To multiply terms with radicals, multiply the coefficients and radicands separately:

3\( \sqrt{7} \) x 5\( \sqrt{7} \)
(3 x 5)\( \sqrt{7 \times 7} \)
15\( \sqrt{49} \)

Now we need to simplify the radical:

15\( \sqrt{49} \)
15\( \sqrt{7^2} \)
(15)(7)
105

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

7\( \sqrt{75} \) - 9\( \sqrt{3} \)
7\( \sqrt{25 \times 3} \) - 9\( \sqrt{3} \)
7\( \sqrt{5^2 \times 3} \) - 9\( \sqrt{3} \)
(7)(5)\( \sqrt{3} \) - 9\( \sqrt{3} \)
35\( \sqrt{3} \) - 9\( \sqrt{3} \)

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 = \( 55mph \times 9h \)
495 miles

The equation for this sequence is:

a_n = a_n-1 + 7

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 + 7
a₆ = 29 + 7
a₆ = 36

Latoya scored 78% on the test meaning she earned 78% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.78 = 94 points. Each question is worth 2 points so she got \( \frac{94}{2} \) = 47 questions right.