A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

3b - 9 > \( \frac{b}{9} \)
9 x (3b - 9) > b
(9 x 3b) + (9 x -9) > b
27b - 81 > b
27b - 81 - b > 0
27b - b > 81
26b > 81
b > \( \frac{81}{26} \)
b > 3\(\frac{3}{26}\)

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -3. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -2) and (2, -4) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = -\(\frac{1}{2}\)x - 3

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

9a⁹ + 9a⁹ = 18a⁹

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)