The amount of flour you need is (2\(\frac{7}{8}\) - 1\(\frac{1}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{23}{8} \) - \( \frac{10}{8} \)) cups
\( \frac{13}{8} \) cups
1\(\frac{5}{8}\) cups

First, solve for \( \left|a + 9\right| \):

\( \left|a + 9\right| \) - 4 = 6
\( \left|a + 9\right| \) = 6 + 4
\( \left|a + 9\right| \) = 10

The value inside the absolute value brackets can be either positive or negative so (a + 9) must equal + 10 or -10 for \( \left|a + 9\right| \) to equal 10:

So, a = -19 or a = 1.

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

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 50mph \times 6h \)
300 miles

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{6} \) x \( \frac{1}{7} \) = \( \frac{2 x 1}{6 x 7} \) = \( \frac{2}{42} \) = \(\frac{1}{21}\)