Open-Ended Write three equations with variables on both sides of the equal sign with one having no solution, one having exactly one solution, and one being an identity. please help guys

Answers

Answer 1

Answer:

Summary. If the equation ends with a false statement (ex: 0=3) then you know that there's no solution. If the equation ends with a true statement (ex: 2=2) then you know that there's infinitely many solutions or all real numbers

Step-by-step explanation:

Answer 2

Answer: answer in the attachment

Step-by-step explanation:

Hope this might have helped you

Open-Ended Write Three Equations With Variables On Both Sides Of The Equal Sign With One Having No Solution,

Related Questions

help me plz can somewon help me

Answers

Answer:

4*10^6

Step-by-step explanation:

Answer:

4 × 10^6

Step-by-step explanation:

[tex]\frac{8\times 10^2^4}{2\times 10^1^8}=\\\\\mathrm{Divide\:the\:numbers:}\:\frac{8}{2}=4\\\\=\frac{10^{24}\times \:4}{10^{18}}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{10^{24}}{10^{18}}=10^{24-18}\\\\=4\times \:10^{24-18}\\\\\mathrm{Subtract\:the\:numbers:}\:24-18=6\\\\=10^6\times \:4\\\\10^6=1000000\\\\=1000000\times \:4\\\\=4000000\\\\= 4\times10^6[/tex]

When purchased, a beach ball is deflated and packaged flat. The package states that when inflated to its maximum capacity, the radius of the inflated ball is 7.6 inches. To the nearest hundredth of a cubic inch, how much air will occupy the space contained by the inflated beach ball? Use 3.14 for [tex]\pi[/tex]. In your final answer, include all of your calculations.

Answers

Step-by-step explanation:

V=(4/3) * πr^3

V=(4/3) * π * 7.6 ^3

V=(4/3) * π * 438.976

V= π * 585.301333

V = 1837.85 inch^3

3.14 for pi btw

v=1837.85 inch is the answer

What is the result of subtracting the second equation from the first?

Answers

Answer: 11x - 8y = -9

Step-by-step explanation:

Subtract it by terms.

8x - (-3x) = 11x  

-4y - (4y) = -8y

-4-5= -9    

order it

11x - 8y =-9

the answer is 11x - 8y = -9

Abby and Katy are selling cheesecakes. There are apple and pecan cheesecakes. Abby sold 14 pecan and 3 apple cheesecakes for a total of $113. Katy sold 7 pecan and 8 apple cheesecakes for a total of $180. What's the cost of one pecan cheesecake and one apple cheesecake?

How would I set this up?​

Answers

If you want to set up the equations:

let the cost of one apple cheesecake be [tex] a[/tex] and the cost of one pecan cheesecake be $p$

from Abby, $14p+3a=113$

and from Katy....?

then solve for both variables

can you take it from here?

Mary bought 10 quarts of juice at the grocery. How many gallons of juice did she buy? A. 1.4 gal B. 2.5 gal C. 3.5 gal D. 4.5 gal

Answers

There are 4 quarts in 1 gallon. So if Mary bought 10 quarts, divide by 4 to get the equal number of gallons. 10/4 = 2.5 so the answer is B.

Answer:

2.5 gallons (B)

Step-by-step explanation:

1 gallon is equal to 4 quarts. So, if Mary bought 10 quarts, that is 10/4 gallons. Simplified, 10/4=5/2=2.5 gallons.

Laura has a step of 50cm She walks along by taking two steps forward and one step back. What is the least number of steps counting forward and backwards step, she takes to reach a step 20m away? ~Thanks - don't know how to solve :(

Answers

Answer:

The least number of steps she takes to reach 20 m is 118 steps

Step-by-step explanation:

For Laura, the length of a walking step = 50 cm = 0.5 m

The repeating number of steps she takes = Two steps forward one step backwards

The number of forward steps it would take for her to reach 20 m = (20 m)/(0.5 m) = 40 steps

Given that she always takes two steps forward and one step backwards, we have;

The number of steps forward every three steps = 2 step forward + (-1) step (backward)

The number of steps forward every three steps = 2 - 1 = 1 step forward

To reach 39 steps forward, she would need 39 × 3 =  117 steps

To get to the 40 steps she needs just a step forward, making the total number of steps to reach 40 steps = 117 + 1 = 118 steps

Therefore, the least number of steps she takes to reach 20 m = 118 steps.

