The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{40}{56} \) = \( \frac{\frac{40}{8}}{\frac{56}{8}} \) = \( \frac{5}{7} \)

April scored 79% on the test meaning she earned 79% of the possible points on the test. There were 400 possible points on the test so she earned 400 x 0.79 = 316 points. Each question is worth 4 points so she got \( \frac{316}{4} \) = 79 questions right.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-9z² x 7z⁵
(-9 x 7)z^{(2 + 5)}
-63z⁷

The equation for this sequence is:

a_n = a_n-1 + 8

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 8
a₆ = 33 + 8
a₆ = 41