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2 years ago

Find the common ratio. Write the answer in lowest terms. 8+12+18+27+...

Mathematics

1 answer:

kozerog [31]2 years ago

4 0

Answer:

$r=\dfrac{3}{2}$

Step-by-step explanation:

Consider the sequance

$a_1=8\\ \\a_2=12\\ \\a_3=18\\ \\a_4=27\\ \\...$

Note that

$\dfrac{a_2}{a_1}=\dfrac{12}{8}=\dfrac{3}{2}\\ \\ \\\dfrac{a_3}{a_2}=\dfrac{18}{12}=\dfrac{3}{2}\\ \\ \\\dfrac{a_4}{a_3}=\dfrac{27}{18}=\dfrac{3}{2}\\ \\...$

So, common ratio is

$r=\dfrac{3}{2}=1\dfrac{1}{2}$

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A walkway forms one diagonal of a square playground. The walkway is 14 m long. How long is a side of the playground?

Vilka [71]

Answer: The side of the playground is around 10 meters long

Step-by-step explanation:

use the diagonal as the hypotenuse of a right triangle, where the sides of the square form the legs of said triangle.

Usually

$a^{2} +b^{2} =c^{2}$

since we know a and b are the same length (sides of a square are congruent) we would have

$a^{2} +a^{2} =c^{2} \\2a^{2} =c^{2}$

We know that c is 14 so

$2a^{2} =14^{2} \\2a^{2} =196\\a^{2} =98\\a=\sqrt{98} \\a= 9.999$

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2 years ago

Can anyone help me out?

Lana71 [14]

Answer:

3y= -42

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Step-by-step explanation:

3y= -42

-42/3= -14

y= -14

3 0

2 years ago

The surface area of a sphere is 576pi square units. Which choice represents the volume of the sphere?

Leona [35]

Answer:

$\large\boxed{V=2304\pi}$

Step-by-step explanation:

The formula of a surface area of a sphere:

$S.A.=4\pi R^2$

R - radius

We have

$S.A.=576\pi$

Substitute and solve for R:

$4\pi R^2=576\pi$ <em>divide both sides by π</em>

$4R^2=576$ <em>divide both sides by 4</em>

$R^2=144\to R=\sqrt{144}\\\\R=12$

The formula of a volume of a sphere:

$V+\dfrac{4}{3}\pi R^3$

Substitute:

$V=\dfrac{4}{3}\pi(12^3)=\dfrac{4}{3}\pi(1728)=(4)\pi(576)=2304\pi$

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2 years ago

Jenna's class brought in 40 pieces of fruit for a celebration and 32 pieces of fruit were eaten. What percentage of the fruit wa

Pepsi [2]

Answer:

20%

Step-by-step explanation:

40 pieces total

32 pieces eaten

40 - 32 = 8

8 pieces not eaten

Percentage = (part / whole) x 100%

Percentage = (8 / 40) x 100% = 0.2 x 100%

Percentage = 20%

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2 years ago

Read 2 more answers

Write 4x2(–2x2 + 5x3) in standard form. Then classify it by degree and number of terms.

umka2103 [35]

$20x^5-8x^4$ polynomial of the 5th degree, with two terms.

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3 years ago