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Stells [14]
2 years ago
6

What is the nth term rule of the quadratic sequence below? 8,14,22,32 ,44, 58, 74...

Mathematics
1 answer:
DanielleElmas [232]2 years ago
8 0

Answer:

y=n^2+3n+4

Step-by-step explanation:

Sequence,S: 8,14,22,32 ,44, 58, 74...

First differences of S: 6,8,10,12,14,16,...

Second differences of S: 2,2,2,2,2,2,....

It is indeed a quadratic since the 1st differences that are the same are the second differences.

So the 1st term is 8. If the 0th term was listes it would be 4 since 8-4=4 and 6-4=2.

This means our quadratic it is in the form

y=an^2+bn+c where c=4.

So we have y=an^2+bn+4.

Now we can find a and b using two points from our sequence to form a system of equations to solve.

(1,8) gives us 8=a(1)^2+b(1)+4

Simplifying gives 8=a+b+4

Subtracting 4 on both sides gives: 4=a+b

(2,14) gives us 14=a(2)^2+b(2)+4

Simplifying gives 14=4a+2b+4

Subtracting 4 on both sides gives 10=4a+2b

So we have the following system to solve:

4=a+b

10=4a+2b

I'm going to solve using elimination/linear combination style.

Dividing second equation by 2 gives the system as:

4=a+b

5=2a+b

Subtract the 2nd equation from the first gives:

-1=-1a

This implies a=1 since -1=-1(1) is true.

If a+b=4 and a=1, then b=3. Because 3+1=4.

So the equation is y=1n^2+3n+4 or y=n^2+3n+4.

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3 years ago
The diagram shows a tile in the shape of a trapezium.
Ann [662]

Answer:

286cm²

Step-by-step explanation:

Let the parallel sides be 12cm and 10cm

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Area of a trapezium = 1/2(a+b) * h

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2 years ago
PLEASE HELP ASAP ILL GIVE 11 points
ser-zykov [4K]

Answer:

11

Step-by-step explanation:

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7 0
2 years ago
Read 2 more answers
Determine whether the pair of triangles below are similar. If they are similar, write the similarity criterion that can be used
Ugo [173]

Answer:

Cannot be determined

Step-by-step explanation:

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8 0
2 years ago
Mark made a scale drawing of a soccer field, using a scale of .5 cm=1m. The actual length of the field is 110 m. What is the len
nataly862011 [7]

Answer:

The length of the field on the drawing is 55 cm.

Step-by-step explanation:

Given:

Mark made a scale drawing of a soccer field.

Using a scale of .5 cm=1 m.

The actual length of the field is 110 m.

Now, to find the length of the field on drawing.

Let the length of the field on drawing be x.

As given 0.5 cm is equivalent to 1 m.

Thus, x is equivalent to 110 m.

Now, to get the length of the field on drawing by using cross multiplication method:

\frac{0.5}{1} =\frac{x}{110}

<em>By cross multiplying we get:</em>

⇒ 55=x

⇒ x=55

Therefore, the length of the field on the drawing is 55 cm.

8 0
3 years ago
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