To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

5x⁴ + 2x⁴
(5 + 2)x⁴
7x⁴

To fill a 4 gallon tank exactly halfway you'll need 2 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{2 \text{ gallons}}{1 \text{ gallons}} \) = 2

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 24 meters so the equation becomes: 2w + 2h = 24.

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

2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h

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

w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4

Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m²

The equation for this sequence is:

a_n = a_n-1 + 3

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 + 3
a₆ = 13 + 3
a₆ = 16

Latoya scored 98% on the test meaning she earned 98% of the possible points on the test. There were 270 possible points on the test so she earned 270 x 0.98 = 264 points. Each question is worth 3 points so she got \( \frac{264}{3} \) = 88 questions right.