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° - 52° = 78°

So, d° = 52° + 78° = 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°

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 9 x 4) + (2 x 4 x 7) + (2 x 9 x 7)
sa = (72) + (56) + (126)
sa = 254

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

a² + 18a + 46 = 4a - 3
a² + 18a + 46 + 3 = 4a
a² + 18a - 4a + 49 = 0
a² + 14a + 49 = 0

Next, factor the quadratic equation:

a² + 14a + 49 = 0
(a + 7)(a + 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, (a + 7) must equal zero:

If (a + 7) = 0, a must equal -7

So the solution is that a = -7

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).

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

a(a - y)
1(3)(3 + 4)
1(3)(7)
(3)(7)
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