Answer:
- Plan: separate the variable term from the constant term; divide by the coefficient of the variable.
- Steps: add 4 to both sides; collect terms; divide both sides by 3.
Step-by-step explanation:
The first step is to look a the equation to see where the variable is in relation to the equal sign, and whether there are any constants on that same side of the equal sign.
Here, the variable terms are on the left, and there is a constant there, as well. The plan for solving the equation is to eliminate the constant that is on the same side of the equation as the variable, then divide by the coefficient of the variable. To find that coefficient, we need to collect terms. In summary, the plan is to ...
- add 4 to both sides of the equation
- collect terms
- divide by the coefficient of the variable (3)
Executing that plan, the steps are ...
-2x -4 +5x +4 = 8 +4 . . . . add 4
3x = 12 . . . . . . . . . . . . . . . collect terms
x = 4 . . . . . . . . . divide by 3
It turns out that 5% of 400 is 20.
(1/20)*400=20.
So Ian was being paid £400 a week before he was given a pay rise.
slope is change in y over change in x
use 2 points from the table so -3,-21 and -6,-39
change in Y: -39 - -21 = -18
change in x = -6 - -3 = -3
slope = -18/-3 = 6
slope = 6
<h3>
Answer: -2w^2 + 25w = 25 or -2w^2 + 25w - 25 = 0</h3>
================================================================
Explanation:
Refer to the diagram below. The width is w. We have two opposite and parallel sides equal to this. The other two parallel congruent sides are L = 25-2w meters long. We start with the total amount of fencing, and then subtract off the two width values, so 25-w-w = 25-2w.
The area of the rectangle is
Area = length*width
Area = L*W
Area = (25-2w)*w
Area = 25w - 2w^2
Area = -2w^2 + 25w
Set this equal to the desired area (25 square meters) to get
-2w^2 + 25w = 25
and we can subtract 25 from both sides to get everything on one side
-2w^2 + 25w - 25 = 0
side note: The two approximate solutions of this equation are w = 1.0961 and w = 11.4039 (use the quadratic formula or a graphing calculator to find this)