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svetoff [14.1K]
3 years ago
12

The third term in an arithmetic sequence is 10 and the fifth term is 26.If the first term is a1,which is an equation for the nth

of this sequence?
Mathematics
1 answer:
Lelechka [254]3 years ago
5 0
Third Term: 10
 Fifth Term: 26

  10 + x = 26
- 10        - 10
           x = 16
16 ÷ 2 = 8

     First Term: -6
Second Term: 2
    Third Term: 10
  Fourth Term: 18
      Fifth Term: 26

-6, 2, 10, 18, 26
 +8  +8  +8  +8

a(n) = a₁ + d(n - 1)
a(n) = -6 + 8(n - 1)
a(n) = -6 + 8(n) - 8(1)
a(n) = -6 + 8n - 8
a(n) = 8n - 6 - 8
a(n) = 8n - 14

The equation for the nth term of this sequence is 8n - 14.
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Emily went to the movie theater for her birthday. A mix of adults and children attended, making a total of 22 people. Each adult
viktelen [127]

Answer:

13 children and 9 adults if the total cost is $152.5

Step-by-step explanation:

Let x children and y adults

x + y = 22 (1)

5.5x + 9y = 125.5 (2)

y = 22 - x

5.5x + 9(22 - x) = 125.5

5.5x + 198 - 9x = 125.5

-3.5x = 125.5 - 198

-3.5x = -72.5

x = 20.7

y = 22 - x = 1.3

Which is not possible

If the total cost is $152.5

x + y = 22 (1)

5.5x + 9y = 152.5 (2)

y = 22 - x

5.5x + 9(22 - x) = 152.5

5.5x + 198 - 9x = 152.5

-3.5x = 152.5 - 198

-3.5x = -45.5

x = 13

y = 22 - 13 = 9

3 0
3 years ago
PLZ answer this question tell me the date for this question 3 months after January
slavikrds [6]

Answer:

April

Step-by-step explanation:

bc you add 3 to 1 2 months after Jan is march 1 month is feb

7 0
4 years ago
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Mrs. Santos is buying binders for the students in her class. She determined that 15 binders would cost $22.50.
atroni [7]

Answer:

It will cost $42 for 28 binders

Step-by-step explanation:

We know that 15 binders = 22.50 dollars . We need to find the cost of 18, 30, 28, and 48 binders to figure out if they match up with the statements. One way to do this is to find the cost for one binder, and then multiply that by the number of binders to find the cost for a certain number of binders. For example, if one binder costs 2 dollars, five binders would cost 2 * 5 = 10 dollars.

To figure out how much one binder costs, we can use the division property of equality to divide both sides of our equation (15 binders = 22.50 dollars) by 15. We divide by 15 because anything divided by itself is equal to 1, and that would make it 1 binder = something dollars.

Applying this, we get

(15 binders)/15 = (22.5 dollars)/15

1 binder = 1.5 dollars

For 18 binders, this would cost 1.5 * 18 = 27 dollars. We know this because we add 1.5 dollars for each binder.

For 30 binders, this would cost 30*15=45 dollars

For 28 binders, this would cost 1.5 * 28 = 42 dollars

For 48 binders, this would cost 1.5*48 = 72 dollars

The only one that matches up is 28 binders for 42 dollars

8 0
3 years ago
Anyone please .help me to solve this​
Wittaler [7]
The Correct Answer Is 10
4 0
3 years ago
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SOMEBODY HELP ME OUT !!
Naddika [18.5K]

Answer:

D

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x, y ) → (y, - x ) , thus

X(- 1, - 3 ) → X'(- 3, 1 )

Y(0, 0 ) → Y'(0, 0 )

Z(1, - 3 ) → Z'(- 3, - 1 )

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3 years ago
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