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dolphi86 [110]
3 years ago
8

If f(1) = 160 and f(n + 1) = –2f(n), what is f(4)?

Mathematics
1 answer:
balandron [24]3 years ago
7 0

Answer with Step-by-step explanation:

f(1) = 160 and f(n + 1) = –2f(n)

⇒ f(2)= -2×f(1)

        = -2×160

       = -320

⇒ f(3)= -2×f(2)

    = -2×(-320)

   = 640

⇒ f(4)= -2×f(3)

    = -2×640

   = -1280

Hence, Value of f(4) is:

- 1280

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Indicate the general rule for the arithmetic sequence with a3 = -12 and a8 = -37
Mandarinka [93]

Answer:

The general rule is a_n = -2 - 5(n-1)

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.

The general rule of an arithmetic sequence is given by:

a_{n} = a_1 + (n-1)d

In which a_1 is the first term and d is the common difference.

We can also find the nth term as a function of a term m, using:

a_n = a_m + (n-m)d

a3 = -12 and a8 = -37

First we find the common difference. So

a_n = a_m + (n-m)d

a_8 = a_3 + (8-3)d

-37 = -12 + 5d

5d = -25

d = -\frac{25}{5}

d = -5

So

a_n = a_1 - 5(n-1)

Finding the first term:

a_n = a_1 - 5(n-1)

Since a_3 = -12

a_n = a_1 - 5(n-1)

a_3 = a_1 - 5(3-1)

a_1 = a_3 + 10 = -12 + 10 = -2

So the general rule is:

a_n = a_1 - 5(n-1)

a_n = -2 - 5(n-1)

6 0
2 years ago
The ratio of the width to the length of a painting is 3 to 7. If the painting is 42 in. long how wide is it
belka [17]

If length is 42 inches, then width is 18 inches.

Step-by-step explanation:

We are given ratio of width to the length of a painting i.e 3 to 7. If the painting is 42 inches long, then how wide it is?

Solving:

\frac{width}{length}=\frac{width}{length}\\ \frac{3}{7}=\frac{w}{42}\\  Cross\,\,multiply:\\3*42=w*7\\126=w*7\\w=\frac{126}{7}\\w=18

So, If length is 42 inches, then width is 18 inches.

Keywords: Ratio

Learn more about Ratio at:

  • brainly.com/question/9880052
  • brainly.com/question/10781917
  • brainly.com/question/2707032

#learnwithBrainly

8 0
2 years ago
F(x)=-x^2-9x find f(-2)
Sloan [31]

Answer:

14

Step-by-step explanation:

put -2 where x is

f(x)=-x^2-9x

f(-2)= -(-2)^2 -9(-2)

f(-2)= -4 + 18

f(-2)= 14

8 0
3 years ago
Which scatterplot does NOT suggest a linear relationship between and y
iren2701 [21]
C; this is because the line of beat fit isn’t linear but curved in that one graph.
5 0
2 years ago
Advance Algebra: please help!
Irina18 [472]

Answer:

   = -x^2 -x +6

D: all real values

Step-by-step explanation:

f(x) = 4-x^2

g(x) = 2-x

f+g = 4-x^2+ 2-x

Combine like terms

     = -x^2 -x +4+2

     = -x^2 -x +6

 The domain is what values can x take

D: all real values

       

8 0
3 years ago
Read 2 more answers
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