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3 years ago

Write the first five terms of the geometric sequence whose first terns 6, and whose common ratio is 3.

Mathematics

1 answer:

Tasya [4]3 years ago

3 0

The first five terms of the geometric sequence is 6, 18, 54, 162 and 486

Geometric progression is given by:

$nth\ term=ar^{n-1}$

where a is the first term, r is the common ratio

Given that first term is 6, and common ratio is 3, Hence a = 6, r = 3

$First\ term=6\\\\Second \ term=6(3)^{2-1}=18\\\\Third \ term=6(3)^{3-1}=54\\\\Fourth \ term=6(3)^{4-1}=162\\\\Fifth \ term=6(3)^{5-1}=486$

The first five terms of the geometric sequence is 6, 18, 54, 162 and 486

Find out more on geometric sequence at: brainly.com/question/24355584

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8.45 At some point in the season, the Unicorns had won 60% of their basketball games. After that point, they won 8 more games an

ololo11 [35]

Answer:

The total number of games won by Unicorn is 40.

Step-by-step explanation:

We are given with a word problem
We are asked to find the number of unicorns played during the season
We can do this in two steps

Step 1: Finding the win percentage

Step 2: Finding the number of unicorns played during the season

Step 1 of 2

Let the number of games played by unicorn be x.The unicorn won 60% of the first x-10 games That is $\frac{60}{100} \times(x-10)$

Combining the 8 games we get,

$\begin{gathered}\frac{60}{100}(x-10)+8=\frac{60}{100} \times x-\frac{60}{100} \times 10+8 \\0.6 x-6+8=0.6 x+2\end{gathered}$

Step 2 of 2

The unicorn totally won 65% of the games played.

That is $\frac{65}{100} \times x=0.65 x$

Equating both the equation gives

$\begin{gathered}0.6 x+2=0.65 x \\2=0.65 x-0.6 x \\2=0.05 x \\\frac{2}{0.05}=x \\40=x\end{gathered}$

5 0

2 years ago

1/6 + 3/8 <br> A. 4/6<br> B. 4/8 <br> C. 4/14<br> D. 13/24

Naddika [18.5K]

Here is you're answer:

In order to get you're answer you need to find the common denominator then add.

$\frac{1}{6} + \frac{3}{8}$
Find the common denominator:
$CD = 48$
$= \frac{26}{48}$
Simplify:
$\frac{26}{48} \div 2 = \frac{13}{24}$
$= \frac{13}{24}$

Therefore you're answer is option D "13/24."

Hope this helps!

8 0

3 years ago

Line a is purpendicular to line b. if the slope of line a is 7 than what is the slope of line b

MA_775_DIABLO [31]

The slope of the perpendicular line b is -1/7 if the slope of the perpendicular line a is 7.

According to the question,

Line 'a' is perpendicular to the line 'b'. If the slope of the line 'a' is 7.

The condition of slopes if two lines are perpendicular m₁ m₂ = -1

(7)(m₂) = -1

m₂ = -1/7

Hence, the slope of the perpendicular line b is -1/7 if the slope of the perpendicular line a is 7.

Learn more about perpendicular lines here

brainly.com/question/2505127

#SPJ4

8 0

2 years ago

Mikayla bought 5 skirts at $x each. Three of the five skirts came with a matching top for an additional $9 each write and simpli

Alisiya [41]

To find the total cost of Mikayla's purchase, we add together the costs of the skirts and tops. The costs of the skirts can be found be multiplying the quantity bought by the cost per skirt. Same goes for the tops.

5x + 3(9)

Simplified:

5x + 27

3 0

3 years ago

Cora makes a scarf with cloth rectangles and triangles. For every 5 pieces of cloth, 2 are rectangles. She needs 15 pieces of cl

PtichkaEL [24]

Answer: There are 6 pieces of cloth are rectangles and 9 pieces of cloth are triangles.

Explanation:

Since we have given that

For every 5 pieces of cloth, 2 are rectangles

So, remaining piece will be of triangle so,

$5-2=3$

3 are triangles.

Ratio of rectangles to triangles is 2:3.

Now, she needs 15 pieces of cloth to complete her scarf,

So, Number of rectangles is needed is given by

$\frac{2}{5}\times 15\\\\=2\times 3\\\\=6$

Number of triangles is needed is given by

$\frac{3}{5}\times 15\\\\=3\times 3\\\\=9$

Hence, there are 6 pieces of cloth are rectangles and 9 pieces of cloth are triangles.

6 0

3 years ago