find the last common denominator for these two rational expressions

Find The Last Common Denominator For These Two Rational Expressions

Answers

Answer 1

Answer:

Least common denominator = (x - 1)²(x - 2)

Step-by-step explanation:

Least common denominator of two rational expressions = LCM of the denominator of the expressions.

[tex]\frac{x^3}{x^2-2x+1}[/tex] and [tex]\frac{-3}{x^{2}-3x+2}[/tex]

Factorize the denominators of these rational expressions,

Since, [tex]x^{2}-2x+1[/tex] = x² - 2x + 1

                             = (x - 1)²

And x² - 3x + 2 = x² - 2x - x + 2

                         = x(x - 2) -1(x - 2)

                         = (x - 1)(x - 2)

Now LCM of the denominators = (x - 1)²(x - 2)

Therefore, Least common denominator will be (x - 1)²(x - 2).


Related Questions

Solve for a.

ab+c=d

a= b + c/d
a = b/(c-d)
a = (d - c)/b

Answers

Answer:

A=d-c/b

Step-by-step explanation:

Answer:

ab+c=d

Step-by-step explanation:

just took the test

Simplify this equation -8a-5a

Answers

Answer:

-13a

Step-by-step explanation:

Since -8 and -5 have like variables, you can subtract them. -8-5 is -13, so the answer is -13a.

Answer:

-13a

Step-by-step explanation:

These two numbers are already like terms, so you can subtract it easily.  

First, don't look at the a.

-8-5= -13 because if something is negative and gets subtracted, that means it'll still be negative.

Now that we now it equals -13, we can add the variable a back onto the answer.  We get -13a.  

PLEASE help me with this question! This is really urgent! No nonsense answers please.

Answers

Answer:

The correct answer is b.

Step-by-step explanation:

if you arrange the data set in ascending order you will have:

x              y

-2            [tex]\frac{1}{100}[/tex]

-1              [tex]\frac{1}{10}[/tex]

0               1

1                10

3               1000

Exponential growth is an increase in a specific way of a data set over time. here, as x increases by a +1, y increases with ×10

There are 45 eighth graders and 20 seventh graders in a school club. The president of this club wants 40% of the club’s members to be seventh graders. How many more seventh-graders must join the club in order to meet the president’s wishes? (Assume that the number of eighth-graders remains the same.)

Answers

Answer: Please Give Brainliest. Thank You!

10 more

The number of seventh-graders that must join the club in order to meet the president's wishes is 10.

Since there are 45 eighth graders and 20 seventh graders in a school club and the president of this club wants 40% of the club’s members to be seventh graders, we need to find the number of seventh graders that will be added to the school club to make their percentage 40 %.

Let the number of seventh-graders to be added be x.

So, the new number of seventh-graders is 20 + x and the new number of people in the club is 45 + 20 + x = 65 + x

Thus, the percentage of seventh graders in the club is thus

[tex]\frac{20 + x}{65 + x} X 100[/tex] %

Since this percentage equals 40 %, we have that

[tex]\frac{20 + x}{65 + x} X 100[/tex]% = 40 %

[tex]\frac{20 + x}{65 + x} = \frac{40}{100} \\\frac{20 + x}{65 + x} = 0.4[/tex]

Cross-multiplying we have

[tex]20 + x = 0.4(65 + x)[/tex]

Expanding the bracket, we have

[tex]20 + x = 26 + 0.4x[/tex]

Subtracting 20 from both sides we have

[tex]x = 26 - 20 + 0.4x\\x = 6 + 0.4x[/tex]

Subtracting 0.4x from both sides, we have

[tex]x - 0.4x = 6\\0.6x = 6[/tex]

dividing both sides by 0.6, we have

x = 6/0.6

x = 10

So, the number of seventh-graders that must join the club in order to meet the president's wishes is 10.

Learn more about percentages here:

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The graphic below shows a protractor, which is used to measure angles. What is the level of accuracy of this measurement tool? its a projractor

Answers

Step-by-step explanation:

A protractor is a handheld to use in measuring angles. It is most cases made up of plastic or glass materials, and can accurately measure angles of circles up to 180°.

However, when measuring straight lengths, a ruler or tape has better measuring accuracy than the protector.

