* Danny wants to earn $500,000 by the time he retires. He puts a huge bonus of $20,000 in an
account. He does not plan on putting any more money in the account. If the account has an
annual interest rate of 11.5%, how long until Danny can retire with $500,000?”

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Step-by-step explanation:

The question is asking:

After how many years, 20,000 will become 500,000 at an annual interest of 11.5%?

So, we need compound growth formula shown below to solve this:

F is future value

P is present amount

r is rate of interest

t is the time of year

Given,

F = 500,000

P = 20,000

r = 11.5% = 11.5/100 = 0.115

t is what we want to find

Now, we take natural log of both sides and solve for t:

Its is going to take about 29.57 years, rounding, 30 years

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)