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

\( \frac{-9z^9}{5z^4} \)
\( \frac{-9}{5} \) z^{(9 - 4)}
-1\(\frac{4}{5}\)z⁵

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{8}{100} \) x 6 = \( \frac{8 \times 6}{100} \) = \( \frac{48}{100} \) = 0.48 errors per hour

So, in an average hour, the machine will produce 6 - 0.48 = 5.52 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 5.52 = 93.8 error free parts were produced yesterday.

The factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 80 and 56 have in common.

To add these radicals together their radicands must be the same:

3\( \sqrt{28} \) + 5\( \sqrt{7} \)
3\( \sqrt{4 \times 7} \) + 5\( \sqrt{7} \)
3\( \sqrt{2^2 \times 7} \) + 5\( \sqrt{7} \)
(3)(2)\( \sqrt{7} \) + 5\( \sqrt{7} \)
6\( \sqrt{7} \) + 5\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).