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.