Mathematics High School

PLEASE HELP ME ASAP

Does the series converge or diverge? If it converges, what is the sum? Show your work

Answers

Answer 1

The series is a convergence series and the sum of the series is -8/3

The type of the series

The series is given as:

[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]

The above series has the following properties:

First term; a = -4Common ratio, r = -1/2

Start by calculating the absolute value of the common ratio

Absolute value = |-1/2|

This gives

Absolute value = 1/2

The above value is less than 1.

It means that the series converges.

The sum of the series

This is calculated using:

[tex]S_{\infty} = \frac{a}{1 -r}[/tex]

So, we have:

[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]

Evaluate the sum

[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]

Evaluate the quotient

[tex]S_{\infty} = \frac{-8}{3}[/tex]

Hence, the sum of the series is -8/3

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Related Questions

Rewrite using exponential notation \root(6)((4\pi )^(3))

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[tex]~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] ~\dotfill\\\\ \sqrt[6]{(4\pi )^3}\implies (4\pi )^{\frac{3}{6}}\implies (4\pi )^{\frac{1}{2}}[/tex]

Can someone please help me with this

Answers

Answer:

6.7 km/liter

Step-by-step explanation:

c = 187 km / 28 l = 6.67 ~ 6.7 km / l to two sig figures

If given the equation y = 3(x + 5)2 - 4, what is the vertex of the parabola

Answers

Answer:

The vertex of the parabola is (5, -4).

Hope this helps!

Help me with this please

Answers

Answer:

See below

Step-by-step explanation:

1 IS a constant

9x IS a factor

9x is NOT a coefficient ( '9' is a coefficient)

yes it is a sum of three terms

9x and 1 are NOT 'like' terms

Which line is being represented by the graph?
A
y = 3/4 X -3
B
y = 3/4x + 4
C
y = -3/4x + 4
D
y = -3/4 x - 3

Answers

Answer:

The answer is C, y= -3/4 + 4

Sherri solved the equatjon 1/5(x-20)=45. For each step, write the name of the property sherri used

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Answer: The awnser is linear.

I hope this helped.

Step-by-step explanation:

What was his mistake?

Answers

Circle the first line.

His mistake was: He substituted y from 2nd equation in 1st equation incorrectly. There is a minus sign before y and it wasn't taken into the account.

The correct steps are:

2x - y = 18

2x - (4x + 2) = 18

2x - 4x - 2 = 18

-2x - 2 = 18

-2x = 20

x = -10

y = 4x + 2

y = 4(-10) + 2

y = -40 + 2

y = -38

Find the midpoint of the line segment. Please hurry 15 points!

Answers

Answer: Hope this helps you

0,0

Simplify the expression (10 + 3i)(10 - 3i).

Answers

Answer:

109

Step-by-step explanation:

[tex]\textbf{Assuming}~ i ~\textbf{as the imaginary unit, where}~ i = \sqrt{-1}~ \textbf{and}~ i^2 = -1\\\\\textbf{Given that,}\\\\~~~(10+3i)(10-3i)\\\\=10^2 -(3i)^2~~~~~~~~~~;\textbf{Difference of two squares} ~a^2 -b^2 = (a+b)(a-b)\\\\=100-9i^2\\\\=100-9(-1)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;{i^2 = -1}\\\\=100+9\\\\=109[/tex]

[tex](a-b)(a+b)=a^2-b^2[/tex]

Therefore

[tex](10 + 3i)(10 - 3i)=100-9i^2[/tex]

A membership at a yoga studio costs $35 per month.
Write an equation for the cost of the membership,that you pay if you keep your membership for months.

Answers

Answer:

35×(m)=c

Step-by-step explanation:

m=months

c=cost

help please dont know how to do this

Answers

The answer is 2.00 dollars left

can someone please answer this fast! thanks

Answers

Answer:

The choice C.

