find LCM of:

x2 - 9, 3x3 + 81​

Answers

Answer 1

Answer:

[tex]\boxed{\pink{\sf (x + 3) \ is\ the \ LCM . }}[/tex]

Step-by-step explanation:

Given two expressions ,

[tex] \qquad (1)\: x^2 - 9 \\\\ \qquad (2)\:3x^3 + 81 [/tex]

And , we need to find the LCM , that is lowest common factor . So , let's factorise them seperately .

Factorising - 9 :-

[tex]= x^2 - 9 \\\\= x^2 - 3^2 \\\\ \red{= (x+3)(x-3)} \qquad\bf [Using \ a^2-b^2 = (a+b)(a-b) ][/tex]

Factorising 3x³ + 81

[tex]= 3x^3 + 81\\\\= 3(x^3+27) \\\\= 3( x^3+27) \\\\ = 3(x^3+3^3) \\\\ \red{= 3 [ (x+3)(x^2+9-3x) ] } \qquad \bf{[ Using \ a^3+b^3=(a+b)(a^2+b^2-ab) ] } [/tex]

Hence we can see that (x+3) is common factor in both expressions.

Hence the LCM is ( x+3 ) .


Related Questions

Which statements are true about the ordered pair (10, 5) and the system of equations?
(Look at the file to answer the question)

Answers

Answers:

The first and third options should be selected.

The ordered pair (10,5) is a solution to the first equation because it makes the first equation true. The ordered pair (10,5) is not a solution to the system because it makes at least one of the equations false.

Explanation:

In order for a point to be a solution to a system of equations, it must make both equations true when its x and y values are substituted in. That being said, we need to test if (10,5) is a solution for the two equations.

Let's try the first equation. Substitute 10 for x and 5 for y and solve:

[tex]2x - 5y = -5\\2(10) - 5(5) = -5\\20 - 25 = -5\\-5 = -5[/tex]

-5 does equal -5, so (10,5) is a solution to the first equation.

Next, let's test the second equation. Do the same:

[tex]x + 2y = 11\\(10) + 2 (5) = 11\\10 + 10 = 11\\20 = 11[/tex]

However, 20 does not equal 11, therefore (10,5) is not a solution to the second equation.

So far, we know that (10,5) is a solution to the first equation, but not the second equation. Knowing this, it cannot  be a solution to the system because it does not make both equations true. Therefore, only the first and third options should be selected.

IF YOU HELP ILL GIVE 100 POINTS AND BRAINLIEST! PLEASE HELP!!Which expression is equivalent to 4(23)?

4(2+13)

4(20+30)

4(2+3)

4(20+3)

Answers

Answer:

4(20+3)

Step-by-step explanation:

4(2+13) = 4(15)

4(20+30) = 4(50)

4(2+3) = 4(5)

4(20+3) = 4(23)

Therefore, 4(20+3) is the answer since it's equivalent to 4(23).

Answer:

............................................4(20+3)

Find the equation of the line specified. The line passes through the points (7, -7) and (6, -5)

a. y = -2x + 7
b. y = 2x -21
c. y = -2x - 7
d. y = 2x - 7​

Answers

Answer:

a. y = -2x + 7

Step-by-step explanation:

First, find the slope by plugging the points into the slope formula, [tex]\frac{-7+5}{7-6}[/tex], which equals -2. Then use the slope and the point (7,-7) to make an equation in slope-point form. y+7=-2(x-7), finally solve for y to get y=-2x+7.

Answer:

A

Step-by-step explanation:

a+4b=-4 a+10b=-16
how to solve this problem ​

Answers

Answer:

a,b=4,-2

Step-by-step explanation:

Subtract:

a-a+4b-10b=-4-(-16)

-6b=-4+16

-6b=12

b=-2.

Plug in:

a+4(-2)=-4

a-8=-4

a=4.