I wrote the answer somewhere else and it wouldn’t let me copy and paste so here’s the screenshot

Lisa read 46 pages on Sunday, 15 pages on Monday, and 19 pages on Tuesday. Which of the following is closest to the mean number of pages she read over the three-day period? A. 19 pages B. 21 pages C. 27 pages D. 35 pages Show all work!!

Answers

Answer:

C. 27 pages

Step-by-step explanation:

First, add all of the numbers together

15+19+46

That would be 80.

Then, once you have the numbers added, divide the number you by how many numbers there are.

80 divided by 3 = 26.7 (rounded)

Now that you have the answer 26.7, that tells you that the answer is 27 pages.

Answer:

c.27

Step-by-step explanation:

You have to add 46,15, and 19 together which gets you 80. Then you divide it by 3 and you get 26.(something) since its a decimal, you need a whole number. You round to 27 because its the closest. (When finding the mean, you must add the numbers and divide by how many numbers there are (3))

What will come in the circle
I will even rate who ever answer
And give brainliest

Answers

Answer:

1st circle: 1.25

Second circle: 2

Step-by-step explanation:

We can use the cross product property here to find the value of what's in the circles.

Let's first look at the first two fractions.

[tex]\frac{x}{5} = \frac{1}{4}[/tex]

We can multiply the cross values and divide by the number that is diagonal to the variable.

[tex]5\cdot1 = 5\\5\div4 = 1.25[/tex]

So 1.25 goes in the first circle.

Now let's look at the last two circles and use the same property to find the missing value.

[tex]\frac{1}{4} = \frac{0.5}{x}\\ 4\cdot0.5 = 2\\2\div1 = 2[/tex]

So 2 goes in the second circle.

Hope this helped!

Answer:

x = 5/4

Step-by-step explanation:

Use the variable 'x' instead of 'the circle.'  Then:

 x         1

----- = ------

 5         4

Cross-multiplying, we get

4x = 5, and so x = 5/4

please solve this fast​

Answers

Answer:

69

Step-by-step explanation:

The graph below shows the relationship between the number of months different students practiced baseball and the number of games they won:

The title of the graph is Baseball Games. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Games Won. The scale on the y axis is from 0 to 22 at increments of 2, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 1 and 1, 3 and 2, 5 and 3, 9 and 4, 10 and 5, 12 and 6, 13 and 7, 14 and 8,17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 1.8 and 2, 5.6 and 4, 9.2 and 6, 13 and 8, 16.5 and 10, 20.5.

Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)

Part B: Write the equation for the line of best fit in slope-intercept form and use it to predict the number of games that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)

Answers

Answer:

(A) The y-intercept of the line is 1.82.

(B) The number of games that could be won after 13 months of practice is 26.

Step-by-step explanation:

The data from the provided graph is:

X Y

0 1

1 3

2 5

3 9

4 10

5 12

6 13

7 14

8 17

9 18

10 20

Here,

X : Number of Months of Practice

Y : Number of Games Won

(A)

Compute the y-intercept of the line as follows:

[tex]a=\frac{\sum Y\cdot \sum X^{2}-\sum X\cdot \sum XY}{n\cdot \sum X^{2}-(\sum X)^{2}}[/tex]

   [tex]=\frac{122\cdot 385-55\cdot 814}{11\cdot 385-(55)^{2}}\\\\=1.818\\\\\approx 1.82[/tex]

The y-intercept of the line is 1.82.

The y-intercept is the average value of the dependent variable, here the number of games won, when the value of the independent variable, here number of months of practice, is 0.

So, a y-intercept of 1.82 indicates that on average 1.82 can be won if the number of months of practice is 0.

(B)

Compute the slope as follows:

[tex]b=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{n\cdot \sum X^{2}-(\sum X)^{2}}[/tex]

  [tex]=\frac{11\cdot 814-55\cdot 122}{11\cdot 385-(55)^{2}}\\\\=1.855\\\\\approx 1.86[/tex]

The equation for the line of best fit in slope-intercept form  is:

[tex]y=1.82+1.85x[/tex]

Predict the number of games that could be won after 13 months of practice as follows:

[tex]y=1.82+1.85x[/tex]

  [tex]=1.82+(1.85\timex 13)\\=25.87\\\approx 26[/tex]

Thus, the number of games that could be won after 13 months of practice is 26.

HELP!!! SHOW WORK PLEASE.

