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 = \( 15mph \times 8h \)
120 miles

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

5\( \sqrt{2} \) x 2\( \sqrt{3} \)
(5 x 2)\( \sqrt{2 \times 3} \)
10\( \sqrt{6} \)

To fill a 8 gallon tank exactly halfway you'll need 4 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{4 \text{ gallons}}{1 \text{ gallons}} \) = 4

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 6 meters so the equation becomes: 2w + 2h = 6.

Putting these two equations together and solving for width (w):

2w + 2h = 6
w + h = \( \frac{6}{2} \)
w + h = 3
w = 3 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

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 + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61