Hope this helps plz hit the crown :D

1/2y=4, x-1/2y=2 the system of equations above has solution (x,y)

Answers

Answer:

(6, 8)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Equality PropertiesSolving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

1/2y = 4

x - 1/2y = 2

Step 2: Solve for y

Define equation:                    1/2y = 4Isolate y:                                 y = 8

Step 3: Solve for x

Define equation:                    x - 1/2y = 2Substitute in y:                       x - 1/2(8) = 2Multiply:                                  x - 4 = 2Isolate x:                                 x = 6

Answer: (6,8)

Step-by-step explanation:

1/2y = 4          

x - 1/2y = 2    

First  solve for y in the first equation.

1/2y = 4      Divide both sides by 1/2

y  =  8  

NOw substitute the value of y into the second equation and solve for x.

x

x - 1/2(8) = 2

x - 4 = 2

  +4     +4

x = 6    

THis makes the solution  (6,8)

Convert 25°C to Fahrenheit. Use the formula F = (1.8)C + 32°.
58.8°F
102.6°F
77°F
52°F

plz help

Answers

Answer:

77 F

Step-by-step explanation:

F = (1.8)*25 + 32

  = 45+32

  = 77

Hope this helps!

Answer:

77 degrees Fahrenheit

Step-by-step explanation:

plug 25 into 'C' in the formula

F = 1.8(25) + 32

PLEASE ANSWER THIS QUESTION RIGHT PLEASE Devante Has a lunch account in the school cafeteria. His starting balance at the beginning of the month is $35.50 The first week Devante But three lunches and his account balance was$28. The second week Devante  Bought five lunches and his account balance was $15.50 in a model that relates the balance of his lunch account as a function of the number of lunches he buys what does the rate of change represent? THE ANSWER CHOICES ARE IN THE PICTURE ABOVE

Answers

Answer:

C) The amount of money in his lunch account

Step-by-step explanation:

Use the following half-angle identity to find the exact value of tan165.
Tan(a/2)= plus or minus the square root of (1-cos a/ 1+cos a)
A. 2- sqrt 3
B. 2+ sqrt 3
C. - sqrt (7-4 sqrt 3)
D. Sqrt (7-4 sqrt 3)

Answers

Answer:

d on edge

Step-by-step explanation:

Pam read 126 pages of her summer reading book in 3 hours. Zac read a 180 pages of his sunday reading book in 4 hours. If they continue to read at the same speeds, will they both finish the 215 page book after 5 total hours of reading. explain

Answers

Answer:

yes they both will because in four they both read more then half the book and one more hours should let them finshed the book

Step-by-step explanation:

Answer:

Zack is able to, but Pam cannot.

Step-by-step explanation:

Number of pages Pam read in 5 hours = 5 x 42 = 210 pages

Number of pages Zack read in 5 hours = 5 x 45 = 225 pages

Zack's pages is greater than 215 while Pam isn't able to read as much.

please help if you think you hot beautiful kind funny cool please help me please

Answers

Answer/Step-by-step explanation:

The equation of the line that passes through the two points would be correct if each point, when substituted into the equation, satisfy the equation.

This is what I mean:

Given the equation of the line, y = 2x - 5, and the two points (-2, -9) and (3, 1):

For the first point, substitute x = -2, and y = -9 into y = 2x - 5.

Thus:

-9 = 2(-2) - 5

-9 = -4 - 5

-9 = -9 (this is true). It means the line runs through the point (-2, -9)

For the second point, substitute x = 3, and y = 1 into y = 2x - 5

This:

1 = 2(3) - 5

1 = 6 - 5

1 = 1 (this is true). This also means the point, (3, 1) is also a point that the equation runs across.

help me please i really need help!

Answers

Answer:

51.3°

Step-by-step explanation:

tan y = 10/8 = 1.25

y = 51.3°

51.3 degrees your welcome

please help me if you think you're kind lovely beautiful super hot please help me

Answers

Answer:

y2-y1

x2-x1

should be correct

Step-by-step explanation:

prove me wrong

Brian purchases an RV for $32,000. The value of the RV is decreasing exponentially at a rate of 5% per year. Write a function that could be used to model the value of the RV where x represents the number of years since the RV was purchased . What will the RV be worth in 20 years? Please show work

Answers

Answer:

the value of the project is $16,096.88

The computation of the value of the project is shown below:

