Use the formula Sn =a (1 - rn ) ÷ (1 – r) to find the sum Sn for each of the infinite and finite geometric series.

9. The first 9 terms of 12, – 6 ,+ 3, - …

10. The first 15 terms of -1, + 1, -…

11. The first 6 terms of 1, + 3, + …

12. The first 10 terms of 2, – 4, + …

Answers

Answer 1

Answer: 11

Step-by-step explanation:

Answer 2

9. The Sum of 9 terms is 513/64.

10. The sum of 15 terms is -1.

11. The sum of 6 terms is 364

12. The sum of 10 terms is -682.

We have,

Sn =a (1 - [tex]r^n[/tex] ) ÷ (1 – r)

9. 12, -6, 3, .....

Here, r=  -6/ 12= -1/2

So, S(9)

= 12 (1- [tex](-1/2)^9[/tex])/ (1 - (-1/2))

= 513/ 64

10.-1, +1, -.....

Here, r= 1/ (-1)= -1

So, S(15) = 1 (1- [tex](-1)^{15[/tex])/ (1 - (-1))

              = -1

11. 1, 3, .....

Here, r = 3/1 = 3

So, S(6) = 1 (1- [tex](3)^{6[/tex])/ (1 - 3)

              = 364

12. 2, -4, ...

Here, r= (-4)/ 2= -2

So, S(10) = -682

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Related Questions

Terry practices the same amount of time each day for his soccer tryouts. In 4 days, he has practiced for 360 minutes. Let x represent the number of days Terry practices, and let y represent the number of minutes he practices. Write an equation that could be used to represent this relationship.

Answers

Answer:

90

Step-by-step explanation:

390 ( 40; 6 )

Carlos is at the store buying pencils. There is a package with 4 pencils that
costs $5 or a package with 5 pencils that costs $6. Which package is the
better buy?
A. The $6 package, because each pencil costs $1.20.
B. The $6 package, because each pencil costs $0.83.
C. The $5 package, because each pencil costs $1.25.
D. The $5 package, because each pencil costs $0.80.

Answers

Answer:

The best answer would be A. because 6 divided by 5 is 1.20. Pls give me brainliest because i am trying to rank up.

Step-by-step explanation:

Pls look at picture for question

Answers

Step-by-step explanation:

30/6+3 = 5+3 = 8

hope this helps you.

Determine if these functions are even, odd, or neither

Answers

Answer:

First Graph: the function is symmetrical around y axis -> Even

Second Graph: the function is neither

Practice using angle relationships.
Assignment
J
What is the measure of JKL?
* 60°
96°
O 80°
O 110°
O 120°
240
H
K L

Answers

Answer:

120

Step-by-step explanation:

24 + 96 = 120

Hope this helps!

The vertices of a triangle are A(0,0),B(3,8) and C(9,0). What is the area of this triangle?

Answers

Answer:

9

Step-by-step explanation:

To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.

Fill in the numbers for each corresponding letter combination within the formula.

Fill in your formula like this: 0(8-10) + 3(0-0) + 9(0-8).

Subtract the numbers within the parentheses.

0 from 8 = 8, 0 from 0 = 0 and 8 from 10 = 2.

Multiply that result by the number to the left of the parentheses.

0 by 8 = 0, 3 by 0 = 0 and 9 by 2 = 18.

Add the three products together.

0 + 0 + 18 = 18

Divide the sum of the three products by 2.

18 ÷ 2 = 9

Answer:36

Step-by-step explanation:

From 36 to 48 what is the percent change? Plz this is sooooo confusing

Answers

Answer:

33.33

Step-by-step explanation:

(48-36):36*100

(48:36-1)*100

133.33333333333-100 = 33.33

Evaluate the given expression for x = 4.
x? + 5x - 8

Answers

Answer:

16

Step-by-step explanation:

[tex]x = 4 \\ 4 + 5(4) - 8 = 16[/tex]

two vectors a and b are inclined at a angle of 60° with each other. its resultant makes angle of 45° with a and value of resultant is 2 sqrt 2 . find the component​

Answers

Answer:

[tex]\blue{\rule{100pt}{999999pt}}[/tex] [tex]\blue{\rule{100pt}{999999pt}}[/tex]

Joe ran 2 miles in 16 minutes. At this rate how long did it take him to run 5 miles.

Answers

Answer:

40min

Step-by-step explanation:

Since the ratio is 2:16, we want simplify. both 2 and 16 are dividable by 2.

2 / 2 = 1

16 / 2 = 8.

Now we can use the ratio 1 mile per 8 min. We want the rate of how many min to miles, so we'd multiply 5 by 8 which equals 40.

Therefore it takes him 40min to run 5 miles.

Hope this helps!

f (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20

Three roots of this polynomial function are −1, 1, and 3 + i.

