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Sholpan [36]
2 years ago
8

Find the 55th term of the arithmetic sequence 2, -18,-38

Mathematics
1 answer:
Simora [160]2 years ago
5 0

Answer:

-1078

Step-by-step explanation:

n=0 is the first term in the sequence.

Every next term is 20 less then the previous term.

In Mathematics you can write this as follows:

f(n) = f(0) - (n-1)*20

f(n) = f(0) - {(n-1)*20}

f(n) = f(0) - {(20n) -20}

Attention: Please note that -1 * -20 = +20

f(n) = f(0) - 20n + 20

Check yourself, find f(2):

f(0) = 2

f(2) = 2 - 20*2 + 20

f(2) = 2 - 40 + 20

f(2) = 2 - 20

f(2) = -18

Check yourself once more, find f(3):

f(0) = 2

f(3) = 2 - 20*3 + 20

f(3) = 2 - 60 + 20

f(3) = 2 - 40

f(3) = -38

Now just find f(55):

f(55) = 2

f(55) = 2 - 20*55 + 20

f(55) = 2 - 1100 + 20

f(55) = 2 - 1080

f(55) = -1078

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Step-by-step explanation:

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3 years ago
What is the answer to this solution. -7r−4≥ 4r+2
tia_tia [17]

Answer:

The solution is:

-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}

Please check the attached line graph below.

Step-by-step explanation:

Given the expression

-7r-4\ge \:4r+2

Add 4 to both sides

-7r-4+4\ge \:4r+2+4

Simplify

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Subtract 4r from both sides

-7r-4r\ge \:4r+6-4r

Simplify

-11r\ge \:6

Multiply both sides by -1 (reverses the inequality)

\left(-11r\right)\left(-1\right)\le \:6\left(-1\right)

Simplify

11r\le \:-6

Divide both sides by 11

\frac{11r}{11}\le \frac{-6}{11}

Simplify

r\le \:-\frac{6}{11}

Therefore, the solution is:

-7r-4\ge \:\:4r+2\quad \::\quad \:\begin{bmatrix}\mathrm{Solution:}\:&\:r\le \:\:-\frac{6}{11}\:\\ \:\:\mathrm{Decimal:}&\:r\le \:\:-0.54545\dots \:\\ \:\:\mathrm{Interval\:Notation:}&\:(-\infty \:\:,\:-\frac{6}{11}]\end{bmatrix}

Please check the attached line graph below.

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2 years ago
Find the perimeter of a square with side a. Are the perimeter of the square and the length of its side directly proportional qua
inna [77]

The perimeter of a square with side a = 7.2 cm is 28.8 cm. Yes there exists a direct proportional relationship between Side length and Perimeter of square

<h3><u>Solution:</u></h3>

Given that side of square "a" = 7.2 cm

We have to find the perimeter of square

<em><u>The perimeter of square is given as:</u></em>

Perimeter of square = 4a

Where "a" represents the length of side of square

Substituting the given value a = 7.2 cm in above formula, we get perimeter of square

Perimeter of square = 4(7.2) = 28.8 cm

<em><u>Are the perimeter of the square and the length of its side directly proportional quantities?</u></em>

\begin{array}{l}{\text { perimeter of square }=4 a=4 \times \text { length of side }} \\\\ {\frac{\text { perimeter of square }}{\text { length of side }}=4}\end{array}

The Perimeter is equal to a constant times the Side length, or the Perimeter divided by the Side length is equal to four. So this is definitely a proportional relationship between Side length and Perimeter.

Two values are said to be in direct proportion when an increase in one results in an increase in the other.

So when length of sides increases, perimeter also increases

Hence perimeter and length of side of square are directly propotional quantities

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Add the variables to the equation.
V = 24 x 10 x 13

Solve
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So the volume of the gift box is 3120 cm
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