= (Expected amount generated per year × (1 - (1 ++ rate of returm)^-time period )) ÷ rate of return

= $36,950 ×  [1 - 1.1^-6] ÷ 0.1

= $16,0926.88

Hence, the value of the project is $16,096.88

We simply applied the above formula so that the correct value could come

And, the same is to be considered

How much would you need to deposit in an account now in order to have $2000 in the account in 10 years? Assume the account earns 2% interest compounded monthly ​

Answers

Step-by-step explanation:

A(t) = amount in t years

P = Principal (original investment)

r = annual interest rate (in decimal form)

n = number of times that interest is compounded each year

A(t) = P(1 + r/n)nt

Substitute in the given values: 2000 = P(1 + 0.04/12)12(10)

2000 = P(1.490832682)

P = $1341.53

The quantity r varies jointly with t and u and inversely with s when t= -12, u= -7, and s= -4, r= -126. Find r when t= -8, u= 8, and s= -6.

Write your answer in exact form.

Answers

Answer:

r = 64

Step-by-step explanation:

r = (k*t*u)/s

Where,

k = constant of proportionality

t = -12,

u= -7,

s= -4,

r= -126.

r = (k*t*u)/s

-126 = (k*-12*-7)/-4

-126 * -4 = 84k

504 = 84k

k = 504/84

k = 6

Find r when t= -8, u= 8, and s= -6.

r = (k*t*u)/s

= (6*-8*8) / -6

= -384 / -6

= 64

r = 64

help me quick!!!..!..!

Answers

Answer:more info needed

Step-by-step explanation:

see the block between path 1 and 2? figure out how big that square is, and subtract how much area triangle ABC takes up. that is your answer

If the value of a in the quadratic function f(x) = ax^2+bx+c is 1/2 the function will:

Answers

lessen it data

and it will become a bigger eqaution

Answer:

open down and have a maximum

Step-by-step explanation:

I took the quiz got it right

9x(-1)-18 divided by (4+5)

Answers

Answer:

Step-by-step explanation:

9x times -1 =-9x

-9x-18 divide

(4+5=)9

divide 18 by the denominator 9 and get

-9x-2

/1

since anything pretty much divided by 1 remains the same this is simplified to

-9x-2 and since you dont know x's variable this is its simplifed form

Answer:

-9x-2

Step-by-step explanation:

[tex]9x(-1)-18/(4+5)[/tex]

Multiply 9x and -1

[tex]-9x-18/(4+5)[/tex]

Add 4 and 5

[tex]-9x-18/9[/tex]

Divide 18 and 9

[tex]-9x-2[/tex]

I hope this helps!

Hurricane Katrina dropped about 14 inches of rain over a 48 hour period. How much rain is this per hour?​

Answers

Answer:

Step-by-step explanation:


Why is looking at cash flow an important step in a good financial plan?

Answers

Answer:

Cash flow refers to the constant movement of money, both where and how much you're spending as well as how much you're earning in return.

Step-by-step explanation:

(3n-9)+(1/5n+13)=(?+1/5n)+(-9+?)=?


Can u halp :C you need to simplify answer

Answers

Answer:

[tex]3\frac{1}{5}n[/tex] + 4

Step-by-step explanation:

First Step: Write the equation

(3n - 9) + ([tex]\frac{1}{5}[/tex]n + 13) =

Second Step: Combine like terms together

(3n + [tex]\frac{1}{5}[/tex]n) + (-9 + 13)=

Third Step: Simplify

[tex]3\frac{1}{5}n[/tex] + 4

Hope this helped! <3

pplease please please please please please please please please please please help me

Answers

Answer:

I'm I'm confused because

Step-by-step explanation:

which question are you talking about?

In a representative sample of 1000 adult Americans, only 400 could name at least one justice who is currently serving on the U.S. Supreme Court. Using a significance level of 0.01, carry out a hypothesis test to determine if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court. (For z give the answer to two decimal places. For P give the answer to three decimal places.)
z=
p=

Answers

Answer:

1) z = -6.32

2) p-value = 0.001 × 10^(-2)

3) we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

Step-by-step explanation:

We are told that In a representative sample of 1000 adult Americans, only 400 could name at least one justice.

