To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

-6c - 7x = 4c + 5x + 5
-6c = 4c + 5x + 5 + 7x
-6c - 4c = 5x + 5 + 7x
-10c = 12x + 5
c = \( \frac{12x + 5}{-10} \)
c = \( \frac{12x}{-10} \) + \( \frac{5}{-10} \)
c = -1\(\frac{1}{5}\)x - \(\frac{1}{2}\)

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 4² + 8²
c² = 16 + 64
c² = 80
c = \( \sqrt{80} \)

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(7²) + 2π(7 x 8)
sa = 2π(49) + 2π(56)
sa = (2 x 49)π + (2 x 56)π
sa = 98π + 112π
sa = 210π

A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 7 x 6) + (2 x 6 x 4) + (2 x 7 x 4)
sa = (84) + (48) + (56)
sa = 188