Rita's company reimburses her expenses on food, lodging, and conveyance during business trips. the company pays $55 a day for food and lodging and $0.45 for each mile traveled. rita drove 300 miles and was reimbursed $2335.

part a: create an equation that will determine the number of days x on the trip (3 points)

part b: solve this equation justifying each step with an algebraic property of equality. (6 points)

part c: how many days did rita spend on this trip? (1 points)

Givens

Notice that the variable must represents the traveled miles, because it variates. So, the expression would be

Where represents the amount of money and represents the number of miles traveled. Notice that $55 is the ratio of change of variable which represents days.

We know that and .

First, we replace the number of miles and the amount of money.

Second, we solve the product.

Third, we subtract 135 at each side of the equation.

Fourth, we divide by 55 each side of the equation.

Therefore, Rita spent 40 days on this trip.

3x3 = 9 and 2x2 = 4

step-by-step explanation:

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).