The length of a box is 5 inches less than twice its width. What is the length, l, in terms of the width, w, of the box?
Start by pulling information from the question. We will use l to represent the length and w to represent the width. If the length of the box is 5 inches less than twice the width, then l = 2w - 5. "Twice the width" is equal to 2w, and 5 inches less than that means that 2w - 5 must equal the length, l.
Solve for x of the following function: x^2 + 8x + 8 = -8
In order to solve this problem, we must begin by factoring the equation. By adding 8 to each side, we obtain the equation x^2 + 8x + 16 = 0. This equation can then be factored into the equation (x + 4) * (x + 4) = 0. Since one of the two parts of the equation must be equal to 0, x + 4 = 0, so x is equal to -4.
What is the slope of a line with the equation 10x - y = 3 ?
The equation of a line is often written in the form y = mx + b. The variables x and y represent the x and y positions of a point on a graph, m represents the slope of the line, and b is the y-intercept. To rearrange the equation above, we can add y to each side. This will produce the equation 10x = 3 + y. If we subtract 3 from each side, we will have the equation 10x - 3 = y. Since this form resembles the general form we have above (y = mx + b), we can see that the slope of the line is 10, since m = 10.