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Contact [7]
2 years ago
12

The first five terms of a sequence are

Mathematics
1 answer:
Elena L [17]2 years ago
5 0

Answer:

(a) 7 + 3( n - 1 )

(b) 1006

Step-by-step explanation:

ARITHMETIC SEQUENCE.

The number of term of an Arithmetic progression has the formular :

nth term = a + ( n - 1 ) d

a = 7

d = 10 - 7 = 3

nth term = 7 + ( n - 1 ) 3

= 7 + 3n - 3

= 7 + 3( n - 1 )

Therefore,

the nth term of the sequence

= 7 + 3( n - 1 )

(b) For the 1000th term

= 7 + 3 ( 1000-1 )

= 7 + ( 999 )

7 + 999 = 1006

Therefore,

the 1000th term = 1006

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An airplane is loaded with cargo and ready to take off. Before it departs, an unknown number
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Answer:

b ≤ 50

Step-by-step explanation:

Since no more than 400 pounds of b number of 8 pound boxes can be taken off to ensure that the plane is in balance, this can be represented by the inequality:

8b ≤ 400

b ≤ 400/8

b ≤ 50

This means that a maximum number of 50 8 pounds boxes can be taken off the plane for a 600 pound crate to be put on ensuring that the plane is in balance.

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3 years ago
PLZ HELP its Triangle Properties and where using the 45º-45º-90º Triangle Theorem and the 30º-60º-90º Triangle Theorem.
den301095 [7]

Answer:

The answer to your questions is below

Step-by-step explanation:

4.-

In a 45°-45°-90° triangle, the length of the legs are "x" and the length of the hypotenuse is x\sqrt{2}

Then, in this problem, the length of the leg is 7 then the length of the hypotenuse will be 7\sqrt{2}

5.- In a 30°-60°-90° triangle, the length of the hypotenuse is 2x, the length of the longer leg is x\sqrt{3} and the length of the shorter leg is x.

In this problem we have the length of the hypotenuse = 20 and find x.

                          2x = 20

                             x = 20/2

                             x = 10

          longer leg = xx\sqrt{3} = 10\sqrt{3}

6.- nonzero

7.- hypotenuse = 20 cm

     Find x

                         2x = 20

                           x = 20/2

                          x = 10

   Shoter leg = x = 10 cm

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3 years ago
Read 2 more answers
Kari is on a trip to Italy. She has made a list of cities she would like to tour while she is there, as well as how much she exp
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Unit conversion is a way of converting some common units into another. Kari cannot afford to see Genoa, because it would put her $84. 48 over budget.

<h3>What are Units conversions?</h3>

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

The cost of the Kari visiting the Vatican, Rome, Naples, Venice, and Milan are €68.77, €95.41, €71.06, €113.38, and €49.69. Therefore, the total cost of visiting these places would be,

Total Cost = €68.77 + €95.41 + €71.06 + €113.38 + €49.69

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Now, as it is given that 1$ is equal to 0.6859€, therefore, if we convert the amount that is already spent by Kari to visit these places in dollars, we will get,

\rm Total\ cost = \dfrac{398.31 }{0.6859} = \$\ 580.72

The amount that is left with Kari,

\rm \text{Amount left with Kari} = (Budget\ of\ Kari)-(Total\ cost)

                                    = \$585-\$580.72\\\\=\$4.28

Also, the cost of visiting Genoa is €60.85, now, if the cost is converted to dollars we will get the cost to visit Genoa,

\text{Cost of visiting Genoa} = \dfrac{60.85}{0.6859}=\$88.72

Thus, the cost of visiting Genoa is $88.72, while the amount of budget that is left with Kari is $4.28, therefore, Kari cannot afford to see Genoa, because it would put her $84. 48 over budget.

Learn more about Units conversion:

brainly.com/question/4736731

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