[tex] {x}^{ \frac{5}{2} } [/tex]

Step-by-step explanation:

[tex] \frac{ {x}^{3} }{ \sqrt{x} } = \frac{ {x}^{3} }{ {x}^{ \frac{1}{2} } } = {x}^{3} \times {x}^{ - \frac{1}{2} } \\ = {x}^{3 \times - \frac{1}{2} } = {x}^{ \frac{5}{2} } [/tex]

Or ;

[tex] \frac{ {x}^{3} }{ \sqrt{x} } = {x}^{2} \sqrt{x} = {x}^{2} \times {x}^{ \frac{1}{2} } \\ = {x}^{2 + \frac{1}{2} } = {x}^{ \frac{5}{2} } [/tex]

Solve the inequality.

−13x+10>17
Which inequality represents the solutions to this inequality?
a) x<7x<7

b) x>−21x>−21

c) x<−21x<−21

d) x>7x>7

Answers

The solution to inequality is less than the negative of 21. Then the correct option is C.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given below.

−(1/3)x + 10 > 17

Then the solution to the inequality will be

−(1/3)x + 10 > 17

−(1/3)x > 17− 10

−(1/3)x > 7

When the sign is changed then the equality sign also changed.

(1/3)x < −7

x < − 21

The value of x is less than the negative of 21.

Thus, the correct option is C.

More about the inequality link is given below.

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If tan theta = -3/4 and theta is in Quadrant IV, cos2theta =, and tan2theta =

Answers

Step-by-step explanation:

please mark me as brainlest

is this true or false? please help

Answers

Answer:

true jufhjjzjsjjajajw

Five dogs were running in a race. Bandit completed the race in 10 seconds after Sergeant and 30 seconds before Sally. Smokey completed the race 10 seconds before Sally and 25 seconds after Tobie. Which list correctly shows the dogs from first to last place?

A B C D

Answers

Answer:

Sergeant, Tobie, Bandit, Smokey, Sally

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find m/1.
130°
1
90°
t

Answers

The measure of the angle m1 is 110 degrees

How to determine the measure of angle m1?

The measures of the arcs are given as:

Arc 1 = 130

Arc 2 = 90

The measure of the angle is calculated using:

Angle = 0.5 * (Arc 1 + Arc 2)

So, we have:

Angle = 0.5 * (130 + 90)

Evaluate

Angle = 110

Hence, the measure of angle m1 is 110 degrees

Answers

Answer:

y=7x

Step-by-step explanation:

The job pays $7 per 1 hour so to find out how much money you get for x hours, you would multiply the hourly rate ($7) by the amount of hours (x)

Answer:

y=7x

Step-by-step explanation:

edge review 2022

WILL MARK BRAINLIEST!!

(07.05 MC)

Which of the following functions best represents the graph?

see attached

Answers

Answer:

the first option

Step-by-step explanation:

i know there's a rule to all of this but it's been a while since i've done this kind of math.

if you plug in the zeros to the equation, they solve

(-2, 0) --> (-2-2)(-2+1)(-2+2) = 0

(-1, 0) --> (-1-2)(-1+1)(-1+2) = 0

(2, 0) --> (2-2)(2+1)(2+2) = 0

The point (-2,-3) is rotated 180 degrees counterclockwise about the origin. What is the y-coordinate of the resulting image

Answers

The rotated point is (2, 3) so the y-coordinate is 3

The direction of rotation is not relevant as going clockwise results in the same location.

I need the answer quickly please

Answers

Answer:

c²=√181=13.45, or 13.5

Step-by-step explanation:

The pythagorean theorem is a²+b²=c²

Given this, we will plug in our numbers like this: 9²+10²=c²

9²+10²=181, but we have to find the square root of that.

c²=√181=13.45, or 13.5

I hope this helps!! :)

Step-by-step explanation:

We have a right triangle which allows us to use the Pythagorean Theorem

In the whole number 70,819, the place value of the digit 1 is

Answers

Answer:

ten

hope this helps....

The function f(x) is shown on the graph.

On a coordinate plane, a curved line with 3 arcs, labeled f of x, crosses the x-axis at (negative 2, 0), (negative 1, 0), (1, 0), and (3, 0), and the y-axis at (0, negative 6).

What is f(0)?

