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frozen [14]
3 years ago
10

What is a1 of the arithmetic sequence for which a3=10 and a51=−182?

Mathematics
1 answer:
LenaWriter [7]3 years ago
6 0

Answer:

a₁ = 18

Step-by-step explanation:

The n th term of an arithmetic sequence is

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₃ = 10 and a₅₁ = - 182, then

a₁ + 2d = 10 → (1)

a₁ + 50d = - 182 → (2)

Subtract (1) from (2) term by term to eliminate a₁

48d = - 192 ( divide both sides by 48 )

d = - 4

Substitute d = - 4 into (1) and evaluate for a₁

a₁ + 2(- 4) = 10

a₁ - 8 = 10 ( add 8 to both sides )

a₁ = 18

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Answer: C. Nine Months, 9/12 = 9÷12 = 0.75

Step-by-step explanation:

Hi, to answer this question we have to convert the fraction into decimals and compare:

A. Three Months, 1/4 = 1÷4 = 0.25

B. Six Months, 6/12 = 6÷12 =0.5

C. Nine Months, 9/12 = 9÷12 = 0.75

D. 1 Month, 1/12 =1÷12 = 0.083333

C. Nine Months, 9/12 = 9÷12 = 0.75

Feel free to ask for more if needed or if you did not understand something.

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3 years ago
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Flying against the wind, an airplane travels 5760 kilometers in 6 hours. Flying with the wind, the same plane travels 6300 kilom
Aleks [24]
<h2>Speed of plane = 1110 kmph</h2><h2>Speed of wind = 150 kmph</h2>

Step-by-step explanation:

Let the speed of plane be p and speed of wind be w.

Flying against the wind, an airplane travels 5760 kilometers in 6 hours.

Here

            Speed = (p-w) kmph

            Time = 6 hours

            Distance = 5760 kmph

            Distance = Speed x Time

            5760 = (p-w) x 6

               p-w = 960 -----eqn 1  

Flying with the wind, the same plane travels 6300 kilometers in 5 hours.

Here

            Speed = (p+w) kmph

            Time = 5 hours

            Distance = 6300 kmph

            Distance = Speed x Time

            6300 = (p+w) x 5

               p+w = 1260 -----eqn 2    

eqn 1 + eqn 2

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                  2p = 2220

                    p = 1110 kmph

Substituting in eqn 2

                1110 + w = 1260

                         w = 150 kmph

Speed of plane = 1110 kmph

Speed of wind = 150 kmph

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3 years ago
To paint a sunset, you make a shade of orange paint using 55 drops of red paint for every 88 drops of yellow paint. If you use 1
alexandr402 [8]
Since the ratio of red drops to yellow drops is 55:88 and you have 1515 red drops, the yellow drops needed is given as
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8 0
4 years ago
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