Midpoint of (-8,3) (10,-4)

Answer:Example 1:

Find the sum of the first 8 terms of the geometric series if a1=1 and r=2.

S8=1(1−28)1−2=255

Example 2:

Find S10 of the geometric sequence 24,12,6,⋯.

First, find r.  

r=r2r1=1224=12

Now, find the sum:

S10=24(1−(12)10)1−12=306964

Example 3:

Evaluate.

∑n=1103(−2)n−1

(You are finding S10 for the series 3−6+12−24+⋯, whose common ratio is −2.)

Sn=a1(1−rn)1−rS10=3[1−(−2)10]1−(−2)=3(1−1024)3=−1023  

In order for an infinite geometric series to have a sum, the common ratio r must be between −1 and 1.  Then as n increases, rn gets closer and closer to 0.  To find the sum of an infinite geometric series having ratios with an absolute value less than one, use the formula, S=a11−r, where a1 is the first term and r is the common ratio.

Example 4:

Find the sum of the infinite geometric sequence

27,18,12,8,⋯.

First find r:  

r=a2a1=1827=23

Then find the sum:

S=a11−r

S=271−23=81

Example 5:

Find the sum of the infinite geometric sequence

8,12,18,27,⋯ if it exists.

First find r:  

r=a2a1=128=32

Since r=32 is not less than one the series has no sum.

Step-by-step explanation:

The y-intercept of the line is 1

Using the slope - intercept relation :

Substituting the values into the relation :

7 = 3(2) + c

7 = 6 + c

c = 7 - 6

c = 1

Therefore, the y-intercept of the line is 1.

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Answer:

$200

Step-by-step explanation:

First Change the percent to a decimal

In this case the percent was %8, change it into a decimal; 8%=.08

Next multiply 2,500 x .08  which gives you 200

The answer is $200! Hope this helps!.

It's 6 srry that guy above just stole free points

Answer:

ok

Step-by-step explanation:

Answer:

angle t is 55 degrees

Step-by-step explanation:

Here's my work:

Isoscelese means two of the same length sides. A triangle is 180 degrees. 180-70=110

110/2=55 (two because those are the two angles associated with the equal sides)

Final Answer: [tex]r = 2[/tex]

Steps/Reasons/Explanation:

Question: [tex]8 = r^{3}[/tex]. [tex]r[/tex] = ?

Step 1: Take the cube root of both sides.

[tex]\sqrt[3]{8} = r[/tex]

Step 2: Calculate using a calculator.

[tex]2 = r[/tex]

Step 3: Switch sides.

[tex]r = 2[/tex]

~I hope I helped you :)~

Answer:

1. ac = 36

2. b = 13

3. 4 and 9

Step-by-step explanation:

Given

6x² + 13x + 6

Required

Fill in the gaps

Solving (1): The value of AC

The general form of an equation is:

ax² + bx + c

By comparison:

a = 6

b = 13

c = 6

So,

ac = a * c

ac = 6 * 6

ac = 36

Solving (2): The value of b

In (1) above, we showed that

b = 13

Solving (3): Two numbers that satisfy product ac and sum b

We have that.

ac = 36

If one of the numbers is 4, then the other number is

Other number = 36/4

Other number = 9

Alternatively, we have that.

b = 13

If one of the numbers is 4, then the other number would be:

Other number = 13 - 4

Other number = 9

Answer:

ac = 36

b = 13

The two numbers that have a product of ac and a sum of b are 4 and 9

Step-by-step explanation:

Answer:

-24

Step-by-step explanation:

Answer: -24

Step-by-step explanation:

3xy

3(4)(-2)

12(-2)

-24

Answer:

y = -2x + 5

Step-by-step explanation:

A(4, -3) ;      B(2, 1)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

          [tex]= \frac{1-[-3]}{2-4}\\\\= \frac{1+3}{2-4}\\\\= \frac{4}{-2}\\\\= -2[/tex]

m = -2 ;  A(4,-3)

[tex]y - y_{1}=m(x-x_{1})\\\\y -[-3] = (-2)(x - 4)\\\\y + 3 = -2*x -4 *(-2)\\\\y + 3 = -2x + 8\\\\ y = -2x + 8 - 3 \\\\ y = -2x + 5[/tex]

Answer:

Dimension of rectangle = 6 inches by 3 inches

Dimension of square = 3 inches by 3 inches

Step-by-step explanation:

Given information:

- Length of rectangle = [tex]6[/tex] inches.

- Width of rectangle is the same as the side length of square.