Factorise using suitable identities (0.1x-0.2y)^2

Answers

Answer:

Step-by-step explanation:

(a - b)² = a² - 2ab + b²

a = 0.1x

b = 0.2y

(0.1x - 0.2y)²= (0.1x)² - 2*0.1x*0.2y + (0.2y)²

                   = (0.1)²x² - 0.04xy + (0.2)²y²

                   = 0.01x² - 0.04xy + 0.04y²

Niko is 3 times as old as Lila. Niko's age is the same as adding Lila's age to the product of 3 and Amber's age. Niko is 45 years old. Kameron's age is equal to 2 times the sum of Amber's age and Lila's age. How old is Kameron? years old

Answers

Answer:

Kameron is 50 years old.

Step-by-step explanation:

We can make equations and start filling in what we already know, assuming [tex]n[/tex] is Niko's age, [tex]L[/tex] is Lila's age, [tex]a[/tex] is Amber's age, and [tex]k[/tex] is Kamerons age.

Our first equation:

n = 3L

We know that Niko is 45, so

45 = 3L

Divide both sides by 3:

L = 15

So, Lila is 15 years old.

Another equation:

n = L + 3a

We already know Niko and Lila's age:

45 = 15 + 3a

Subtract 15 from both sides:

30 = 3a

Divide both sides by 3:

a = 10

So Amber is 10 years old.

Another equation:

k = 2(a + L)

We know Amber and Lila's age:

k = 2(10 + 15)

k = 2(25)

k = 50

So Kameron is 50 years old.

Hope this helped!

The Cube root of 66 is between which two integers?

Answers

Answer:

4 and 5

Step-by-step explanation:

cube root of 66 is 4.041240021

(04.01 LC) The science club surveyed 50 students about the number of science courses in which they were enrolled and the time it took them to complete their homework. Classify the random variables from the survey. (2 points) Select one: a. Number of science courses, continuous; time to complete homework, continuous b. Number of science courses, continuous; time to complete homework, discrete c. Number of science courses, discrete; time to complete homework, continuous d. Number of science courses, discrete; time to complete homework, discrete e. Unable to determine from information given

Answers

Answer:

The correct option is;

c. Number of science courses, discrete; time to complete homework, continuous

Step-by-step explanation:

There are two types of random variables, discrete random variables and continuous  random variables

Discrete random variables are variables that are always re-presentable by a finite countable number, such that discrete random variables can be taken as a count of items count

Therefore, as the number of science courses are fixed and such that a specific number can be ascribed to the courses at any time (except there are changes), is a discrete random variable

A continuous random variable is one whose possible values are infinite and are generally measurements of values of such as weight, height, time, and amount

Therefore, the time to complete the homework is a continuous random variable.

It cost Lori $14 to go to the movies. She bought popcorn for $3.50 and a soda for $2.50. How much was her ticket?

Answers

Her ticket was 12.00

Answer:

$8.00

Step-by-step explanation:

You need to add 3.50 and 2.50. your answer will be 6.00. If you subtract 6.00 from 14.00 you will get your answer which is 8.00

Please Help Answer :(

Answers

Answer:

8 ^ 20

Step-by-step explanation:

(8 ^ 10) ^2

We know that a^ b^ c = a^ ( b*c)

8 ^ (10*2)

8 ^ 20

Use the figure below to find the measure of angle x.​

Answers

Answer:

70 degrees

Step-by-step explanation: this is an equilateral triangle. All of its angles are the same.

Please please please help

Answers

Answer:

[tex]\boxed{s=3}[/tex]

Step-by-step explanation:

Use a proportion to solve for the missing side length - a/c = b/d.

AB = XYBC = YZ

4/2 = 6/s cross-multiply

4s = 12 divide by 4

[tex]\boxed{s=3}[/tex]

Answer:

Step-by-step explanation:

Because these triangles are similar, their sides exist in proportion to one another. Their angles are exactly the same. but their sides are proprtionate IF they are similar. We are told they are so setting up the proportion:

[tex]\frac{4}{2}=\frac{6}{s}[/tex] and cross multiply:

4s = 12 so

s = 3

You could also look at the fact that the height of the larger triangle is 4 and the height of the smaller is 2, so the larger is twice as big as the smaller; likewise, the smaller is half the size of the larger (that means the same thing). So if the larger side is 6, half of that is 3.

The length and width of a book cover are 22.2 centimeters and 12 centimeters respectively. The actual length (and width) can be 0.3 unit less than the measured length (and width) or 0.3 unit greater than the measured length (and width). a. Find the minimum and maximum possible lengths and widths of the book cover. b. Calculate the minimum and maximum possible areas of the book cover.