Answers

[tex]\dfrac{x}{4}=\dfrac{x+9}{4+12}\\\\16x=4(x+9)\\16x=4x+36\\12x=36\\x=3[/tex]

The answer is x = 3 I hope you understand

4. Multiple-Choice
1. Two complementary angles measure (12r - 18)° and (5x + 23)°. What
is the measure of the smaller angle?
(1) 5°
(2) 42°
(3) 48°
(4) 90°

I already know that the answer is 42 but I don’t know how to get that! Please help.

Answers

Sry i couldn't find the answer

Answer:

(2) 42°

Step-by-step explanation:

Copy of the given problem:

4. Multiple-Choice

1. Two complementary angles measure (12r - 18)° and (5x + 23)°. What

is the measure of the smaller angle?

(1) 5°

(2) 42°

(3) 48°

(4) 90°

Solution:

The sum of the measures of complementary angles is 90 deg.

12r - 18 + 5x + 23 = 90

We have 1 equation with two different variables, so we cannot solve the equation to find unique values of the variables.

I assume the above is an error, and both variables should be the same.

12r - 18 + 5r + 23 = 90

Combine like terms on the left side. Terms with r are combined. Terms with no variable are combined.

12r + 5r - 18 + 23 = 90

17r + 5 = 90

Subtract 5 from both sides.

17r = 85

Divide both sides by 5.

r = 5

The measures of the angles are:

12r - 18 = 12(5) - 18 = 60 - 18 = 42

5r + 23 = 5(5) + 23 = 25 + 23 = 48

The measures of the two angles are 42°  and 48°.

The smaller angle measures 42°

Answer: (2) 42°

what is the domain of the function shown in the graph below?

answer type: Interval, all real numbers, all values except one, all values except two
interval:

Answers

Answer:

  all values except one (-2)

Step-by-step explanation:

The function heads off toward infinity at x=-2, so it is not defined there. The function is defined for all values except one.

All values except 1 (-2)

find the mean, median, mode, and midrange. Then decide which you think is the most meaningful measure of average for that data set. For larger data sets, you should consider using technology. The number of beds at all licensed hospital in Hillsborough County, Florida, in 2015: 98 120 493 206 73 102 183 870 76 60 60 112 147 1,018 201

Answers

Answer:

mean = 254.6

median = 120

mode = 60

midrange = 958

For average data sets i prefer by finding the mean

Step-by-step explanation:

mean :

(98+120+493+206+73+102+183+870+76+60+60+112+147+1018+201) ÷ 15 = 254.6

median : 60 60 73 76 98 102 112 120 147 183 201 206 493 870 1018

find the middle number

= 120

mode :

number that is more than one

= 60

midrange :

highest number - smallest number

= 1018 - 60

= 958

Are minerals renewable or not?

PLEASE HELP ME WITH MY HOMEWORK!! ASAP! WILL PICK BRAINLIEST! DUE IN 15 MINUTES!!!

Answers

Answer:

watch 11:39 . clock is 11:24 .    210m .    1mm .   12 degrees . 3/4hrs .    

Step-by-step explanation:

Step-by-step explanation:

10. It says the watch is 9 minutes fast and the time announced is 11:30 that will be 9 minutes added to the 11:30 which will give 11:39

Now, for the clock , it says the clock is 6 minutes slow, that will be 11:30 - 6 minutes the six minutes will be minused from the 30 minutes which will give 11:24

11. since it is 10 m above the ground and the full length is 220 m which part of is under the ground since we are given the length above the ground in order to find the length of the ground we say 220-10 which will give 210

so the distance of the bottom of the drill from there ground level is 210

12. x + 5

x - 3

to give their difference that will be 5+3 which will be 8

cross check

using 5 to represent x

5+5 =10

5-3 =2

the difference between them is 8 you can use another number to represent x but the difference will still be 8

13. To find the temperature if the frozen meat that will be 34 + 22 degree that gives 56

14. it says she was at the airport 1hr 30 minutes before the appointed time so if the plane was to take off by 9:00 that means she reached there 7:30 then it was 9:00 the plane was late again for 3/4 of hour late so 60 minutes makes up an hour that gives 60×3/4 that gives 45 meaning the plane was late for another 45 minutes how long does she wait that gives 1hr 30 minutes plus 45 minutes convert all to minutes =60 minutes + 30 minutes + 45 minutes which is 135 minutes convert to hour 2 minutes gives 120 seconds so 135-120 =15

so she waited at the airport for 2 hrs 15 minutes

15. since out of the 6400 Dani he paid his debt of 600 and gave it sola who has only 1900

that will be 6400-600 and 1900+600

so sola has 2500 while Dani has 5800

16. she can only pay back 40

B. (not sure)

17. meaning the sister owes 800 naira

b. by 1700+800 =2500

18. that gives 950000-97000 =853000


Phillip deposited $5,670 into a savings account 19 years ago. The account has an interest rate of 4.1% and the balance is currently $12,356.04. How often does the
interest compound?

