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3 years ago

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Which of the following represents the correct expansion of (x + 2)^5?

1 answer:

otez555 [7]3 years ago

8 0

(x + 2)^5 = (x + 2) (x + 2) (x + 2)(x + 2)(x + 2) =
(x2 + 4x + 4)(x2+4x+4)(x+2) = ( x4 + 4x3 + 4x2 + 4x3 + 16x2 + 16x + 4x2 +16x + 16)(x+2) = ( x4 + 8x3 + 24x2 + 32x + 16)(x+2) = ( x5 + 8x4 + 24x3 + 32x2 + 16x + 2x4 + 16x3 + 48x2 + 64x + 32) =
x5 + 10x4 + 40x3 + 80x2 + 80x + 32
Answer D

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An exponential function f(x)= ab^x passes through the points (0,10) and (3,1250). What are the values of a and b?

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Answer:

a = 10 and b = 5

Step-by-step explanation:

We write out f(x)= ab^x for x = 0 and x = 3 to create two equations in a and b that must be solved simultaneously:

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This tells us that 10 = a*1, or a = 10.

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Could someone help me with B

pishuonlain [190]

Answer:

$a_n = 12 - 3n$

Step-by-step explanation:

The first term is 9.

Term 1 is 9.

Term 2 is 9 - 3.

Term 3 is 9 - 2(3).

Term 4 is 9 - 3(3).

Term 5 is 9 - 4(5)

Notice the pattern in terms 3 through 5. For each term, subtract 1 less than the term number multiplied by 3 from 9.

For term n, you subtract 1 less than n times 3 from 9.

The nth term is 9 - (n - 1) * 3

$a_n = 9 - (n - 1) \times 3$

Now we simplify the expression on the right side.

$a_n = 9 - 3(n - 1)$

$a_n = 9 - 3n + 3$

The expression for the nth term is

$a_n = 12 - 3n$

Let's see if it works.

n = 1

$a_n = 12 - 3(1) = 12 - 3 = 9$

n = 2

$a_n = 12 - 3(2) = 12 - 6 = 6$

n = 3

$a_n = 12 - 3(3) = 12 - 9 = 3$

n = 4

$a_n = 12 - 3(4) = 12 - 12 = 0$

n = 5

$a_n = 12 - 3(5) = 12 - 15 = -3$

n = 6

$a_n = 12 - 3(6) = 12 - 18 = -6$

As you can see, following this rule fro the nth term, we got the same first siz terms you got above. Our answer is correct.

Answer: $a_n = 12 - 3n$

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