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3 years ago

Find the third, fifth, and seventeenth terms of the sequence described by each explicit formula

Mathematics

2 answers:

Sedaia [141]3 years ago

7 0

Are you familiar with that?

Iteru [2.4K]3 years ago

4 0

Answer:

3rd, 5th and 17th terms are 14, 20, 56 respectively.

Step-by-step explanation:

The given question is incomplete; find the complete question in the attachment.

In this question explicit formula has been given as,

f(n) = 8 + 3(n -1)

We have to find the 3rd, 5th and 17th term of the sequence described by the explicit formula given above.

For 3rd term,

Substitute n = 3 in the formula,

f(3) = 8 + 3(3 - 1)

= 8 + (3 ×2)

= 8 + 6

= 14

Similarly. for n = 5,

f(5) = 8 + 3(5 - 1)

= 8 + 3(4)

= 8 + 12

= 20

For n = 17,

f(17) = 8 + 3(17 - 1)

= 8 + 3(16)

= 8 + 48

= 56

Therefore, 3rd, 5th and 17th terms are 14, 20 and 56 respectively.

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Step-by-step explanation:

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13. You are buying plants and soil for your garden. The soil costs $4.00 per bag and the plants cost $10.00 each. You want to bu

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Answer:

Part a) The system of linear inequalities is

y\geq 5y≥5

4x+10y\leq 1004x+10y≤100

Part b) The graph in the attached figure

Part c) A solution could be (5,7) (see the explanation)

Step-by-step explanation:

The complete question is

You are buying plants and soil for your garden. The soil cost 4.00 dollars per bag and the plants cost 10.00 each. You want to buy at least 5 plants and can spend no more than10.00each.Youwanttobuyatleast5plantsandcanspendnomorethan100

a) write a system of linear inequalities to model the situation

b) Graph the system of linear inequalities

c) Identify and interpret a solution to the system

Part a) write a system of linear inequalities to model the situation

Let

x -----> the number of bags of soil

y ----> number of plants

we know that

The word "at least" means "greater than or equal"

y\geq 5y≥5 ----> inequality A

The word "no more" means "less than or equal"

4x+10y\leq 1004x+10y≤100 ----> inequality B

Part b) Graph the system of linear inequalities

we have

y\geq 5y≥5 ----> inequality A

4x+10y\leq 1004x+10y≤100 ----> inequality B

using a graphing tool

the solution is the triangular shaded area

see the attached figure

Part c) Identify and interpret a solution to the system

we know that

If a ordered pair is a solution to the system, then the ordered pair must lie on the shaded area of the solution

i take the point (5,7)

the point (5,7) lie on the shaded area of the solution

is a solution of the system

That means ----> You are buying 5 bags of soil and 7 plants for your garden

Verify the solution

Remember

If a ordered pair is a solution to the system, then the ordered pair must satisfy both inequalities

Verify inequality A

7\geq 57≥5 ----> is true

The ordered pair (5,7) satisfy inequality A

Verify inequality B

4(5)+10(7)\leq 1004(5)+10(7)≤100

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The ordered pair (5,7) satisfy inequality B

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3 years ago

Solve for kkk. 8(10-k)=2k8(10−k)=2k

Ivan

Answer:

k = 8

Step-by-step explanation:

We know that 8(10-k) = 2k so:

8(10−k)=2k

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8(10−k)=2k

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Subtract 2k from both sides:

−8k+80−2k=2k−2k

−10k+80=0

Subtract 80 from both sides:

−10k+80−80=0−80

−10k=−80

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$\frac{-10k}{-10} =\frac{-80}{-10}$

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