Is t = −2 a solution?
Is t = 3 a solution?

no yes

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For the equation u + 42 = u :
Is u = −6 a solution?
Is u = 7 a solution?

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In the following exercises, solve.

5 v 2 + 5 = 0

no solution

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2 m + 1 + 4 = 0

no solution

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u 3 + 3 = u
x + 1 x + 1 = 0

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v 10 + 10 = v
y + 4 y + 2 = 0

10 , 11 5

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r 1 r = −1
z + 100 z + 10 = 0

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s 8 s = −8
w + 25 w + 5 = 0

8 , 9 11

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4 v + 3 = v 6

not a real number

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12 c + 6 = 10 4 c

1 4

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a + 2 = a + 4
b 2 + 1 = 3 b + 2

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r + 6 = r + 8
s 3 + 2 = s + 4

no solution 57 16

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u + 1 = u + 4
n 5 + 4 = 3 n + 7

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x + 10 = x + 2
y 2 + 2 = 2 y + 4

no solution 6

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8 u + 1 + 9 = 0

no solution

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Use Square Roots in Applications

In the following exercises, solve. Round approximations to one decimal place.

Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of 75 square feet. Use the formula s = A to find the length of each side of his garden. Round your answer to the nearest tenth of a foot.

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Landscaping Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 130 square feet. Use the formula s = A to find the length of each side of his patio. Round your answer to the nearest tenth of a foot.

11.4 feet

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Gravity While putting up holiday decorations, Renee dropped a light bulb from the top of a 64 foot tall tree. Use the formula t = h 4 to find how many seconds it took for the light bulb to reach the ground.

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Gravity An airplane dropped a flare from a height of 1024 feet above a lake. Use the formula t = h 4 to find how many seconds it took for the flare to reach the water.

8 seconds

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Gravity A hang glider dropped his cell phone from a height of 350 feet. Use the formula t = h 4 to find how many seconds it took for the cell phone to reach the ground.

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Gravity A construction worker dropped a hammer while building the Grand Canyon skywalk, 4000 feet above the Colorado River. Use the formula t = h 4 to find how many seconds it took for the hammer to reach the river.

15.8 seconds

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Accident investigation The skid marks for a car involved in an accident measured 54 feet. Use the formula s = 24 d to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

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Accident investigation The skid marks for a car involved in an accident measured 216 feet. Use the formula s = 24 d to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.

72 feet

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Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175 feet. Use the formula s = 24 d to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

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Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 117 feet. Use the formula s = 24 d to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

53.0 feet

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Writing exercises

Explain why an equation of the form x + 1 = 0 has no solution.

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  1. Solve the equation r + 4 r + 2 = 0 .
  2. Explain why one of the “solutions” that was found was not actually a solution to the equation.

Answers will vary.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has two rows and four columns. The first row labels each column, “I can…,” “Confidently,” “With some help,” and “No minus I don’t get it!” The row under “I can…,” reads, “use square roots in applications.” All the other rows are empty.

After reviewing this checklist, what will you do to become confident for all objectives?

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Practice Key Terms 1

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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