You need to find the value of b so solve the first equation in terms of y:

-8b + y = 9
y = 9 + 8b

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

-4b - 1(9 + 8b) = -6
-4b + (-1 x 9) + (-1 x 8b) = -6
-4b - 9 - 8b = -6
-4b - 8b = -6 + 9
-12b = 3
b = \( \frac{3}{-12} \)
b = -\(\frac{1}{4}\)

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

c² = a² + b²
c² = 3² + 7²
c² = 9 + 49
c² = 58
c = \( \sqrt{58} \)

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(6 + 4)(2)
a = ½(10)(2)
a = ½(20) = \( \frac{20}{2} \)
a = 10

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with b° = 165, the value of c° is 15.