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Algebra : Solving Equations and Word Problems

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1. Solve by factoring:
x^2 - 9x = -8

2. Solve using the square root property:
2x^2 - 5 = 93

3. Solve using the square root property:
(x + 4)^2 = 81

4. Solve by completing the square:
x^2 + 6x + 2 = 0

5. Solve using the quadratic formula:
x^2 - 3x = -6x - 1

6. Solve using the quadratic formula:
x^2 - 10x - 1 = -10

7. Solve the equation.

y^2 - 13 y + 22 = 0

8. Write the equation x(x - 6) + 5 = 0 in quadratic form and then solve it by factoring.

9. Write the equation 6 x(x - 3) = - 12 in quadratic form and then solve it by factoring.

10. Choose from the following a quadratic equation with solutions of 9 and 6.

x^2 - 15x + 54 = 0

x^2 - 18x + 51 = 0

x^2 - 15x + 57 = 0

x^2 - 12x + 54 = 0

11. The height h (in feet) of an object that is dropped from the height of s feet is given by the formula h = s - 16t 2 , where t is the time the object has been falling. A 6 foot tall woman on a sidewalk looks directly overhead and sees a window washer drop a bottle from the 2 story. How long does she have to get out of the way? Round to the nearest tenth. (A story is 12 feet.) Choose the answer from the following:

12. Use the quadratic formula to solve the equation: x 2 - 3 x + 2 = 0.

13. Use the quadratic formula to solve the equation: 4x^2 - 30x = 1

14. The hypotenuse of a right triangle is 2.7 units long. The longer leg is 1.4 units longer than the shorter leg. Find the lengths of the sides of the triangle.

15. We have learned to solve quadratic equations using a variety of methods including completing the square and the quadratic formula. Give an example using either completing the square or the quadratic formula and explain each step as if you were teaching someone who had never used the method before.

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Solution Summary

Equations and word problems are solved. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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