The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

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

9\( \sqrt{125} \) - 6\( \sqrt{5} \)
9\( \sqrt{25 \times 5} \) - 6\( \sqrt{5} \)
9\( \sqrt{5^2 \times 5} \) - 6\( \sqrt{5} \)
(9)(5)\( \sqrt{5} \) - 6\( \sqrt{5} \)
45\( \sqrt{5} \) - 6\( \sqrt{5} \)

Now that the radicands are identical, you can subtract them:

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 = \( 35mph \times 7h \)
245 miles

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

5 + (5 + 2) ÷ 4 x 5 - 4²
P: 5 + (7) ÷ 4 x 5 - 4²
E: 5 + 7 ÷ 4 x 5 - 16
MD: 5 + \( \frac{7}{4} \) x 5 - 16
MD: 5 + \( \frac{35}{4} \) - 16
AS: \( \frac{20}{4} \) + \( \frac{35}{4} \) - 16
AS: \( \frac{55}{4} \) - 16
AS: \( \frac{55 - 64}{4} \)
\( \frac{-9}{4} \)
-2\(\frac{1}{4}\)

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.