Which of the following describes the number and nature of all the roots of this function?


f (x) has two real roots and one imaginary root.

f (x) has three real roots.

f (x) has five real roots.

f (x) has three real roots and two imaginary roots.

Answers

Answer:

  f(x) has three real roots and two imaginary roots.

Step-by-step explanation:

The function is degree 5, so will have 5 roots in total. 2 real roots and one complex root are shown. Complex roots come in pairs, so there will be one more, but cannot be two more.

  f(x) has three real roots and two imaginary roots.

__

All five roots must be accounted for. This leaves out the first two choices. The given complex root eliminates the third choice.

Answer:

D

Step-by-step explanation:

did the test

WORTH 50 POINT + BRAINLIEST FOR GOOD ANSWER!!

Bob was accused of stealing chocolate from a chocolate factory, and was put on criminal trial in the state of Pennsylvania. If Bob were convicted, to which higher court could he appeal?

A. State court of appeals
B. Supreme Court of the United States
C. Federal appellate court
D. Bob is constitutionally protected from a second trial

BTW reason the subject ios math is because no one is helping me when I put other subject. :(

Answers

Answer:

. Bob is constitutionally protected from a second trial like its not possible that person who steals choclate get in to the jail

Answer:

i believe that it is d

Step-by-step explanation:

becuase if hes convicted of the crime he doesn't have to be on trial for it again

The sum of the angles of a triangle is 180°. If one angle of a triangle measures x and the second
angle measures (4x + 7)º, express the measure of the third angle in terms of x. Simplify the
expression.
.....

Answers

Answer:

-5x+173

Step-by-step explanation:

x+4x+7      (sum of the 2 angles that you know)

5x+7

180-5x+7

-5x+173

The shape of f(x) = x^3, but shifted four units to the left, eight units down, and then reflected in the y-axis (in that order)

Answers

Answer:

steps below

Step-by-step explanation:

f(x) = x³

1. shifted four units to the left: f'(x) = (x+4)³

2. eight units down: f''(x) = (x+4)³ - 8

3. reflected in the y-axis: f'''(x) = (-x+4)³ - 8

The final shape after the transformation is f(x) = -(x + 4)³ - 8.

Original function: f(x) = x³

Shifted four units to the left: f(x) = (x + 4)³

Shifted eight units down: f(x) = (x + 4)³ - 8

Reflected in the y-axis: f(x) = -(x + 4)³ - 8

Hence, the final shape of the function after these transformations is f(x) = -(x + 4)³ - 8.

Learn more about transformation here:

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Solve for x in the following inequality: 3(-2x - 4) > 18

Answers

Answer:

x < -5

Step-by-step explanation:

3 ( -2x - 4 ) > 18

→ Expand the brackets

-6x - 12 > 18

→ Add 12 to both sides

-6x > 30

→ Divide both sides by -6

x < -5

Answer:

[tex]\boxed {\boxed {\sf x< -5}}[/tex]

Step-by-step explanation:

We are asked to solve the following inequality for x.

[tex]3(-2x-4) > 18[/tex]

Solve for x by isolating it and performing the inverse operations.

3 is being multiplied by (-2x-4). The inverse operation of multiplication is division. Divide both sides of the inequality by 3.

[tex]\frac {3(-2x-4)}{3} > \frac{18}{3}[/tex]

[tex](-2x-4) > \frac{18}{3}[/tex]

[tex]-2x-4 > 6[/tex]

4 is being subtracted from -2x. The inverse operation of subtraction is addition. Add 4 to both sides of the inequality.

[tex]-2x-4+4 > 6+4 \\[/tex]

[tex]-2x > 10[/tex]

x is being multiplied by -2. The inverse operation of multiplication is division. Divide both sides by -2.

[tex]\frac {-2x}{-2} > \frac {10}{-2}[/tex]

[tex]x> \frac {10}{-2}[/tex]

Since we divided by a negative number, the inequality sign must be flipped.

[tex]x< \frac{10}{-2}[/tex]

[tex]x < -5[/tex]

A restaurant has two sizes of milkshakes, small and regular. The ratio of small milkshakes purchased to regular milkshakes purchased is 14 to 6. What percent of milkshakes purchased are small?

Answers

Answer:

70%

Step-by-step explanation:

the ratio is 14 to 6 so if you have 14 small milkshakes you would also have 6 regular milkshakes

to find a percentage we can buff up the ratio to add up to 100

14 + 6 = 20

100 / 20 = 5

that means we must multiply each side by 5

14 * 5 = 70

6 * 5 = 30

the ratio is now 70 to 30

you would have 70% of milkshakes that are small

How do you solve multistep equations with variables on both sides
of the equals sign?

Answers

5x - 8 = 3x + 12

- 3x -3x

You have to subtract them both.

