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Sladkaya [172]
3 years ago
5

What is the general rule for the arithmetic sequence? 15, 12, 9, 6, … A. 3n – 18 B. 6(3 – n) C. 3n + 12 D. 18 – 3n

Mathematics
1 answer:
slavikrds [6]3 years ago
3 0
A1 = first term
a1 = 15
---------------------------------------------
d = common difference 
d = (second term) - (first term)
d = a2 - a1
d = 9-12
d = -3
The negative common difference indicates that the terms are decreasing
Each time we subtract 3, or add -3, to get the next term.
----------------------------------------------
nth term of arithmetic sequence
an = a1 + d(n-1)
an = 15 + (-3)(n-1)
an = 15- 3n + 3
an = 18 - 3n

Answer is choice D
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AfilCa [17]

Answer:

\frac{15}{4802}, \frac{15}{9604}, \frac{9}{2401}, \frac{9}{4802}

Step-by-step explanation:

The bag has a total of (4+2+3+5) = 14 balls. Set up the proportions:

Red: \frac{4}{14}

green: \frac{2}{14}

yellow: \frac{3}{14}

blue: \frac{5}{14}

Now solve!

Removing 1 yellow, 1 red, 1 green, and 1 blue = \frac{3}{14} \cdot \frac{4}{14}  \cdot \frac{2}{14}  \cdot \frac{5}{14} =\frac{15}{4802}

Removing 1 blue, 1 green, 1 green, and 1 yellow = \frac{5}{14} \cdot \frac{2}{14}  \cdot \frac{2}{14}  \cdot \frac{3}{14} =\frac{15}{9604}

Removing 1 red, 1 red, 1 yellow, and 1 yellow = \frac{4}{14} \cdot \frac{4}{14}  \cdot \frac{3}{14}  \cdot \frac{3}{14} =\frac{9}{2401}

Removing 1 green, 1 yellow, 1 yellow, and 1 red = \frac{2}{14} \cdot \frac{3}{14}  \cdot \frac{3}{14}  \cdot \frac{4}{14} =\frac{9}{4802}

4 0
2 years ago
Explain how to find the missing exponent given the base and the value
drek231 [11]

Answer:

To find the value of missing exponent, we have to split the number which is in other side of equal sign (which is not having power) as the multiple of base of the missing exponent.

On both sides, powers have the same base, so their exponents must be equal.

Step-by-step explanation:

<h3>Problem 1:</h3>

Write the missing exponent:

25=5^x

Let x be the missing exponent.

To find the value missing exponent, we have to split the number which is in the left side as the multiple of the base of the missing exponent.

That is,

25=5*5 or 5^2

Now,

5^2=5^x

Powers have the same base so their exponent must be equal.

Hence the missing exponent is 2

6 0
3 years ago
77+ 2(3x – 5) = 8 – 3(2x + 1)<br> 78 2 + 3(2 -7) – 0 - 13 I 1).
nika2105 [10]

Answer:

-31/6

Step-by-step explanation:

77+2(3x-5)=8-3(2x+1)

77+6x-10=8-6x-3

77-10+6x=8-3-6x

67+6x=5-6x

67+6x-(-6x)=5

67+6x+6x=5

67+12x=5

12x=5-67

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3 0
3 years ago
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I took the quiz

5 0
3 years ago
The credit remaining on a phone card (in dollors) is a linear function of the total calling trime made with the card ( in minute
KATRIN_1 [288]

After 85 minutes of calls, there are $27.25 left on the card.

<h3>What is the remaining credit after 85 minutes of calls?</h3>

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y = a*x + b

Where a is the slope.

If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:

a = \frac{y_2 - y_1}{x_2 - x_1}

In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)

(points of the form (time, dollars)).

So the slope is:

a = \frac{32.2 - 36.7}{52 -22} = -0.15

The linear equation is then:

y = -0.15*x + b

To find the value of b, we use the point (22. 36.7)

36.7 = -0.15*22 + b

36.7 + 0.15*22 = b = 40

Then the linear equation is:

y = -0.15*x +40

The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.

y = -0.15*85 + 40 = 27.25

This means that after 85 minutes of calls, there are $27.25 left on the card.

If you want to learn more about linear equations:

brainly.com/question/1884491

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7 0
2 years ago
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