Answer:
The equation for the general term of the sequence is:
[tex]a_{n} = -6(-\frac{2}{3})^{n-1}[/tex]
The sequence converges to 0.
Step-by-step explanation:
First, we need to find the formula for the general term of the sequence, which is a geometric sequence, meaning that it has a common ratio, given by:
[tex]r = \frac{4}{-6} = \frac{-\frac{8}{3}}{4} = -\frac{2}{3}[/tex]
The equation of a geometric sequence has the following format:
[tex]a_{n} = a_{1}(r)^{n-1}[/tex]
In which [tex]a_{1}[/tex] is the first term.
In this question, we have that [tex]a_{1} = -6, r = -\frac{2}{3}[/tex]. So, the equation for the general term is:
[tex]a_{n} = a_{1}(r)^{n-1} = -6(-\frac{2}{3})^{n-1}[/tex]
To find if the sequence converges, we find the limit of [tex]a_{n}[/tex] as [tex]n \rightarrow \infty[/tex]. So
[tex]\lim_{n \rightarrow \infty} a_{n} = \lim_{n \rightarrow \infty} -6(-\frac{2}{3})^{n-1} = -6(-\frac{2}{3})^(\infty) = 0[/tex]
A number between 0 and 1 elevated to infinity tends to 0, so the sequence converges to zero.
The required nth term is [tex]a_n=a(-\frac{2}{3} )^n[/tex]
Geometric Series:The Geometric series formula or the geometric sequence formula gives the sum of a finite geometric sequence.
Given that,
First Term=[tex]-6[/tex]
Common Ratio is,
[tex]\frac{4}{-6}=\frac{2}{-3} \\\frac{4}{\frac{-8}{3} }= \frac{2}{-3}[/tex]
So, the given sequence is in a geometric sequence.
So, the nth term of the given series is,
[tex]a_n=ar^{n-1}\\=-6(-\frac{2}{3} )^{n-1}\\a_n=a(-\frac{2}{3} )^n[/tex]
Learn more about the topic Geometric Series:
https://brainly.com/question/26042879
m + 4 = 17
Please help
Answer: m=13
Step-by-step explanation:
Basically you solve this by finding out what plus 4 equals 17. You can do this by subtracting 4 from 17.
17-4=13
This is how you find the value of m.
Answer:
13!
Step-by-step explanation:
first subtract 4 on both sides!
m+4=17
m+4-4=17-4
simplify/subtract 17-4=13!
(also stop reporting my comment and my answers!)
A statistical question produces data that varies.
Which question below will produce data that varies?
How many days are in a leap year?
How many quarts are in a gallon?
How many senses are there?
How many students are in each class?
Answer:
How many students will be varied.
all other questions have definite answers.
HELP I WILL NAME YOU BRAINIEST !!!!!!!!!!!!!
Go to your math tools and open the Graph tool to graph Gwen’s and Tristan’s equations. Hint: To create the graph, select the correct relationship and then enter the values for the variables. You will need to change the scales for the x- and y-axes. When deciding the scale, ask yourself what x and y stand for, and what would be reasonable amounts for their minimum and maximums.
Do the two lines intersect? Why or why not? What does this mean in terms of the situation? If the lines intersect, at what point do they intersect and what does this point mean in terms of the situation? Paste a screenshot of your graph in the space provided.
Part E
Go to your math tools and open the Graph tool to graph Gwen’s and Keith’s equations. Be sure to remove Tristan’s equation before adding Keith’s equation.
Do the two lines intersect? Why or why not? What does this mean in terms of the situation? If they intersect, at what point do they intersect and what does this point mean in terms of the situation? Paste a screenshot of your graph in the space provided.
Answer:
The graph of the equations (y = 10x + 100), (y = 10x), and (y = 12.5x) can be drawn by using the rules of transformation.
Given :
y = 100 + 10x
y = 10x
y = 12.5x
The following steps can be used to sketch the graph of the given line (y = 100 + 10x):
Step 1 - First sketch the graph of (y = x).
Step 2 - Then Multiply the x-axis by a factor of 10. The resulting graph is the graph of (y = 10x)
Step 3 - Then find the y-intercept from the given equation. Then draw the line that passes through (0,100). The resulting line is the graph of (y = 100 + 10x).
The following steps can be used to sketch the graph of the given line (y = 10x):
Step 1 - First sketch the graph of (y = x).
Step 2 - Then Multiply the x-axis by a factor of 10. The resulting graph is the graph of (y = 10x)
The following steps can be used to sketch the graph of the given line (y = 12.5x):
Step 1 - First sketch the graph of (y = x).