Answers

Part (a)

The length is supposed to be 22.2 cm, but it could be 0.3 cm less

So 22.2 - 0.3 = 21.9 cm is the smallest value for the length. This is the lower bound of the length.

The upper bound is 22.2 + 0.3 = 22.5 cm as it is the largest the length can get.

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

Use this for the width as well

The width is supposed to be 12 cm, but it could be as small as 12-0.3 = 11.7 cm and as large as 12+0.3 = 12.3 cm

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

Answers:smallest length = 21.9 cmlargest length = 22.5 cmsmallest width = 11.7 cmlargest width = 12.3 cm

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

Part (b)

Use the smallest length and width to get the smallest possible area

smallest area = (smallest width)*(smallest length) = 11.7*21.9 = 256.23

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

Repeat the same idea but for the largest length and width to get the largest possible area

largest area = (largest width)*(largest length) = 12.3*22.5 = 276.75

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

Answers:smallest area = 256.23 square cmlargest area = 276.75 square cm

Boden is making a prize wheel for the school fair. The ratio of winning spaces to losing spaces is shown in the diagram. The table shows the number of winning and losing spaces that could be on the wheel. Based on the ratio, complete the missing values in the table.

Answers

The correct answers are Losing 12; Winning 15

Explanation:

The ratio of winning to losing is 5: 6 or 5/6. This means for every 5 winning spaces in the wheel there are 6 losing spaces. This ration should be used to complete the values of the table.

1. The first row shows there are 10 winning and you need to calculate the number of losing spaces. The process is shown below.

[tex]\frac{5}{6} = \frac{10}{x}[/tex] - Express the ratios using fractions; use x to show the missing value

[tex]5x = 60[/tex] - Cross multiply to find the value of x

[tex]x = 60 / 5[/tex] - Solve the equation to find x

[tex]x = 12[/tex] - The number of losing is 12 if there are 10 winning spaces

2. The second row shows there are 18 losing spaces, and you need to calculate the number of winning spaces. Repeat the process.

[tex]\frac{5}{6} = \frac{x}{18}[/tex]

[tex]6x = 90[/tex]

[tex]x = 90 / 6[/tex]

[tex]x =15[/tex] - The number of winning spaces is 15 if there are 18 losing spaces

Answer:

22 and 15 i know because i got it right on khan

Step-by-step explanation:

Please mark mine the brainliest !!

A pair of parallel lines intersected by a transversal and forms same side interior angles that are in a 5:1 ratio. what are the measures of two same side interior angles?

Answers

Answer:

1st side: 150

2nd side: 30

f(x) = x^2. What is g(x)?

Answers

The point shown on g(x) is (1,3)

If x = 1 and y = 3, this means x is multiplied by 3 ( 1 x 3 = 3)

This makes g(x) 3x^2

The answer is A.

Determine if the ordered pair (6, 4) is a solution to the inequality

Answers

Answer:

[tex]\Large \boxed{\mathrm{Option \ D}}[/tex]

Step-by-step explanation:

(6, 4)

x = 6 and y = 4

y > -1/2x + 7

Plug in the values to check if it is true.

4 > -1/2(6) + 7

4 > -3 + 7

4 > 4

This statement is false.

(6, 4) lies on the line.

Try making 100 using:

5,5,5,5,5

?=100

Help ASAP!

Answers

Answer:

(5+5+5+5)*5

20*5=100

[tex]5\cdot5\cdot5-5\cdot5=125-25=100[/tex]

*URGENT* Suppose 12 is raised to the second power, like this: 12^2.
Which answers show the inverse operation?
There is more than one correct answer. Select all that apply.

Answers

Answer:

12 ^ 1/2 or [tex]\sqrt{12}[/tex]

Step-by-step explanation:

12^2

We want to do the inverse operation, which is the square root

We can write the square root as

^ 1/2  or as [tex]\sqrt{ }[/tex]

So the inverse of squaring 12 is

12 ^ 1/2 or [tex]\sqrt{12}[/tex]

Two answers: Choice B, Choice D

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

Explanation:

Both of these represent the same idea. Square root notation is probably what you're more familiar with. It turns out that raising any positive number to the 1/2 power is the same as a square root. We can write

[tex]\sqrt{x} = x^{1/2}[/tex]

The 1/2 power notation may seem more clunky or confusing, but its helpful to extend to things like cube roots, fourth roots, etc.

