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Sphinxa [80]
3 years ago
6

Write down in terms of n, an expression for the nth term

Mathematics
1 answer:
Nimfa-mama [501]3 years ago
7 0

Answer:

a_{n} = - 7n - 1

Step-by-step explanation:

There is a common difference between consecutive terms , that is

- 15 - (- 8) = - 22 - (- 15) = - 29 - (- 22) = - 36 - (- 29) = - 7

This indicates the sequence is arithmetic with nth term

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 8 and d = - 7 , then

a_{n} = - 8 - 7(n - 1) = - 8 - 7n + 7 = - 7n - 1

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Answer:

3 inches

Step-by-step explanation:

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4 0
3 years ago
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Calculate the slope of the line that passes through (12,15) and (10, 21). Reduce answer to lowest terms if
gulaghasi [49]

Answer:

-3

Step-by-step explanation:

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3 0
2 years ago
A company’s profit in dollars is modeled by the equation p(x) = –0.5x2 + 100x, where x represents the number of units sold.
serg [7]

Answers:

a. The company needs to sell 100 units to reach the maxmum profit.

b. The company's maximum profit is $5,000.

Solution:

a. How many unit does the company need to sell to reach the maximum profit?

p(x)=-0.5x^2+100x

This is a quadratic equation, and its graph is a parabola vertical (because the veriable "x" is square). Comparing with the general form:

p(x)=ax^2+bx+c; a=-0.5, b=100, c=0

a=-0.5<0 (negative), then the parabola opens downward, and it has a maximimun value (maximum profit) at its vertex.

We can find the abscissa of the vertex (units that the company needs to sell to reach the maximum profit using the following formula:

x=-b/(2a)

Replacing b by 100 and a by -0.5 in the formula above:

x=-100/[2(-0.5)]

x=-100/(-1)

x=100

The company needs to sell 100 units to reach the maximum profit.


b. What's the company's maximum profit?  

To determine the maximum profit we substitute the value of "x" obrained in part "a" in the quadratic equation:

x=100→p(100)=-0.5(100)^2+100(100)

p(100)=-0.5(10,000)+10,000

p(100)=-5,000+10,000

p(100)=5,000

The company's maximum profit is $5,000.

6 0
3 years ago
You cut a 54-inch rope into four pieces. Twoof the pieces are the same length, a thirdpiece is twice as long as each of the twoe
antiseptic1488 [7]

Let's use the variable x to represent the length of the first and second pieces.

If the third piece has twice the length of the first and second, its length is 2x.

If the fourth piece has half the length of the first and second, its length is 0.5*x.

Adding all four pieces and equating to 54 inches, we have:

\begin{gathered} x+x+2x+0.5x=54 \\ 4.5x=54 \\ x=\frac{54}{4.5} \\ x=12 \end{gathered}

So the length of each piece is:

12 inches, 12 inches, 24 inches and 6 inches.

5 0
1 year ago
Reese deposited $7500 for two years into a money market account. At the end of two years, she earned $1200 interest. What rate o
icang [17]

Answer:

She deposited $7500. So it is the principal.

At the end of  years, she had total of $8700.

So the total amount is $8700 and the time period is 2 years.

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We need the rate of interest.

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⇒R = 1200*100/7500*2

⇒R = 120000/15000 = 8%

Rate of interest is 8%

Step-by-step explanation:

6 0
3 years ago
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