Please help me by checking the following answers for me.
3. A student is attempting to solve the equation below for the variable x. Which of the statements below best applies to the mathematical work shown?
Given √(4x-6)=12, I square both sides, so (√4x)^2-6=〖12〗^2, or 4x -6 = 144. I can then solve for x, yielding x = 37 1/2 as my final answer.
A. The student did not correctly square both sides of the equation. - (This is my second answer.)
B. The student did not properly isolate the variable after squaring both sides of the equation.
C. The student omitted a negative solution to the equation.
D. The mathematical work is correct. - (I know it is not this because I got it wrong.)
4. Solve for x.
〖5x〗^2+3=-122
A. No solution. - (This is my second answer.)
B. -5 - (I know it is not the answer because I got it wrong.)
C. ±5
D. ±25
9. The acceleration of an object can be described by the equation a= 2d/t^2, where a is acceleration, d is the distance, and t is time. If an object accelerates at a rate of 2 m/s^2 for 10 meters, what is the total time elapsed?
A. 1/10 seconds - (This is my second answer.)
B. √(1/10) seconds
C. √10 seconds
D. 10 seconds - (I know it is not answer because I got it wrong.)
Please check them to see if I am correct. Any help will really be appreciated! :)
Let's go through each question and check the answers together:
3. A student is attempting to solve the equation √(4x-6)=12 for the variable x. The student squared both sides of the equation to eliminate the square root. The algebraic work shown is:
Given √(4x-6)=12, I square both sides, so (√4x)^2-6=〖12〗^2, or 4x -6 = 144. I can then solve for x, yielding x = 37 1/2 as my final answer.
To check the student's work, you need to simplify (√4x)^2-6=〖12〗^2:
(√4x)^2 - 6 = 144
(4x) - 6 = 144
4x = 150
x = 150/4
x = 37.5
Therefore, the student's work is correct. The answer is D. The mathematical work is correct.
4. Solve for x in the equation 〖5x〗^2+3=-122.
To solve this equation, we need to isolate the term with x:
〖5x〗^2 + 3 = -122
〖5x〗^2 = -122 - 3
〖5x〗^2 = -125
Since we cannot take the square root of a negative number and have a real solution, this equation has no solution. Therefore, the answer is A. No solution.
9. The acceleration of an object is described by the equation a = 2d/t^2. If an object accelerates at a rate of 2 m/s^2 for 10 meters, what is the total time elapsed?
We have the equation a = 2d/t^2, where a is the acceleration, d is the distance, and t is the time.
Substituting the values we have, we get:
2 = 2(10)/t^2
2 = 20/t^2
To solve for t, we need to isolate t^2:
t^2 = 20/2
t^2 = 10
Taking the square root of both sides, we have:
t = √(10)
Therefore, the answer is C. √10 seconds.