The Calm Spa charges annual fee of $125 plus $10 per hour of use. The Relax Spa charges annual dues of $230 plus $7 per hour of use. For what number of hours would be cost be the same for both spas?

The total number of hours = 35 hours.

Step-by-step explanation:

The annual fee of Calm Spa = $125

Per hour charge of Calm Spa = $10

Annual fee of Relax Spa = $230

Per hour charge of Relax Spa = $7

Now we have to find the number of hours for which both have same cost.

Let the number of hours = x

Thus, 125 + 10x = 230 + 7x

10x-7x = 230 – 125

3x = 105

x = 35

The total number of hours = 35 hours.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

60 for the first and 130 for the second

step-by-step explanation: