Please help me by checking the following answers for me(There are 3 problems that I need someone to check).

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! :)

For 3, I don't see anything wrong with the work unless the initial equation is supposed to be sqrt(4x)-6=12 in which case the squaring wasn't done correctly, but based off what I see there D IS correct. For 4, A is the correct answer. You cannot take the square root of a -ve number. For 5, the correct answer is C. you have 2(10)/t^2=2, which leads to 20=2t^2. Then, 10=t^2 which therefore leaves t=sqrt(10)

Thank you, Dayton! :)

Sure! Let me help you check the answers for these problems:

3. The correct answer is B. The student did not properly isolate the variable after squaring both sides of the equation. The correct work would be: (√(4x-6))^2 = (12)^2, which simplifies to 4x - 6 = 144. Then, isolating the variable, we have 4x = 150, and solving for x gives x = 37.5.

4. The correct answer is C. ±5. To solve this quadratic equation, you would start by moving the constant term to the other side to get 5x^2 = -125. Then divide both sides by 5 to get x^2 = -25. Taking the square root of both sides gives x = ±5.

9. The correct answer is C. √10 seconds. To solve for the time elapsed, we can rearrange the formula a = 2d/t^2 to solve for t. This gives t^2 = 2d/a, so t = √(2d/a). Plugging in the given values (d = 10m, a = 2m/s^2) gives t = √(2*10/2) = √10 seconds.

So, the correct answers are:
3. B. The student did not properly isolate the variable after squaring both sides of the equation.
4. C. ±5.
9. C. √10 seconds.

Hope that helps! Let me know if you have any other questions.

3. To check the first problem, we can start by substituting the value of x obtained by the student back into the original equation (√(4x-6)=12) and see if it holds true. Let's do that:

Given x = 37 1/2, we have √(4(37 1/2)-6)=12.

Evaluating the expression inside the square root: 4(37 1/2)-6 = 150 - 6 = 144.

Taking the square root of 144: √144 = 12.

Since the left side of the equation equals the right side, we can conclude that the value of x = 37 1/2 is indeed a correct solution. This means the mathematical work shown is correct. Therefore, the correct answer is:

D. The mathematical work is correct.

4. To solve the second problem, we need to isolate the variable x. Let's follow the steps:

Start with the equation: 〖5x〗^2+3=-122

Subtract 3 from both sides: 〖5x〗^2 = -125

Divide by 5 on both sides to isolate x^2: x^2 = -25

Now, take the square root of both sides: √(x^2)=√(-25)

Remember that the square root of -25 is not a real number. Therefore, there is no real solution to this equation. The correct answer is:

A. No solution.

9. To find the total time elapsed, we can rearrange the equation a = 2d/t^2 to solve for t:

Given a = 2 m/s^2 and d = 10 meters, we have 2 = 2(10)/t^2.

Simplifying, we get 2 = 20/t^2.

To isolate t^2, we multiply both sides by t^2: 2t^2 = 20.

Now divide both sides by 2: t^2 = 10.

To find t, we take the square root of both sides: √(t^2) = √10.

Since time cannot be negative, we disregard the negative solution. Therefore, the correct answer is:

C. √10 seconds.