Sandy is upgrading her internet service. fast internet charges $60 for installation $50.45 per month. quick internet has free installation but charges $57.95 per month write an equation that can be used to find the number of months for which the internet service would cost the same

Step-by-step explanation:

Given months as ,

Cost of Fast Internet:

$60 for installation and $50.45 per month for months =

Cost of Quick Internet:

Free installation and $57.95 per month for months =

We want to know in how many months BOTH COSTS WOULD BE SAME. So we EQUATE the expressions for both. We have:

This equation can be solved for x to find the number of months for which the internet service would cost the same.

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)