Step 2 - Then Multiply the x-axis by a factor of 12.5. The resulting graph is the graph of (y = 12.5x)
The graph of all the equations together is attached below.
Red line shows the graph of (y = 10x + 100).
Blue line shows the graph of (y = 10x)
Green line shows the graph of (y = 12.5x)
Step-by-step explanation:
Evaluate 20-z when z=-12 please
answer is 8
Step-by-step explanation:
z=12
20-z= 20-12
=8
what is the nearest percent increase from $65 and $144
Answer:
Step-by-step explanation:
I got 121.54% as the percent of increase.
2.1, 1.4, 0.7, 0, ...
What is the average of all multiples of five from 5 to 50 inclusive
Answer:
add all the multiples together then divide by 10?
275/10 = 27.5
Garth's taxable income last year was $97,450. According to the tax table
below, how much tax does he have to pay if he files with the Single status?
Answer:
$21,013
Step-by-step explanation:
9 times what number equals 800?
Answer:
9 times 800/9 equals 800. (Answer is 800/9)
Step-by-step explanation:
Key skills needed: Equation, Division, Fractions
1) Let's say the number is the variable "x".
2) So this means 9 times x = 800
9x = 800
3) Divide both sides by 9 and you will get x equal to 800/9. If you want this in mixed number form, it is --> 88 8/9
Hope you understood and have a nice day!! :D
88.8888888889
The equation to any of these sorts of questions is the larger number (800) divided by the smaller number (9).
You can check your answer by multiplying the quotient by the smaller number (9). If you get the larger number (800), you were correct, anything else, the equation was done wrong.
Hope this helps, if not, comment below please!!!
What is the equation of the line that passes through the point (1,3) and has a slope
of -- 32
Answer:
The equation of the line that passes through the point (1,3) and has a slope of -32.
[tex]y=-32x+35[/tex]
Please check the attached graph too.
Step-by-step explanation:
Given
Point (1, 3) The slope m = -32The point-slope form:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
m is the slope of the line (x₁, y₁) is the pointIn our case:
m = -32
(x₁, y₁) = (1, 3)
substituting m = -32 and (x₁, y₁) = (1, 3) in the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-3=-32\left(x-1\right)[/tex]
Add 3 to both sides
[tex]y-3+3=-32\left(x-1\right)+3[/tex]
Simplify
[tex]y=-32x+35[/tex]
Therefore, the equation of the line that passes through the point (1,3) and has a slope of -32.
[tex]y=-32x+35[/tex]
Please check the attached graph too.
Subtract.
(6x + 5) - (x + 3)
A. 5x + 2
B. 6x + 2
C! 6x + 8
D. 5x + 8
Answer: 5x + 2
Step-by-step explanation:
Answer:
Its A. 5x + 2
Step-by-step explanation:
a p e x ! <3
Which undefined geometric term can be described as a one-dimensional set of points that has no beginning or end?
point
line
X plane
distance
the correct answer is “ line “
Answer:
Sorry but I'm sort of confused, are you asking the question or not because you said "the correct answer is “ line “ so I'm not sure if you're giving the answer or asking a question.
Step-by-step explanation:
I am confused with this
Answer:
Answer is A) HL
Step-by-step explanation:
Line a is parallel to line b. If the measure of 2 is 78 degrees, what is the measure of 8?
Answer:
78 degrees
Step-by-step explanation:
From the diagram;
<2 = 78 degrees
<2 = <6 = 78degrees (corresponding angles)
<6 = <8 = 78 degrees (vertically opposite angles)
Hence the measure of 8 is 78 degrees
Answer:
78 degrees
Step-by-step explanation:
I NEED HELP ASAP!!
Select all the correct answers.
You're given two side lengths of 3 centimeters and 5 centimeters. Which measurement can you use for the length of the third side to construct a
valid triangle?
8 centimeters
6 centimeters
ооооо
4 centimeters
10 centimeters
2 centimeters
Answer:
8 and 2
Step-by-step explanation:
5+3=8
5-3=2
What force is needed to accelerate a 56Kg mass across a surface with an acceleration of 7m/s2?
Answer:
use the calculator i sent you
Step-by-step explanation:
There are 8 boys in a class, and these boys make up 40% of the total students. How many students in the class are girls? *
Answer:
12 girls
Step-by-step explanation:
do you want an explanation?
plz brainliest :)
What is the missing step in the given proof
Answer:definition of a supplementary angle
Step-by-step explanation:
in order to get to the next step you need to state what equation you’re substituting for
Please help me I have no clue what this is steps would be great I have a exam and I have no clue what I'm doing anyways... HELP MEEEEEE if you have time to help me with this that would be amazing.