The more general rule is

[tex]\sqrt[n]{x} = x^{1/n}[/tex]

which says the nth root of x is the same as x^(1/n).

Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was times the weight of the first fish, another was more than times the weight of the first fish, the next was the weight of the first fish, and the last was the weight of the first fish. Bridget's dad caught four fish. The first fish he caught weighed more than times the weight of the first fish caught that day. One fish weighed the weight of the first fish caught that day, one weighed more than times the weight of the first fish caught that day, and the last weighed the weight of the first fish caught that day.

Answers

Answer:

Bridget's first fish =f = 5 ounces

Bridget's dad first fish weighs 17 ounces

Step-by-step explanation:

Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was 2 times the weight of the first fish, another was 2 more than 3 times the weight of the first fish, the next was 1/2 the weight of the first fish, and the last was 3/5 the weight of the first fish. Bridget’s dad caught four fish. The first fish he caught weighed 2 more than 3 times the weight of the first fish caught that day. One fish weighed 4/5 the weight of the first fish caught that day, one weighed 4 more than 2 times the weight of the first fish caught that day, and the last weighed 1/2 the weight of the first fish caught that day. If all the fish Bridget caught have the same total weight as all the fish her dad caught, then the first fish Bridget caught weighed___ ounces and the first fish her dad caught___ weighed ounces.

Solution:

Bridget's fishes:

f ounces

2f ounces

3f+2 ounces

1/2f ounces

3/5f ounces

Total= f +2f + (3f+2) + 1/2f +3/5f

=3f + 3f + 2 + 5f+6f/10

=6f + 2 + 11f/10

=60f+11f/10 +2

=71/10f +2

Bridget's dad fishes

3f+2

4/5f

2f+4

1/2f

Total =(3f+2) + (2f+4) + 4/5f +1/2f

=3f+2+2f+4 + 8f+5f/10

=5f + 6 + 13/10f

= 50f+13f/10 + 6

=63/10f +6

Equate the total weight

71/10f +2=63/10f +6

Collect like terms

71/10f - 63/10f =6-2

71f-63f/10 = 4

8f/10=4

Cross product

8f=40

Divide both sides by 8

f=5

Bridget's first fish =f = 5 ounces

Bridget's dad first fish = 3f +2

=3(5)+2

=15+2

=17 ounces

Bridget's dad first fish weighs 17 ounces

A rope 40m long is used to form a rectangle. If the length of the rectangle formed is 4m longer than the width. Calculate the area of the rectangle

Answers

Answer:

96 sq. m

Step-by-step explanation:

If the width is x, the length is x + 4 and since perimeter = 2 * (length + width), we can write:

40 = 2(x + x + 4)

40 = 2(2x + 4)

20 = 2x + 4

16 = 2x

x = 8 so x + 4 = 12, therefore the area is 8 * 12 = 96 square meters.

Answer:

96m^2

Step-by-step explanation:

40=2(x+x+4)--> 2(2x+4).

20=2x+4

20-4=2x

16=2x

8=x

8✖️12=96m^2

Marcus played 3 different activities this week after school. The time he spent playing is described below. Swam forof an hour Played soccer for 9/10 2/3 2/4 of an hour Jogged forof an hour Which statement correctly compares the times of 2 of his activities?

Answers

Answer:

A

Step-by-step explanation:

We can find a common denominator for all of these fractions, compute, and then compare the values to find the right answer.

Write the last 4 digits of a telephone number (each digit MUST be different--ex. 5237). List all the 4-digit numbers you can make using those 4 digits.

Answers

Answer:

5040

Step-by-step explanation:

All the possible Numbers that can be placed in the last for places =0,1,2,3,4,5,6,7,8,9

If all the digits  have be different , then

= 10 x 9 x 8 x 7

= 90 x 56

=  5040   are total no. of 4-digit numbers can be made using those 4 digits.

An NFL kicker will get paid based on the average hang time of his kicks. His average hang time is modeled by the following question: h=-16t^2 +97.6t. How many seconds do his kicks remain in the air on average?

Answers

Answer:

6.1 seconds

Step-by-step explanation:

set the equation equal to zero

0 = -16t² + 97.6t

factor out t

t(-16t + 97.6) = 0

-16t =- 97.6

t =  6.1

The NFL kicker's kicks remain in the air on average for approximately 3.05 seconds.

