You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

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

7a + x = 9
x = 9 - 7a

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

6a - 2(9 - 7a) = -3
6a + (-2 x 9) + (-2 x -7a) = -3
6a - 18 + 14a = -3
6a + 14a = -3 + 18
20a = 15
a = \( \frac{15}{20} \)
a = \(\frac{3}{4}\)

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).

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.

(7a)(3ab) + (4a²)(6b)
(7 x 3)(a x a x b) + (4 x 6)(a² x b)
(21)(a¹⁺¹ x b) + (24)(a²b)
21a²b + 24a²b
45a²b

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

c² = a² + b²
c² = 9² + 5²
c² = 81 + 25
c² = 106
c = \( \sqrt{106} \)