Thus:

Sample proportion; p^ = 400/1000 = 0.4

Sample size: n = 1000

We want to find if there is convincing evidence to support the claim that fewer than half of adult Americans can name at least one justice.

Thus, the hypothesis is defined as;

Null hypothesis:H0: p ≥ 0.5

Alternative hypothesis: Ha < 0.5

Formula for the test statistic is;

z = (p^ - p)/√(p(1 - p)/n)

Plugging in the relevant values;

z = (0.4 - 0.5)/√(0.5(1 - 0.5)/1000)

z = -6.32

From online p-value from z-score calculator attached, using z = -6.32; significance level of 0.01; one tailed hypothesis;

We have:

p-value = 0.00001 = 0.001 × 10^(-2)

The p-value is less than the significance level and so we will reject the null hypothesis and conclude that there is enough evidence to support the claim that fewer than half of adult Americans can name at least one justice currently serving on the Supreme Court

Jim rides his bike 4 miles in 30 minutes. If he maintains this rate, how far will he ride in 3 hours? 60 minutes = 1 hour

Answers

You have to convert the three hours into minutes which will be 180 minutes the multiply that by the miles (4) and then divide by the 30 minutes which will be 24


Demetrius Scored 28 points in5 56 minutes duringa game of tennis. How many points did he average per minute during that
5 and 56 minutes? Type your answer as a simplified improper fraction

Answers

Answer:

420/89

Step-by-step explanation:

What we know:

Demetrius scored 28 points in 356 seconds.

To get the per second rate divide 28 by 356.

28/356 = 7/89

Here, we're looking for the per minute rate, so multiply the previous rate by 60.

(7*60)/89 = 420/89 (Since this asks for an improper fraction, I'll keep it as so.)

katie collets stamp she has stamps from canada, United Staes,ands Rest of the world in a ratio of 1:1.2:1.5 she has 135 stamps from rest of the world

Answers

Answer:

90 stamps from Canada, 108 stamps from the United States, and 135 stamps from the Rest of the World

Step-by-step explanation:

Since this is a problem of proportion we can use the Rule of three to solve this. We do this by multiplying the diagonal available values and dividing by the third value in order to get the missing variable, which in this case would be the number of stamps in the other country. Like so...

1.5  <=====>  135 stamps

1.2  <=====>  x  stamps (United States)

(1.2 * 135) / 1.5 = 108 stamps (United States)

1.5  <=====>  135 stamps

1  <=====>  x  stamps (Canada)

(1 * 135) / 1.5 = 90 stamps (Canada)

Finally, we can see that Katie had 90 stamps from Canada, 108 stamps from the United States, and 135 stamps from the Rest of the World. All creating a ratio or 1:1.2:1.5

multiply y by 9, then divide 10 by the result

Answers

Answer:

10/(9y)

Step-by-step explanation:

multiply y by 9: 9y

then divide 10 by the result: 10/(9y)

Which equation is equivalent to y=2/3x-6

A.2x+3y=-6
B.3x-2y=6
C.3x-2y=12
D.2x-3y=18

Answers

d.2x-3y=18 thankssss

which graph shows a trend line that best fits the data?

Answers

Answer:

B

Step-by-step explanation:

Here is the meaning of the "Line of Best Fit" refers to a line through a scatter plot of data points that best expresses the relationship between those points. A straight line will result from a simple linear regression analysis of two or more independent variables.

Here is the rule for the "Line of Best Fit"

A line of best fit can only be drawn if there is strong positive or negative correlation. The line of best fit does not have to go through the origin. The line of best fit shows the trend, but it is only approximate and any readings taken from it will be estimations.

Answer:

B

Step-by-step explanation:

The line starts where the points starts and the line ends where the points end .

Solve for x using the
distributive property.
4(3x - 1) = 56

Answers

Answer:

Step-by-step explanation:

12x - 4 = 56

add 4 to each side

12x = 60

divide each side by 12

x = 5

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