To find the average hang time of the NFL kicker's kicks, we need to determine the time at which the height (h) reaches its maximum value. The maximum height corresponds to the peak hang time.

The equation that models the hang time is given as: h = -16t^2 + 97.6t

This is a quadratic equation in the form: h = at^2 + bt + c

In our case, a = -16, b = 97.6, and c = 0 (since there is no constant term).

The time (t) at which the height (h) reaches its maximum value can be found using the formula: t = -b / 2a

Let's calculate the time (t):

t = -b / 2a

t = -97.6 / (2 * -16)

t = -97.6 / -32

t = 3.05 seconds (rounded to two decimal places)

So, the NFL kicker's kicks remain in the air on average for approximately 3.05 seconds.

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A white-tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5,280 feet in one mile. A deer is 10 miles per hour faster than a bison.

Answers

3520/5280 = 2/3 of a mile per minute.

2/3 x 60 minutes per hour = 40 miles per hour.

40-30 = 10

Bison runs 40 miles per hour

The bison runs 10 miles an hour faster than the deer

Answer:

American bison is faster than the white-tailed deer by 10 more miles per hour.

Step-by-step explanation:

In 1 hour there are 60 minutes.

=> 3520 feet = 1 minute

=> 60 minutes = 3520 x 60

=> 211200 feet = 60 minutes

So, 211200 feet can be converted in miles.

=> 1 mile = 5280 feet

=> 211200 feet = x miles

=> x = 211200 / 5280

=> x = 40 miles per hour.

So, a white-tailed deer can run up to 30 miles per hour.

     an American bison can run up to 40 miles per hour.

American bison runs 10 more miles per hour than a white-tailed deer.

!urgent! PLEASE HELP thanks​ will give brainliest

Answers

Answer:

the first four answers are all correct

12. Write 0.8 as a fraction,
Pls explain in full detail.

Answers

Answer:

8/10

Step-by-step explanation:

10x10 is 100 8x10 would be 80 so 80/100=8/10

Answer:

8/10 = 4/5

Step-by-step explanation:

0.8 is 8-10th which means 8 divided by 10

reducing 8/10 to its lowest term since 8 and 10 has 2 as common factor, then

(8=2*4)/(10=2*5)

if 2 cancels out, then you are left with 4/5

Find the surface area of the pyramid.

A.)311.4
B.)230.4
C.)212.6
D.)200.4
Please someone help I am struggling with this

Answers

Answer:

A. 311.4 ft²

Step-by-step explanation:

Use the formula for the surface area of a square pyramid: SA = 2bs + b², where b is the length of a side of the base and s is the slant height.

Plug in the values and solve:

SA = 2(9)(12.8) + 9²

SA = 230.4 + 81

SA = 311.4 ft²

The surface area of the pyramid is 311.4 square units

The surface area of a pyramid is given by the formula:

Surface Area = 1/2 × base area × slant height + perimeter of base × slant height

The base area of the pyramid is 9 × 9 = 81 square units.

The slant height of the pyramid is the length of a line segment that connects a vertex of the pyramid to the midpoint of a side of the base.

We can find the slant height of the pyramid using the Pythagorean Theorem.

slant [tex]h^{2}[/tex] = [tex]h^{2}[/tex] + [tex](base/2)^{2}[/tex]

slant [tex]h^{2}[/tex] = [tex]12.8^{2}[/tex] + [tex]9/2^{2}[/tex] = 230.4

slant height = 15.2

Therefore, the surface area of the pyramid is:

Surface Area = 1/2 × 81 × 15.2 + 4 × × 15.2 = 311.4 square units

So the answer is A.

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sin theta upon 1 + cos theta + 1 + cos theta upon sin theta is equals to 2 cosec theta prove ​

Answers

Answer:

Step-by-step explanation:

I'll use x  instead of theta.

So we have:

sin x / ( 1 + cos x) + (1 +cos x) / sinx

The LCM is sin x(1 + cos x) so we have

sin^2 x + (1 + cos x)^2 /  sin x(1 + cos x)

= sin^2 x + cos^2x + 2 cos x + 1 /  sin x(1 + cos x)

Now sin^2x + cos^2x = 1 so:

= 2 + 2 cos x /  sin x(1 + cos x)

= 2(1+ cos x) /  sin x(1 + cos x)

The 1 + cos x is common so we have:

2 / sin x

= 2 cosec x.

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