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Serga [27]
3 years ago
15

Find the first term and common ratio for the geometric sequence a2 =2.5,a4=62.5

Mathematics
1 answer:
fenix001 [56]3 years ago
6 0

Answer:

a1 = 0.5; common ratio = 5

Step-by-step explanation:

Let the common ratio = r

a2 = 2.5

a3 = 2.5r

a4 = 2.5r * r = 2.5r^2

We are told a4 = 62.5, so

2.5r^2 = 62.5

Divide both sides by 2.5

r^2 = 25

r = 5

a2 = a1 * r

a1 = a2/r = 2.5/5 = 0.5

Answer: a1 = 0.5; common ratio = 5

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Find the number the comes next 1.2.6,21.88,?​
Nataly_w [17]

Answer

455

Step-by-step explanation:

(1×1) + 1 = 2

(2×2) + 2 = 6

(6×3) + 3 = 21

(21×4)+4 = 88

(88×5)+5 = 445

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CAN SOMEbody please help me
tensa zangetsu [6.8K]
Https://www.calculatorsoup.com/calculators/geometry-solids/surfacearea.php
use this calculator it’s super helpful with lots of these kinds of questions!
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2 years ago
Please I really need help
ohaa [14]

9514 1404 393

Answer:

  • scale factor: 3
  • rule: (x, y) ⇒ (3x +15, 3y -24)
  • center: (-7.5, 12)

Step-by-step explanation:

The scale factor can be found by comparing the length of CB to the length of RQ.

  B-C = (-2, 8) -(-4, 9) = (2, -1)

  Q-R = (9, 0) -(3, 3) = (6, -3)

The length of RQ is clearly 3 times the length of CB, so the scale factor (k) is ...

  ratio of corresponding differences = 6/2 = -3/-1 = 3 . . . . . scale factor

__

We know that for dilation about a point O, the distance from O is multiplied by the scale factor. For dilation of point B to point Q, this means ...

  k(B -O) = (Q -O)

Solving for Q, we get ...

  Q = kB -kO +O . . . . this is what our dilation rule will look like.

The quantity O-kO can be found by subtracting kB:

  Q -kB = O -kO = O(1 -k)

This is what we need for our dilation rule.

  Q -kB = (9, 0) -3(-2, 8) = (9+6, 0-24) = (15, -24)

So, our dilation rule is ...

  (x, y) ⇒ k(x, y) +(15, -24)

  (x, y) ⇒ (3x +15, 3y -24) . . . . . dilation rule

__

The center of dilation can be found from ...

  (Q -kB)/(1 -k) = O

  O = (15, -24)/(1 -3) = (-7.5, 12)

The center of dilation is (-7.5, 12).

_____

<em>Additional comments</em>

On the graph, the center of dilation can be found by drawing a line through a point and its image. (Points are always dilated along a line through the center of dilation.) The intersection of two such lines is the center of dilation.

On this graph, the center is just above the top edge of the chart, at point (-7.5, 12). You can see this if you carefully draw lines BQ and AP.

You usually have coordinates for two original points and two image points, so finding the scale factor the way we did is not difficult. If you just have one point on the original and the image, the scale factor is found by finding their distances from the center of dilation. Each image point is k times as far as each original point from that center.

7 0
2 years ago
I NEED HELP SOMEONE ASAP
Dvinal [7]

Answer:  x⁴y²⁰

Step-by-step explanation: Distribute the exponent ⁴ over the parentheses

(x y⁴)⁴ becomes x⁴y¹⁶  (multiply exponents)

then take the 4th root of y¹⁶  (divide the exponent of the radicand by the index)  ⁴√y¹⁶  becomes y⁴

Then multiply the factors. Add exponents

x⁴y¹⁶ * y⁴  becomes x⁴y²⁰

8 0
2 years ago
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