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Dennis_Churaev [7]
3 years ago
5

Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15.

Mathematics
1 answer:
Naya [18.7K]3 years ago
8 0
It's a geometric sequence.

4,-12,36,... \\ \\
a_1=4 \\
r=\frac{a_2}{a_1}=\frac{-12}{4}=-3 \\ \\
a_n=a_1 \times r^{n-1} \\
a_n=4 \times (-3)^{n-1} \\
a_n=4 \times (-3)^{-1} \times (-3)^n \\
a_n=4 \times (-\frac{1}{3}) \times (-3)^n \\
a_n=-\frac{4}{3}(-3)^n

It's the sum for term 4 through term 15.

 \boxed{ \sum\limits_{n=4}^{15} (\frac{4}{3}(-3)^n)}
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Which point(s) on the diagram show(s) the solution(s) to the equation x = x2 - 2x - 8?
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Step-by-step explanation:

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3 years ago
The length of a rectangle is 5 inches more than its width, x. The area of a rectangle can be represented by the equation x 2 + 5
Arada [10]

Answer:

Width = 15 inches             Length = 20 inches

Step-by-step explanation:

The area of a rectangle is calculated using the following formula.

A = Lx   (1)

Where L is the length and x is the width of the rectangle

In this case we know that the length of the rectangle is 5 inches greater than its width. This means that:

L = x + 5   (2)

Also The area of a rectangle can be represented by the equation x^2 + 5x = 300

so to find the width x we solve the equation

x^2 + 5x -300=0   (3)

For an equation of the form ax ^ 2 + bx + c = 0 the quadratic formula is:

x=\frac{-b\±\sqrt{b^2-4ac}}{2a}

In this case note that:

a=1\\b=5\\c=-300

Then:

x=\frac{-5\±\sqrt{(5)^2-4(1)(-300)}}{2(1)}

x=\frac{-5\±\sqrt{25+1200}}{2}

x=\frac{-5\±\sqrt{1225}}{2}

x=\frac{-5\±35}{2}

x_1=\frac{-5+35}{2}  →  x_1=15

x_2=\frac{-5-35}{2}  →   x_2=-20

We take the positive solution x=15\ in

Now we use equation (2) to find L

L = x + 5

L = 15 + 5

L = 20\ in

8 0
4 years ago
Determine the next three terms in the following sequence:
IrinaVladis [17]
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4 0
4 years ago
A cell phone company charges a flat fee of 20 dollars plus 3 cents a call. What is the total bill if there was a total of 200 ca
34kurt

Answer:

Total Bill = 4006 dollars

Step-by-step explanation:

A cell phone company charges a flat fee of 20 dollars plus 3 cents a call.

If there was a total of 200 calls for the month, the total charge by the cell phone company will be.

Let me convert all to cent first

100 cent = 1 dollar

20 dollar =20 *100

29 dollar = 2000 cent

Charge by the company for a call is 2003 cent

Let me put down the equation.

1 call = 2003 cent

200 calls =( 200 calls* 2003cent)/1 call

200 calls = 200 * 2003cent

200 calls = 400600 cent

Let's convert back to dollar

100 cent = 1 dollar

400600 cent = 400600/100

400600 cent = 4006 dollars

8 0
3 years ago
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