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Nastasia [14]
2 years ago
9

The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).

Mathematics
1 answer:
kramer2 years ago
5 0

Given:

The sequence is:

16,80,400,...

To find:

The 6th term of the given sequence.

Solution:

We have,

16,80,400,...

Here, the first term is:

a=16

The ratio between consecutive terms are:

\dfrac{80}{16}=5

\dfrac{400}{80}=5

The given sequence has a common ratio 5. So, the given sequence is a geometric sequence.

The nth term of a geometric sequence is:

a_n=a(r)^{n-1}

Where, a is the first term and r is the common ratio.

Substitute a=16,r=5,n=6 to get the 6th term.

a_6=16(5)^{6-1}

a_6=16(5)^{5}

a_6=16(3125)

a_6=50000

Therefore, the 6th term of the given sequence is 50000.

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dalvyx [7]
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3 0
3 years ago
If the streets of a city are straight lines and the intersections are points, show how Principle 2 and Principle 3 might be illu
Naily [24]

Step-by-step explanation:

In the plane geometry Abeka, second edition, it is given :

Principle 2 states that between any two points, only one straight line can be drawn.

And according to principle 3 two straight lines interacts at one point only.

Thus this can be well illustrated by two straight lines which are represented by the streets of a city and these two streets intersects at a point.

6 0
3 years ago
The measure of central angle XYZ is 1.25 radians. What is the area of the shaded sector?
galben [10]
A sector is the area bounded by two radii and the included arc.
To calculate for the area of the sector, you’ll use the formula A=n/360(pi)(radius)^{2}.
The n in the formula refers to the measure of the central angle in degrees.
The given data in the problem is in radians, convert it by multiplying 1.25 by \frac{180}{ \pi }.
Now input the converted value to the formula of finding the area of the sector.<span> 

</span>
3 0
3 years ago
Read 2 more answers
Please show me how you got the answer. Will give brainliest.
umka21 [38]

Answer:          410 possible points

To solve for the possible points in the course, use a proportion and cross multiply.

<h2>What is a proportion?</h2>

A proportion is two fractions that are equal to each other. For the fractions to be equal, they are proportionate. In our math problem, percentage is proportionate the the number of points.

The fractions represent information you have, and one variable will represent what you are solving for.

<h2 /><h3>Given</h3>

Your points = 361

Points to get an 'A' = your points + 8

'A' = 90% of possible points

<h3>Find the points needed for an 'A' at 90%</h3>

Points to get an 'A' = your points + 8

= 361 + 8

= 369

<h3>State variables</h3>

let <em>x</em> be the amount of possible points

<h3 /><h3>Write a proportion</h3>

We know the number of points for 90% is 369 points. Remember that 90% is the same as 90/100.

Keep the information with the same units inside the same fraction. Here, percentage is represented by the first fraction. Points is represented by the second fraction.

\displaystyle{\frac{90}{100}=\frac{369}{x}}

<h3>Solve</h3>

We can solve using cross multiplication. This is when we multiply each numerator by the denominator from the other fraction.

90x = 369*100        Simplify by multiplying.

90x = 36,900            Isolate the variable <em>x</em>.

\displaystyle{\frac{90x}{90} = \frac{36,900}{90}}           Divide both sides by 90 to cancel out 90 on the left.

\displaystyle{x = \frac{36,900}{90}}              Divide.

x = 410                    Solved for <em>x</em>, representing the possible points.

∴ The possible points in the art course is 410.

Learn more about finding a missing number given percentage here: brainly.com/question/26535441

4 0
1 year ago
Factorise:<br> 8 x 3 + 729 +10800² + 486X.
hjlf

Answer:

(2x+9)  ^3

Step-by-step explanation:

 (((8 • (x3)) +  729) +  (22•33x2)) +  486x

 ((23x3 +  729) +  (22•33x2)) +  486x

Factoring:  8x3+108x2+486x+729  

 8x3+108x2+486x+729  is a perfect cube which means it is the cube of another polynomial  

 In our case, the cubic root of  8x3+108x2+486x+729  is  2x+9  

 Factorization is  (2x+9)3

Hope this helped

8 0
3 years ago
Read 2 more answers
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