2x - 8 = 12


What is the sum of £4(0.5) "1?
n=1
O S=1.5
OS = 2
O S = 4.5
O S= 8

Answers

B. 2 …………………………,.,,,,,.,.,.,.,.,,,.,

WILL GIVE BRAINLIEST!

Answers

Answer:

425

Step-by-step explanation:

225/24 then multiply the answer by 40

Yoni has a ribbon that measures 5/3 yards. She wants to cut it into 3 equal pieces. What is the length of each piece of ribbon? 5\8 yards 5/6 yards 5/9 yards 5/3 yards

Answers

Answer:

Step-by-step explanation:

[tex]\frac{1}{3} * \frac{5}{3} = \frac{1 * 5}{3*3} = \frac{5}{9}[/tex]

The answer is 5/9 as you can see. 5/9 = 20 inches each.

1 yard = 36 inches

(5/9 * 36)  = 5 * 4 = 20 inches.

Answer:

5/9

Step-by-step explanation:

I have a trick id like to teach here. Whenever you have a fraction being divided by a whole number, you can multiply the denominator by the diviser

So what I did was multiply the 3 by the diviser(3) and got 9

This left me with 5/9

en.
If the graph is reflected over the x-axis, what is the
domain of the function?
all real numbers
O all real numbers greater than or equal to 0
O all real numbers greater than or equal to -2
O all real numbers less than or equal to -2

Answers

Answer:

Step-by-step explanation:

Domain means all the x's on the graph. The x's that you can literally see on the graph and for what you can't see it's all the x's you can put into the equation...for this graph, when you reflect it across the x-axis it is still the same shape, just a peak instead of a V. So the y's (range) are VERY different on the graph and its reflection. But the x's (that's the domain!) Are all still there, still on the graph, still allowed in the equation. See image

The domain of the function are all real numbers greater than or equal to 0.

What is domain and range of a function?

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

If the graph is reflected over the x-axis, then we need to find domain of the function.

Domain means all the x values on the graph. The x values  that you can literally see on the graph and for what you can't see it's all the x values  you can put into the equation...for this graph.

when you reflect it across the x-axis it is still the same shape, just a peak instead of a V.

So the y values  (range) are VERY different on the graph and its reflection.

Therefore, The domain of the function are all real numbers greater than or equal to 0.

Learn more about appropriate domain here:

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Solve the proportion. x/6 = 20/24

Answers

X/6 = 20/24

Cross multiply:

24x = 120

Divide both sides by 24

X = 5

Answer: x = 5

Please help me! Im a little bit stumped!

Answers

Answer:

2x+34=4x+20

14=2x

x=7

Step-by-step explanation:

So the answer is 7

Answer:

some bedmas laws you have to use

first do the 4(x+5) since its distubutive

you get 2x + 34 = 4x + 20 normally i like to keep x positive so i dont have to divide by -1 at the end so subtract 5 to the other side qnd subtract 2x to the other side and you get

2x= 14

x = 7 is the answer

please help ill mark brainliestO​

Answers

Answer:

56

Step-by-step explanation:

simplify the expression (9n+ 4)-(-1/2n-7)

Answers

Answer:

9 1/2n + 11

Step-by-step explanation:

9n + 1/2n + 4 + 7

9 1/2n + 11  or 19/2n + 11

How many servings are there in an 8-pound roast, if the suggested
serving is 2/3 pound?

Answers

an 8 pound roast can feed 7-8 adults

Harold bought 3 points of red apples and 4.2 pounds of green apples from a grocery store, where both kinds of apple are 1.75 a pound. How much did Harold spend on apples?

Answers

Answer:

12.6

Step-by-step explanation:

total weight of apples = 3+ 4.2

= 7.2 pounds

total money spent on apples = 1.75 × 7.2

= $12.6

Answer:

12.6

Step-by-step explanation:

he had 3 points of red apples and 4.2 pounds of green apple and 1.75 pounds so he spend 12.6

IR = V (solve for R) *

Answers

Answer:

R = [tex]\frac{V}{I}[/tex]

Step-by-step explanation:

IR = V ( isolate R by dividing both sides by I )

R = [tex]\frac{V}{I}[/tex]

Which sign makes the statement true?
A. <
B. >
C. =

Answers

It is B correct please
B makes the statement true

Will mark as brainliest if answer is correct
Which describes the graph of y=(x-4)^2-1?

A. Opens down with a vertex at (-4,-1)

B. Opens up with a vertex at (-4,-1)

C. Opens up with a vertex at (4,-1)

D. Opens down with a vertex at (4,-1)​

Answers

Answer:

B

Step-by-step explanation:

The term in the () is usually the x coordinate, and the last term (-1) is usually the y coordinate.

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