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).

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

9c + z = -8
z = -8 - 9c

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

-2c + 7(-8 - 9c) = 1
-2c + (7 x -8) + (7 x -9c) = 1
-2c - 56 - 63c = 1
-2c - 63c = 1 + 56
-65c = 57
c = \( \frac{57}{-65} \)
c = -\(\frac{57}{65}\)

The area of a parallelogram is equal to its length x width:

a = l x w
a = a x b
a = 5 x 9
a = 45

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 = \( \sqrt{a} \) = \( \sqrt{16} \) = 4

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 = 4² + 4²
c² = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)

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.