To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(6a)(5ab) - (9a²)(4b)
(6 x 5)(a x a x b) - (9 x 4)(a² x b)
(30)(a¹⁺¹ x b) - (36)(a²b)
30a²b - 36a²b
-6a²b

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

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 = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

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 = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.

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

-9a + y = -7
y = -7 + 9a

then substitute the result (-7 - -9a) into the second equation:

-5a - 6(-7 + 9a) = -5
-5a + (-6 x -7) + (-6 x 9a) = -5
-5a + 42 - 54a = -5
-5a - 54a = -5 - 42
-59a = -47
a = \( \frac{-47}{-59} \)
a = \(\frac{47}{59}\)