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.

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 50° - 31° = 99°

So, d° = 31° + 99° = 130°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 50° = 130°

You need to find the value of a so solve the first equation in terms of z:

-9a + z = -8
z = -8 + 9a

then substitute the result (-8 - -9a) into the second equation:

9a - 7(-8 + 9a) = -4
9a + (-7 x -8) + (-7 x 9a) = -4
9a + 56 - 63a = -4
9a - 63a = -4 - 56
-54a = -60
a = \( \frac{-60}{-54} \)
a = 1\(\frac{1}{9}\)

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

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

3b - 3y = -9b - 9y - 9
3b = -9b - 9y - 9 + 3y
3b + 9b = -9y - 9 + 3y
12b = -6y - 9
b = \( \frac{-6y - 9}{12} \)
b = \( \frac{-6y}{12} \) + \( \frac{-9}{12} \)
b = -\(\frac{1}{2}\)y - \(\frac{3}{4}\)