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Vinil7 [7]
3 years ago
11

Which of the following are geometric sequences? Check all that apply.

Mathematics
1 answer:
kolezko [41]3 years ago
6 0

Answers:

<h2>C & D</h2>

Step-by-step explanation:

There are two general types of sequences that follow a pattern, geometric and arithmetic. Let's see the difference between the two:

An arithmetic sequence is produced by adding the same number to all the terms in the sequence.

EXAMPLE:

5, 7, 9, 11, 13, 15, 17 (The number 2 is added to all terms)

To figure out if a sequence is arithmetic, subtract the first term from the second, then the second from the third and so on until you have checked all the terms.

7 - 5 = 2

9 - 7 = 2

11 - 9 = 2

13 - 11 = 2

15 - 13 = 2

17 - 15 = 2

All results equal 2, so the sequence is arithmetic

From your list: The following sequences are arithmetic

A. 5, 10, 15, 20, 25 (common difference of 5)

The next type of sequence is the geometric sequence.

A geometric sequence is produced when the all the terms in the sequence are multiplied or divided by the same number.

EXAMPLE:

100, 50, 25 (Each term is divided by 2)

To figure this out, we divide each term in the sequence by the next term.

100 / 50 = 2

50 / 25 = 2

All results are two, so this sequence can be confirmed to be geometric

From your list: The following sequences are geometric

C. 10, 5, 2.5, 1.25, 0.625, 0.3125 (common quotient of 2)

D. -9, -3, -1, -1/3, -1/9, -1/27 (common quotient of -3)

There is one final type of sequence, which has no common difference, sum, quotient, or product.

EXAMPLE:

5, 6, 8, 9, 11, 12, 14, 15

This sequence has a pattern, the differences between the numbers are not common.

6 - 5 = 1

8 - 6 = 2

9 - 8 = 1

11 - 9 = 2

12 - 11 = 1

14 - 12 = 2

15 - 14 = 1

From your list: The following sequences are neither geometric nor arithmetic

B. 1, 1, 2, 3, 5, 8, 13 (No pattern)

I'n always happy to help :)

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Answer: f(x) =3^{-x}-4

Step-by-step explanation:

Some transformations for a function f(x) are shown below:

If f(x)+k, the function is translated up "k" units.

If f(x)-k, the function is translated down "k" units.

If -f(x), the function is reflected across the x-axis.

If f(-x), the function is reflected across the y-axis.

Therefore, knowing those transformations and given the exponential parent function:

f(x) = 3^x

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3 years ago
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3 years ago
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g100num [7]

Heya!

Question #15:

To find the perimeter of the object, you can count the amount of squares that are on the outside of the object. After you country all around the object, the perimeters is 22 units (Option D)

Question #16:

Since we know the total perimeter, we can divide by the amount of sides a hexagon has because all of the sides are the same length. A hexagon has 6 sides. 42 / 6 = 7 inches (Option A)

Question #17:

To calculate the perimeter of the rectangle, you can add all the sides together. First, find common denominators.

6 1/2 = 6 2/4 and 3 1/4

Now, add all the sides together.

6 2/4 + 6 2/4 + 3 1/4 + 3 1/4 = 19 1/2 cm (Option B)

Question #18:

We can find the perimeter of the semi circle and square separately. Only take the perimeter of the square using 3 sides since the fourth sides is in the semi circle.

8 + 8 + 8 = 24 inches

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