Answers

Answer:

$12165.97

Step-by-step explanation:

100 + 4.1 = 104.1%

104.1% = 1.041

$5670 x 1.041^19 = $12165.97

Answer:

daily

Step-by-step explanation:

To answer this try plugging in each type of compund: daily, monthly, quarterly, and annually.

5670(1+0.041/365)^(365*19)

= 12356.04

365= daily

so your answer would be that the interest compounds daily.

What is the coefficient of x5y5 in the expansion of (x + y)10?

Answers

Answer:

C=252

Step-by-step explanation:

Given:

x^5y^5

(x+y)^10

Find the coefficient of x^5y^5

To get the coefficient of x^5y^5,

we will put r = 5, in the below given general term.

The general term is : nCr =x^ry^n-r

We get:

Coefficient is = 10C5

= 10!/5!*5!

= 252

The coefficient of x^5y^5 is 252

C. 252

252

GOD BLESS U. Sorry if I’m wrong I tried my best

Given that F( x ) = x 2 + 2, evaluate F(1) + F(5).

Answers

Hi there! :)

Answer:

[tex]\huge\boxed{f(1) + f(5) = 30}[/tex]

Given:

[tex]f(x) = x^{2} + 2[/tex]

Evaluate [tex]f(1) + f(5)[/tex]

Solve for each:

[tex]f(1) = (1)^{2} + 2 = 3[/tex]

[tex]f(5) = (5)^{2} + 2 = 27[/tex]

[tex]27 + 3 = 30[/tex]

Answer:

30

Step-by-step explanation:

Someone explain to me if this is correct?

Answers

Answer:

Yes, that is correct.

Step-by-step explanation:

W = x

L = ?

A = x^2 + 12x

(x^2 + 12x)/x = x + 12

L = x + 12

Subbing in 10 for each X, we get:

Perimeter: 64

2(10) + 2(10 + 12) = 20 + 44 = 64

Area: 220

10 * 22 = 220

Part A looks perfect. You've shown that x^2+12x factors into x(x+12) indicating that x is the width and x+12 is the length. Convention usually has the length be longer than the width, but to be honest, the order doesn't really matter (since we can multiply in any order we want).

----------------

Part B is a bit hazy. You show that 10 * 22 = 220 is the area, so you imply that the rectangle has width 10 and length 22. However, you don't directly mention the dimensions of the rectangle.

You can pick either x^2+12x or x(x+12). I prefer x(x+12) as its easier in my opinion. You don't need to do both.

All you really need to do is say that if x is the width and x = 10, then the width is 10. Furthermore, if x+12 is the length then x+12 = 10+12 = 22 is the length.

9x^3-16x^2=0. Solve and show all steps.

Answers

Answer Step one x=16/9 =1.778

Last step is x²=0

Hope I helped you

Answer:

the roots are {0, 0, 16/9}

Step-by-step explanation:

The trick to solving this is to factor out x^2 from both terms on the left:

x^2*9*x - 16x^2=0, or

x^2(9x - 16) = 0

Then, either x^2 = 0 or (9x - 16) = 0.

Thus, the roots are {0, 0, 16/9}

in the figure above, pqrs is a parallelogram. What is the value of x?​

Answers

Answer:

x = 162 degrees.

Step-by-step explanation:

m < RSP = 180 - 72

= 106 degrees (adjacent angles)

m < Q = m < RSP ( Opposite angles in a parallelogram are equal).

So m < Q = 180 degrees.

m < x = 360 - 90 - 108

= 360 - 198

= 162 degrees.

Using the appropriate angle theorems, the value of the angle, x in the parallelogram would be 162°

At angle S :

S + 72 = 180 (sum of straight line angles)

S = 180° - 72°

S = 108°

S = Q (opposite angles of a parallelogram)

Q = 108°

Hence,

Q + x + right angle = 360° (sum of angles at a point)

108° + x + 90 = 360

x = 360 - (108 + 90)

x = 162°

Hence, the value of x is 162°

Learn more : https://brainly.com/question/16144029

Find the measure of of RA. A. 24 B. 2 C. 12 D. 3

Answers

Answer: 24

Step-by-step explanation:

R= 3

You can find this using simple algebra

The measure of RA is 24 units after using the concept of congruent triangle option (A) 24 is correct.

