Mathematics, 20.07.2021 20:30 julietmusyoki5

Riley wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 4.5% and the other bank is offering a rate of 4.5% compounded annually. Which is the better deal?

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Answer from: mia2286

The bank that offers compound interest should get Riley more money.

let's assume he puts 10,000 in each account, and he is saving for 10 years.

the account that gives him simple interest will give him .045 * 10,000 * 10 = 4500 in interest, which gives him a total of 14,500 at the end of 10 years.

the account that gives him annual compound interest will give him 10,000 * 1.045 ^ 10 = 15,529.69422 at the end of the 10 years.

the difference is that he is earning interest on his interest in the annual compound account, while he is only earning interest on his principal in the simple interest account.

Hope this helps. Good luck !!

Answer from: Quest

2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation

step-by-step explanation:

equation

you are asked to write the equation

expression = 0

using the given expression. when you do that, you have

2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

(x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

-6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

x - 3 = 0

x = 3 . . . add 3 to both sides of the equation

x +2 = 0

x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.