- Area of rectangle is twice the area of square

Variable to define:

Let [tex]s[/tex] = side length of the square and the width of the rectangle

Finding dimensions of rectangle and square:

From the information given, we can write the equation:

[tex]6s=2s^2[/tex]  (Area of rectangle is twice the area of square)

[tex]6=2s[/tex] (Divide [tex]s[/tex] on both sides)

[tex]s = 3[/tex] inches

Dimension of rectangle = length by width

= 6 inches by 3 inches

Dimension of square = side by side

= 3 inches by 3 inches

Hope this helps :)

Answer:

2010

Step-by-step explanation:

1/2(24)(20)=240

50*45=2250

2250-240=2010

Answer:

=5x2+5x

Step-by-step explanation:

Let's simplify step-by-step.

3x+3x2+2x2+2x

Answer:

d

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation: the answer is c

Answer:The Last One

Step-by-step explanation:

Option (B) an association cannot be determined between the categorical variables because the relative frequencies are similar in value is the correct answer.

The relative frequency of an event is defined as the number of times that the event occurs during experimental trials, divided by the total number of trials conducted. The sum of all relative frequencies will be one.

For the given situation,

The relative frequencies are 0.48 and 0.52.

A two-way frequency table can be used to show, analyze, and examine the relationships that exists between two categorical variables.

The two relative frequencies have the values that are similar to (close to) each other. So, there will be no association between the categorical values.

Hence we can conclude that option (B) an association cannot be determined between the categorical variables because the relative frequencies are similar in value is the correct answer.

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Answer:

It should be B- an=3n+1 because it seems to be adding one every time

Step-by-step explanation:

Answer:

We will count number of squares

first term is 4

so,

second term is 7

so,

third term is 10

so,

We can see that this sequence is in arithematic sequence

we can use nth term formula

where

an is nth terms

a1 is first term

d is common difference

n is total number of terms

now, we can plug values

and we get

b 3n+1

Step-by-step explanation:

Answer:

200 is the decrease ............

Answer:

the percent of decrease=28.57%

Step-by-step explanation:

(Old Price - New Price)/Old Price (and multiply that number by 100)

[(700-500)/700]*100=28.57%  

Answer:

1: Patriotic

2: Global

3: Graphic

4:heroic

5: betrayel

6:angelic

7: dramatic

8: bacterial

Step-by-step explanation:

I think this is it

9514 1404 393

Answer:

  8, 9. Correct

  10. 6.1×t

Step-by-step explanation:

8, 9. The answers shown are correct.

__

10. The only product in the given expression is 6.1t, which can be written as ...

  6.1×t

when a symbol is used to represent multiplication.

The parts of the product are the multiplicand and the multiplier. Those parts are also called factors.

Answer:

G

Step-by-step explanation:

(x)0 months: (y)15 toys, 1:17, 2:19, 3:21, 4:23, 5:25, 6:27, 7:29, 8:31, etc.

The equation that represents best shows this relationship between the number of toys Rudolfo has will be y = 2x + 15. Then the correct option is G.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Rudolfo has 15 toys in his toy box, and he adds 2 new toys every month.

Let x be the number of months and y be the total number of toys. Then the equation is given as,

y = 2x + 15

The equation that represents best shows this relationship between the number of toys Rudolfo has will be y = 2x + 15. Then the correct option is G.

More about the linear equation link is given below.

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Answer:

7   1/3

Step-by-step explanation:

Lets do this in steps ok? K!

Important!!!: Look what operation is first in order of operation no parentheses or exponents so division and multiplication is first!

Step 1-- 4 x 7=28

Step 2-- 62 divided by 3 = 20      2/3

Step 3-- 28- 20   2/3

Step 4-- 27   3/3 - 20    2/3= 7    1/3

Hope this helps ∞<3

Answer:

[tex]-11.3333333333[/tex] [tex]or[/tex] [tex]-\frac{34}{3}[/tex] [tex]or[/tex] [tex]7\ \frac{1}{3}[/tex]

Step-by-step explanation:

[tex]--------------------------------------------[/tex]

[tex]\frac{4\cdot7-62}{3}[/tex] = [tex]?[/tex]

[tex]4\cdot7[/tex] = [tex]28[/tex]

[tex]\frac{28-62}{3}[/tex] = [tex]?[/tex]

[tex]28-62[/tex] = [tex]-34[/tex]

[tex]\frac{-34}{3}[/tex] = [tex]?[/tex]

[tex]\frac{-34}{3}[/tex] = [tex]-11.3333333333[/tex] = [tex]7\ \frac{1}{3}[/tex]

[tex]--------------------------------------------[/tex]

Hope this helps! <3

[tex]--------------------------------------------[/tex]

Answer:

a. True

b. True

c. True

d. False

e. False

I hope this helped! Thank You!

Answer:

a. False

b. True

c. True

d. False

e. False

Answer:

-11

Step-by-step explanation:

Answer:

ratio number 1-  14:12

ratio number 2- 21:18

ratio number 3- 28:24