What is the congruent triangle?

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

We have a triangle shown in the picture.

It is required to find the measure of the RA

To find the measure of the RA we can apply the concept of congruent triangle:

In the triangle LRU and triangle LAU

LU = LU (common side)

LR = LA (equal sides)

Angle RLU = Angle ALU (equal)

The triangles are congruent.

RU = UA

18 - 2r = 4r

6r  = 18

r = 18/6 = 3

The measure of the RA = 18 - 2r + 4r = 18 + 2r

The measure of the RA = 18 + 2(3) = 18+6 = 24 units

Thus, the measure of RA is 24 units after using the concept of congruent triangle option (A) 24 is correct.

Learn more about the congruent triangle here:

brainly.com/question/12413243

#SPJ2

Perform the indicated operations. (2x+5y+z-6)+(6x-4y-z+7)+(-4x+y-3z-4)

Answers

Answer:

your anwser is 4 x + 2 y − 3 z − 3

Step-by-step explanation:

Simplify:4 x + 2 y − 3 z − 3

Answer:

4x + 2y - 3z -3.

Step-by-step explanation:

2x+5y+z-6)+(6x-4y-z+7)+(-4x+y-3z-4)

Removing the parentheses:

= 2x + 5y + z - 6 + 6x - 4y - z + 7 - 4x + y - 3z - 4

Bringing like terms together:

= 2x + 6x - 4x + 5y - 4y + y + z - z - 3z - 6 + 7 - 4

Simplifying like terms we have:

4x + 2y - 3z -3.

I have 31 stamps total. I have 4 more 1-cent stamps than 8-cent stamps and twice as many one cent stamps as 12 cent stamps. If my stamps are worth $1.78 altogether how many one cent stamps do I have?

Answers

Answer: 14 1-cent stamps (in case anyone else still needs)

Step-by-step explanation:

1-cent stamps=x

8-cent stamps=x-4

12-cent stamp=.5x

x+x-4+.5x=31

2.5x-4=31

2.5x=35

x=14

You can use the $1.78 to double check:

(1*14)+(8*10)+(12*7)

14+80+84=178 cents (or $1.78)

Calculate the average speed in miles per hour of a journey of 36 miles which took 45 minutes. with explanation pls thx

Answers

Speed= distance/time
So your distance is 36 miles and the time is 45 minutes. U convert the time to hours and you’ll get 0.75 hours.

Speed = 36/0.75
= 48 miles/hour

Answer:

= 48 miles/hour

Step-by-step explanation:

Speed=distance/time

Speed = 36/0.75

Which numbers can be classified as rational? Select all that apply.

5/6

[tex] \sqrt{11} [/tex]
6.565656...

0.23

0.32416

-5 3/8

Answers

Answer:

5/6, 0.23, -5 3/8

Step-by-step explanation:

The answer is 5/6 with .

Type the correct answer in each box. If necessary, use / for the fraction bar.
Complete the statements about series A and B.
Series A: 10 + 4 +8/5 + 16/25 + 13/125 + ...
Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...

Series (a or b) has an r value of (blank) where 0<|r|<1. So, we can find the sum of the series. The sum of the series is (blank) ​

Answers

Answer:

Step-by-step explanation:

Given two  series A and B;

Series A: 10 + 4 +8/5 + 16/25 + 13/125 + ...

Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...

Both series are geometric series since they have the same common ratio. Given the geometric series T₁, T₂, T₃, T₄..., the common ratio r is expressed as [tex]\frac{T_2}{T_1} =\frac{T_3}{T_2} =\frac{T_4}{T_3} = r[/tex].

a) For series A, Given T₁ = 10, T₂ = 4, T₃ = 8/5 and T₄ = 13/125

Its common ratio is expressed as [tex]\frac{4}{10} =\frac{8/5}{4} =\frac{13/125}{8/5} = 2/5[/tex]

Hence the common ratio of series A is 2/5

The sum to infinity of the geometric series will be expressed as [tex]s_\infty = \dfrac{a}{1-r}[/tex]

Note that the sum to infifnity is used since the series is tending to infinity.

a is the first term if the series = 10

r - 2/5

On substituting this values into the formula;

[tex]s_\infty = \dfrac{10}{1-2/5} \\\\s_\infty = \dfrac{10}{3/5} \\\\s_\infty = 10* 5/3\\s_\infty = 50/3[/tex]

Hence the sum of the series is 50/3

b) For the series B;

Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...

