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alexandr1967 [171]
3 years ago
6

F is between E and G. EF=3X, EG= 11x-2, FG= 5x+16. Find the value of the variable

Mathematics
1 answer:
Salsk061 [2.6K]3 years ago
3 0

9514 1404 393

Answer:

  x = 6

Step-by-step explanation:

The sum of segments is used:

  EF +FG = EG

  3x +(5x +16) = 11x -2 . . . . substitute given expressions

  8x +18 = 11x . . . . . . . . add 2

  18 = 3x . . . . . . . . subtract 8x

  6 = x . . . . . . divide by 3

The value of the variable is 6.

__

<em>Check</em>

The segment lengths are ...

  EF = 3x = 3·6 = 18

  FG = 5x+16 = 5·6 +16 = 46

  EG = 11x -2 = 11·6 -2 = 64 = 18+46 . . . answer is correct

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nevsk [136]

Answer:

( 1 , -2 , 4 , -8 , 16 , ... )

( 9 , 3 , 1 , 1/3 , 1/9 , ... )

Step-by-step explanation:

A geometric sequence has a common ratio in consecutive terms,

In sequence,

1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}.....

\frac{1/2}{1}\neq \frac{1/6}{1/2}\neq \frac{1/24}{1/6}\neq \frac{1/120}{1/24}...

i.e.

1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}..... is not a Geometric sequence,

1 , -2 , 3 , -4 , 5 , ...

\frac{-2}{1}\neq \frac{3}{-2}\neq \frac{-4}{3}\neq \frac{5}{-4}...

i.e. 1 , -2 , 3 , -4 , 5 , ... is not a Geometric sequence,

In sequence,

1 , -2 , 4 , -8 , 16 , ...

\frac{-2}{1}=\frac{4}{-2}= \frac{-8}{4}= \frac{16}{-8}...

i.e. 1 , -2 , 4 , -8 , 16 , .... is a Geometric sequence,

In sequence,

0 , 1 , 0 , -1 , 0 , .....

\frac{1}{0}\neq \frac{0}{1}\neq \frac{-1}{0}\neq \frac{0}{-1}...

i.e. 0 , 1 , 0 , -1 , 0 , .....is not a Geometric sequence,

In sequence,

9 , 3 , 1 , 1/3 , 1/9 , ...

\frac{3}{9}=\frac{1}{3}= \frac{1/3}{1}= \frac{1/9}{1/3}...

i.e.  9 , 3 , 1 , 1/3 , 1/9 , ... is a Geometric sequence,

In sequence,

1 , 3 , 5 , 7 , 9 , ...

\frac{3}{1}\neq \frac{5}{3}\neq \frac{7}{5}\neq \frac{9}{7}...

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4 0
2 years ago
What is the surface area of the regular pyramid
Ugo [173]

Answer:

The answer is 144.

Step-by-step explanation:

Cause, 6 x 6 for the square is 36. For the triangle, 9 x 6 is 54, and 54 divided by 2 is 27. 27 x 4 is equal to 108. Now, we just add 108 and 36 to make 144.

6 0
3 years ago
Please help and thank you
ycow [4]

Answer:

D) 130 workers

Step-by-step explanation:

We have the equation, <em>y = 2x + 40</em>, and <em>y, 300</em> (since the y-coordinate represents the # of bottles made), so we can solve for x, <em>the number of workers needed</em>.

Substitute: <em>300 = 2x + 40</em>

Subtract: <em>260 = 2x</em>

Divide: <em>x = 130</em>

Since x = 130 when y = 300, 130 workers are required to make 300 bottles in a day.

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3 years ago
In an arithmetic series, the sum of the first 12 terms is equal to ten times the sum of the first 3 terms. If the first term is
arlik [135]

Answer:

Step-by-step explanation:

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Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

If a = 5, the expression for the sum of the first 12 terms is

S12 = 12/2[2 × 5 + (12 - 1)d]

S12 = 6[10 + 11d]

S12 = 60 + 66d

Also, the expression for the sum of the first 3 terms is

S3 = 3/2[2 × 5 + (3 - 1)d]

S3 = 1.5[10 + 2d]

S3 = 15 + 3d

The sum of the first 12 terms is equal to ten times the sum of the first 3 terms. Therefore,

60 + 66d = 10(15 + 3d)

60 + 66d = 150 + 30d

66d + 30d = 150 - 60

36d = 90

d = 90/36

d = 2.5

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S20 = 20/2[2 × 5 + (20 - 1)2.5]

S20 = 10[10 + 47.5)

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Answer:

25

Step-by-step explanation:

You add 2+3 and get 5. Then you square it to get 25.

4 0
3 years ago
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