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Fofino [41]
3 years ago
6

Find the 8th term of the arithmetic sequence -2x+5−2x+5, -7x+8−7x+8, -12x+11, ...

Mathematics
1 answer:
miss Akunina [59]3 years ago
7 0

Answer:

  -37x+26

Step-by-step explanation:

The x-coefficients have the sequence ...

  -2, -7, -12, ...

which has first term -2 and common difference of (-7 -(-2)) = -5. Then the 8th x-coefficient is ...

  -2 + (-5)(8 -1) = -37

__

The constants have the sequence ...

  5, 8, 11, ...

which has first term 5 and common difference 8 -5 = 3. Then the 8th constant term is ...

  5 +(3)(8 -1) = 26

The 8th term of the sequence is -37x +26.

_____

The general term of an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 +d(n -1)

In the above, we have used n=8 to find the 8th term.

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or </span><span>interval notations: x</span>∈(-5;4)
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3 years ago
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AleksAgata [21]

Answer:

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Step-by-step explanation:

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Read 2 more answers
Charlie runs a book rental business. He currently charges $3 per book and rents out an average of 38 books a day.
liberstina [14]

Answer:

b(x) = (3+0.5x) (38-4x)

Step-by-step explanation:

Let the generated revenue per day be b(x)

Let x be the number for every 50cents($0.5) price increase

Formula to be used to generate the revenue generated is expressed using the formula:

b(x) = Price × Quantity

Next is to derive the price and quantity function in terms of x.

For the price:

If he currently charges $3 per book

Let derive the price function for the model and x number of price increase for every 50 cents, then

Price = ($0.5 of x)+$3

Price = $3+$0.5x

Price = $(3+0.5x)

For the quantity:

Number of books rent out per day = 38

If for every 50cents increase in rental price x, the average business can expect to lose 4 rentals a day, then the total lost per quantity = 4x

Quantity per time = Number of books rent out daily - loss on each book

Quantity = $(38-4x)

Next is to substitute the price and quantity function into the revenue formula above:

Revenue = Price × Quantity

Revenue = (3+0.5x)(38-4x)

Hence the equation that models this scenario, where b(x) is the revenue generated and x is the number of 50 price increases is b(x) = (3+0.5x)(38-4x)

7 0
3 years ago
How does the graph of g(x)=2⌈x⌉ differ from the graph of f(x)=⌈x⌉?
andrezito [222]

Answer:

B is the Answer.

Step-by-step explanation:

A transformation of a function can be represented by

a(bx - h) + k

where a is the vertical stretch or compression, b is the horizontal stretch or compression. H is the shift horizontally and k is the shift vertically.

The new function has a 2 instead of 1 on the orginally function. The function will stretch since 2 is greater than 1.

B is the answer.

5 0
3 years ago
What is the value of y?
zubka84 [21]

Answer:

y = 40

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

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3y+60 = 180

Subtract 60 from each side

3y+60-60 = 180-60

3y = 120

Divide each side by 3

3y/3 = 120/3

y = 40

7 0
3 years ago
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