The common ratio of the series is expressed as shown;

[tex]\frac{3/5}{1/5} =\frac{9/5}{3/5}= \frac{27/5}{9/5 } = r\\ r = (3/5 * 5/1) = 9/5*5/3 = 27/5*5/9 = 3[/tex]

Hence its common ratio is 3.

Sun of the series is expressed similarly as:

[tex]s_\infty = \frac{a}{1-r}\\ s_\infty = \frac{1/5}{1-3}\\\\s_\infty = \frac{1/5}{-2}\\\\[/tex]

[tex]s_\infty = 1/5 * -1/2\\s_\infty = -1/10[/tex]

Hence the sum of series B is -1/10

Plzz help me I’ll mark brainliest

Answers

Answer:

The answer is option B

Step-by-step explanation:

To find the side adjacent to the 50° angle we use tan

[tex] \tan( \alpha ) = \frac{opposite}{adjacent} [/tex]

From the question

The opposite is 6m

The adjacent is ?

So we have

[tex] \tan(50) = \frac{6}{?} [/tex]

[tex]? \tan(50) = 6[/tex]

[tex]? = 6 \times \frac{1}{ \tan(50) } [/tex]

But

[tex] \frac{1}{ \tan(x) } = \cot(x) [/tex]

So we have

[tex] \frac{1}{ \tan(50) } = \cot(50) [/tex]

Substitute it into the expression

That's

We have the final answer as

[tex]? = 6 \cot(50) [/tex]

Hope this helps you

Answer: 6*cot(50),  choice B

=====================================================

Explanation:

We're given an opposite side and an adjacent side. The tangent rule ties these two sides together. "tangent" is nowhere to be found in any of the answer choices, but cotangent is. Recall that

cot = 1/tan

which means

tan = opposite/adjacent

cot = adjacent/opposite

one is the reciprocal of the other

-----------

This means

cot(angle) = adjacent/opposite

cot(50) = x/6

6*cot(50) = x

x = 6*cot(50)

for n prove by
[tex]3 + 3 {}^{2} + 3 {}^{3} ... + 3 {}^{n} = \frac{3(3 {}^{n} - 1) }{2} [/tex]
thank you​

Answers

Answer:

[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]

Step-by-step explanation:

Given

[tex]3 + 3^2 + 3^3 ...+ 3^n[/tex]

Required

Show that the sum of the series is [tex]\frac{3(3^{n}-1)}{2}[/tex]

The above shows the sum of a geometric series and this will be calculated as shown below;

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]

Where

a = First term;

[tex]a = 3[/tex]

r = common ratio

[tex]r = \frac{3^2}{3} = \frac{3^3}{3^2}[/tex]

[tex]r = 3[/tex]

Substitute 3 for r and 3 for a in the formula above;

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex] becomes

[tex]S_n = \frac{3(3^n - 1)}{3 - 1}[/tex]

[tex]S_n = \frac{3(3^n - 1)}{2}[/tex]

Hence;

[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]

12 5 that is the answer for your question

8 w 4 + 10 w 3 − 12 w 2 Factor completely

Answers

Answer:

[tex] 2w^2(w + 2)(4w - 3) [/tex]

Step-by-step explanation:

[tex] 8w^4 + 10w^3 − 12w^2 = [/tex]

First, factor out the GCF of all terms, 2w^2:

[tex] = 2w^2(4w^2 + 5w - 6) [/tex]

Now we work on the trinomial.

Think of ax^2 + bx + c.

Multiply ac

ac = 4 * (-6) = -24

Now we need two numbers whose product is -24 and whose sum is 5.

They are -3 and 8.

We break up the middle term, 5w, into a sum using these two numbers.

5w = 8x - 3w

[tex] = 2w^2(4w^2 + 8w - 3w - 6) [/tex]

Now we factor by parts. We factor a common factor out of the first two terms, and we factor a common factor out of the last two terms.

[tex] = 2w^2[4w(w + 2) - 3(w + 2)] [/tex]

[tex] = 2w^2(w + 2)(4w - 3) [/tex]

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