Tutor profile: Jessica S.
3x + 12 = 23. Solve for x.
The key thing to keep in mind is to make sure the left hand (LH) and right hand (RH) side of the equations remain equal. When solving for a variable, you have to isolate the variable to one side of the equation. So first, subtract 12 from both sides of the equation. This will give you 3x = 23 - 12 which is equal to 3x = 11. Then, to get x by itself, divide both sides of the equation by 3. So you end up with x=11/3 as the final answer.
The length, in inches, of a box is 2.5 inches less than twice its width, in inches. Which of the following gives the length, L inches, in terms of the width, W inches, of the box?
This is a typical ACT question that asks you to convert a words problem into a math equation. "The length is 2.5 inches less than twice its width" is the same as "L is 2.5 inches less than 2*W". Since "less" indicates subtraction, this can then be written as "L is 2*W - 2.5". Therefore, the final answer is L = 2W - 2.5
Find k so that the lines with equations -4x + k*y = 10 and 4y + x = -9 are perpendicular.
First, find the slope of the second equation listed. Subtracting x from both sides will result in: 4y = -x - 9. Then divide both sides by 4 will give you: y = (-1/4) * x - (9/4), which is in y=mx+b form. Thus, the slope is m = -1/4. Doing the same for the first equation listed will give you a slope of m = 4/k. Since the two lines must be perpendicular, the slope of the first equation must be the negative reciprocal of the other, meaning: 4/k=4. Thus, k=1.
needs and Jessica will reply soon.