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Elina [12.6K]
2 years ago
6

⎧

Mathematics
1 answer:
MrRissso [65]2 years ago
7 0

Answer:

f(n)=-5-3n

Step-by-step explanation:

Given the recursive formula of a sequence

f(1)=−8

f(n)=f(n−1)−3

We are to determine an explicit formula for the sequence.

f(2)=f(2-1)-3

=f(1)-3

=-8-3

f(2)=-11

f(3)=f(3-1)-3

=f(2)-3

=-11-3

f(3)=-14

We write the first few terms of the sequence.

-8, -11, -14, ...

This is an arithmetic sequence where the:

First term, a= -8

Common difference, d=-11-(-8)=-11+8

d=-3

The nth term of an arithmetic sequence is determined using the formula:

T(n)=a+(n-1)d

Substituting the derived values, we have:

T(n)=-8-3(n-1)

=-8-3n+3

T(n)=-5-3n

Therefore, the explicit formula for f(n) can be written as:

f(n)=-5-3n

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A window is 21 inches wide, and its perimeter is 112 inches. What is the length of the window?
Kazeer [188]

Answer:

The length of the window is 35 inches.  

Step-by-step explanation:

Perimeter of an object can be found using the general formula:  P = 2W + 2L, where P = perimeter, W = width and L= length.  Since both the width and perimeter of the window are given, we can plug these values into the formula to solve for the missing variable 'L':  112 = 2(21) + 2L, or 112 = 42 + 2L.  We can then use inverse (opposite) operations to isolate the variable and solve.  Whatever we do to one side of the equation, we do to the other.  We will start by subtracting 42 from each side:  112 - 42 = 42 - 42 + 2L or 70 = 2L.  Next, we divide both sides by 2 to solve for L:  70/2 = 2L/2 or L = 35.  So, the final length of the window is 35 inches.  

8 0
3 years ago
A car needs 3 gallons of gas for 70 miles. How much gas would it need for 105 miles?
galben [10]
315 is the answerd for 3X105 is 105
4 0
3 years ago
Read 2 more answers
Please help fast will give brainliest
MrRa [10]

Answer:

MN = 160

Step-by-step explanation:

We know that arc MN = arc NO

17g - 10 = 14g+ 20

Subtract 14g from each side

3g -10 = 14g-14g+20

3g -10 =20

Add 10 to each side

3g = 20+10

3g = 30

Divide by 3

3g/3= 30/3

g= 10

We want the arc MN

17g - 10

17(10) - 10

170 -10

160

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2 years ago
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zlopas [31]

Answer:

Step-by-step explanation:

We can calculate probability by looking at the outcomes of an experiment or by reasoning about the possible outcomes.

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