Ava has $500 to put into a savings account. The interest rate for the simple interest account is 5.20%, which is represented by the function P(t)=500+26t. The interest rate for the compound interest account is 3.25%, which is represented by the function P(t)=500(1.0325)t. Ava wants to know how long she needs to keep the money in the account to make the compound savings account a better deal. Which statements are true? Select all that apply.

The compound interest account will always have more money than the simple interest account.

The simple interest account will always have more money than the compound interest account.

Within the first 10 years, the compound interest account will surpass the simple interest account.

It takes more than 25 years for the compound interest account to surpass the simple interest account.

In year 10, the compound interest account will have about $70 more than the simple interest account.

In year 10, the simple interest account will have about $70 more than the compound interest account.

i think the answer is b)

step-by-step explanation:

answer: 25.4 units

step-by-step explanation: radius = 12.7 units

diameter = twice the radius

diameter = 12.7 x 2

= 25.4

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.