Answer:
D. Infinitely Many Answers
Step-by-step explanation:
Simply the function -x+4(x-2)
-x+4x-8
3x-8
Notice it is the same with the the first function
Thus, they are the same function, so they intersect each other infinitely many.
Sameen bought 2 1/5 pounds of carrots for $6.60 at the rate how much would 1pound of carrots cost
Answer:
$3.00
Step-by-step explanation:
What is the greatest common factor of 15 and 21?
The Greatest Common Factor of 15 and 21 is 3.
What is Greatest Common Factor?The greatest common factor is the largest number that is a factor of two or more numbers (GCF). The greatest number (factor) divides them, yielding a Natural number. Once all of the number's variables have been identified, there are a handful that are shared by both. The greatest common factor is the largest number found among the common factors. The GCF is often referred to as the Highest Common Factor (HCF)
Given:
We have to find the greatest common factor of 15 and 21 .
So factorizing each number
15 = 3 x 5
21 = 3 x 7
So, the Greatest Common Factor is 3.
Learn more about Greatest Common Factor here:
brainly.com/question/11221202
#SPJ2
Please just help me now! Offering 59 Brainly points!
Answer:
number 2
Step-by-step explanation:
brainly plz
What is 3 2/3-1/9? What is the answer?
Answer:
3 5/9 or 32/9
Step-by-step explanation:
Answer:
3 5/9
Step-by-step explanation:
Which expression is equivalent to 4t + 3t
Answer:
C
Step-by-step explanation:
i think
Answer:
C. 7t
Step-by-step explanation:
What we know:
We are looking for an expression equal to 4t + 3t.
There are 4 choices:
1. 7t²
2. 7 + 2t
3. 7t
4. 12t
The answer does end in t, but is only one term, so B is eliminated.
An exponent is not involved either, so A is also eliminated.
It shows an addition sign, not multiplication, so D is also out.
This leaves C, which is 7t.
Doing this mathematically, add like terms.
4t + 3t
7t
Someone please check my work
I need help to get good grade
Answer:
scale factor: 3
Step-by-step explanation:
For this I will take both A and A' points. So A is (2,2) and A' is (6,6) and since the shape increased in size that means our scale factor must be greater than 1. So all that we have to do is know is how did we get from this x value to that x value or in other words 2 times what equals 6 and it's 3. Then we would do the same for the y value but since it would be the same 2 times what equals 6 and it's still 3 so 3 is the scale factor.
A school club sold 143 balloons for $3.50 each. They bought 150 balloons for $1.29 each, plus $8.92 for shipping. How much did they make selling balloons?
Answer:
OMG, Nickkkkk. It's Nyla from your 3rd block math classs. Lol, I literally looked up this question with no luck of an answer.
Step-by-step explanation:
The school club made $298.08 by selling the balloons.
What is Profit?Profit is calculated as total revenue less total expenses.
Given that, a school club sold 143 balloons for $3.50 each. They bought 150 balloons for $1.29 each, plus $8.92 for shipping.
Cost of balloons when they brought them = 1.29*150 = $193.5
Total cost = $193.5 + (shipping price) = $193.5 + $8.92
Total cost = $202.42
Cost at which they sold the balloons = 143*$3.50 = $500.5
Therefore, their total profit = $500.5 - $202.42 = $298.08
Hence, The school club made $298.08 by selling the balloons
For more references on Profit, click;
https://brainly.com/question/15573174
#SPJ2
8x+6x=112+1x+7x=89
solve this
A triangle has side lengths of ( 5.9 k + 9.3 m ) (5.9k+9.3m) centimeters, ( 3.6 k − 3.9 n ) (3.6k−3.9n) centimeters, and ( 3.5 n + 3.4 m ) (3.5n+3.4m) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer:
(9.5k + 12.7m -0.4n) cm
Step-by-step explanation:
(5.9k+9.3m) + (3.6k−3.9n) + (3.5n+3.4m) = 9.5k + 12.7m -0.4n
What is x/6 + 1 = 4 and what is 7x + 4 = 11
Answer:x/6 + 1 = 4
x= 18
7x+ 4=11
x=1
Step-by-step explanation:
For both questions do inverse operation.
Look at pic to see how it was solved ;)
hope it helps