The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

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 equal sign and the answer on the other.

6y + 4 = 3 + 7y
6y = 3 + 7y - 4
6y - 7y = 3 - 4
-y = -1
y = \( \frac{-1}{-1} \)
y = 1

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

-4a + y = -4
y = -4 + 4a

then substitute the result (-4 - -4a) into the second equation:

-3a + 9(-4 + 4a) = 1
-3a + (9 x -4) + (9 x 4a) = 1
-3a - 36 + 36a = 1
-3a + 36a = 1 + 36
33a = 37
a = \( \frac{37}{33} \)
a = 1\(\frac{4}{33}\)

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 4 x 1) + (2 x 1 x 2) + (2 x 4 x 2)
sa = (8) + (4) + (16)
sa = 28