0 only
–6 only
–2, –1, 1, and 3 only
–6, –2, –1, 1, and 3 only

Answers

By using the description of the graph, we conclude that f(0) = -6 only.

The correct option is the second one.

What is f(0)?

Here we want to know the value of the function when evaluated in 0. Remember that the points on the graph of the function are of the form:

(x, f(x)).

Now, in the description of the graph you say:

"... and the y-axis at (0, negative 6)."

So we know that the graph passes through (0, -6), which means that when evaluated in 0, the function is equal to -6.

So the correct option is the second one: –6 only

If you want to learn more about graphs:

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Answer:

Step-by-step explanation:

if f(x) = 4x²-2 then f(-3) is

Answers

Step-by-step explanation:

We are going to plug -3 into the equation of f(x) = 4x²-2.

f(-3) = 4(-3)²-2

f(-3)=36-2

f(-3)=34

The answer to this question is 34.

I hope this helps!! :)

how do you distribute this
(x+5)(x-5)

Answers

see the attachment photo.

Answer:

2x-5

Step-by-step explanation:

Thats the answer

Need help with this

Answers

n = 66

Step-by-step explanation:

you can make a proportion 3/99 = 2/x

[tex] \frac{3}{99} = \frac{2}{x} [/tex]

99 * 2= 198

3 * x = 3x

so the equation would be 198 = 3x

than do 198 ÷ 3 on ur calculator

so x (or n in this context) would equal 66

How many units is -14 away from 0

Answers

Answer:

Step-by-step explanation:

|-14|=14

Germaine measured the height of a plant, H, in centimeters (cm) as a function of days, d, since he planted it in
his yard. The following table shows his data.
d 0 2 4 6 8 10 12
H(d) 8.2 9.6 11.0 12.4 13.8 15.2 16.6
What is the rate of change of the function?
O 1.7 cm per day
O 8.4 cm per day
O 1.4 cm per day
O 0.7 cm per day

Answers

The rate of change of the function the height of a plant is gotten as; D: 0.7

How to find the rate of change?

To find the rate of change, we will use the formula;

Rate of change = (y2 - y1)/(x2 - x1)

From the given table, we can solve for the rate of change by picking two consecutive points to get;

Rate of change = (9.6 - 8.2)/(2 - 0)

Rate of change = 1.4/2

Rate of change = 0.7

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On a coordinate plane, a circle has a center at (negative 2, 0). Point (negative 2, 4) lies on the circle.
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot

Does the point (1, StartRoot 7 EndRoot) lie on the circle shown?
Explain.

Yes, the distance from (–2, 4) to (1, ) is 4 units.
Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units.
No, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is not 4 units.
No, the distance from (–2, 4) to (1, StartRoot 7 EndRoot) is not 4 units.

Answers

The correct answer to where the point(1, StartRoot 7 EndRoot) lies on the circle is A. Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units

What is a Coordinate Plane?

This refers to the tool that is used to graph points on a two-dimensional plane that intersects two number lines.

Hence, given the information in the given diagram, there is a coordinate plane that shows a circle at the center that has certain values on the y and x-axis.

We can state that the point (1, StartRoot 7 EndRoot) lies on the circle shown because the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units.

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Answer: A on edge

Step-by-step explanation:

because i said so

You move left 5 units. You end at (-1, 5). Where did you start?

Answers

Answer:

(4,5)

Step-by-step explanation:

Hello!

If you move 5 units to the left, you change the x-value in (x, y) by -5.

Let the original x-value be x:

x - 5 = -1x = 4

The original x-value is 4. Since you didn't change the y-value (up/down), you can keep the same y-value for the coordinate.

The original point was at (4,5)

Answer:

You started at (4, 5)

Step-by-step explanation:

The first number of coordinate pair is x. you started at the right and THEN moved the the left, as stated in the question. So -1 + 5 is 4.
So you started at (4, 5)

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PLEASE HELP ME ASAP Does the series converge or diverge? If it converges, what is the sum? Show your work

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PLEASE HELP ME ASAP

Does the series converge or diverge? If it converges, what is the sum? Show your work