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zalisa [80]
2 years ago
12

Write a short description of the pattern in this sequence of six numbers and then follow that pattern to write the next three nu

mbers in the sequence 1/5 2/8 3/11 4/14 5/17 6/20
Mathematics
1 answer:
denpristay [2]2 years ago
8 0

Answer: The next three terms are \dfrac{7}{23},\dfrac{8}{26},\dfrac{9}{29}

Step-by-step explanation:

Since we have given that

\dfrac{1}{5},\dfrac{2}{8},\dfrac{3}{11},\dfrac{4}{14},\dfrac{5}{17},\dfrac{6}{20}

After analyzing the above pattern, we get that

In numerator , numbers are run in consecutive manner.

In denominator, number is added to 3 to get the next term.

So, the general form would be \dfrac{n}{3n+2}

So, the next three terms would be

\dfrac{7}{3\times 7+2}=\dfrac{7}{23}\\\\\dfrac{8}{3\times 8+2}=\dfrac{8}{26}\\\\\dfrac{9}{3\times 9+2}=\dfrac{9}{29}

Hence, the next three terms are

\dfrac{7}{23},\dfrac{8}{26},\dfrac{9}{29}

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Answer:

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HOPE THIS HELPS

3 0
3 years ago
Simplify: <br>5√3+4√12-2√75​
svlad2 [7]

Answer:

8 + 5\sqrt{3}-10\sqrt{7}

Step-by-step explanation:

i just wrote 5\sqrt{3} as a decimal

times 2 with 4\sqrt{1} and

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3 0
3 years ago
F(x) = x + 4 and g(x) = 2x + 3, evaluate each expression.
Rom4ik [11]

Answer:

15.~f(g(2))=\Large\boxed{11}\\

16.~g(f(2.5))=\Large\boxed{16}

17.~g(f(-5))=\Large\boxed{1}

18.~f(g(-5))=\Large\boxed{-3}

Step-by-step explanation:

<h3>Given information</h3>

f(x)=x+4

g(x)=2x+3

<h3>Question 15. f(g(2))</h3>

<u>Substitute values into the first function</u>

g(2)=2(2)+3

g(2)=4+3

g(2)=7

<u>Substitute the values of the first function into the second</u>

f(g(2))=f(7)

f(7)=(7)+4

f(7)=\Large\boxed{11}

<h3>Question 16. g(f(2.5))</h3>

<u>Substitute values into the first function</u>

f(2.5)=(2.5)+4

f(2.5)=6.5

<u />

<u>Substitute the values of the first function into the second</u>

g(f(2.5))=g(6.5)

g(6.5)=2(6.5)+3

g(6.5)=13+3

g(6.5)=\Large\boxed{16}

<h3>Question 17. g(f(-5))</h3>

<u>Substitute values into the first function</u>

f(-5)=(-5)+4

f(-5)=-1

<u>Substitute the values of the first function into the second</u>

g(f(-5))=g(-1)

g(-1)=2(-1)+3

g(-1)=-2+3

g(-1)=\Large\boxed{1}

<h3>Question 18. f(g(-5))</h3>

<u>Substitute values into the first function</u>

g(-5)=2(-5)+3

g(-5)=-10+3

g(-5)=-7

<u>Substitute the values of the first function into the second</u>

f(g(-5))=f(-7)

f(-7)=(-7)+4

f(-7)=\Large\boxed{-3}

Hope this helps!! :)

Please let me know if you have any questions

7 0
1 year ago
Which of the following shows a circle circumscribed about a triangle?
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Answer: The first option.

Step-by-step explanation:

1. By definition,  when a circle circumscribed about a triangle it passes through all the vertices of that triangle (As you know, a triangle has three vertices).

2. As you can see in the figure attached, the only circle that passes through three vertices of the triangle is the the circle of the first optin. Therefore, you can conclude that that circle is circumscribed about the triangle.

5 0
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it can not be a function because functions only have ONE input to each output

5 0
3 years ago
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