Multiplying and dividing radical expressions and leaving them in factored form. I am trying to find the best and easy way to get the factored form correctly. This is my problem: 3x+8 over 36-2x / 27x^2+72x over 3x^2-27.

Answers

Answer 1

Answer:

[tex]\frac{3x + 8}{36 - 2x} / \frac{27x^2 + 72x}{3x^2 - 27} = \frac{(x - 3)(x+3)}{6x(18 - x)}[/tex]

Step-by-step explanation:

Given

[tex]\frac{3x + 8}{36 - 2x} / \frac{27x^2 + 72x}{3x^2 - 27}[/tex]

Required

Solve

Change / to *

[tex]\frac{3x + 8}{36 - 2x} * \frac{3x^2 - 27}{27x^2 + 72x}[/tex]

Factor out 3

[tex]\frac{3x + 8}{36 - 2x} * \frac{3(x^2 - 9)}{3(9x^2 + 24x)}[/tex]

[tex]\frac{3x + 8}{36 - 2x} * \frac{(x^2 - 9)}{(9x^2 + 24x)}[/tex]

Factorize:

[tex]\frac{3x + 8}{36 - 2x} * \frac{(x^2 - 9)}{3x(3x + 8)}[/tex]

Cancel out 3x + 8

[tex]\frac{1}{36 - 2x} * \frac{(x^2 - 9)}{3x}[/tex]

Factorize:

[tex]\frac{1}{2(18 - x)} * \frac{(x^2 - 9)}{3x}[/tex]

Combine

[tex]\frac{x^2 - 9}{2*3x(18 - x)}[/tex]

[tex]\frac{x^2 - 9}{6x(18 - x)}[/tex]

Express the numerator as a difference of two squares

[tex]\frac{(x - 3)(x+3)}{6x(18 - x)}[/tex]

Hence:

[tex]\frac{3x + 8}{36 - 2x} / \frac{27x^2 + 72x}{3x^2 - 27} = \frac{(x - 3)(x+3)}{6x(18 - x)}[/tex]


Related Questions

PLEASE HELP!!! :(
Consider the following figure
What is BD? ​

Answers

Answer:

BD = 16

Step-by-step explanation:

32/BD = BD/8

BD² = 256

BD = 16

Monthly grocery cost based on the average number of shopping trips is predicted using the least-square regression line, ŷ = 275.3 + 90.7x, where ŷ represents the predicted monthly expense and x represents the average number of trips. A shopper visits the grocery store an average of 3.2 times and has a monthly cost of $520. What is the residual for the shopper?

45.54
76.47
−45.54
−76.47
90.7

Answers

Answer:

−45.54

Step-by-step explanation:

Just took the test

The residual for the shopper will be equal to -45.54. Hence, option C is correct.

What is an equation?

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given data provided in the question,

The given equation is,

y = 275.3 + 90.7 x

Here, x is the number of trips and y is the total monthly expense.

Then,

Shopper monthly cost = $520

Number of visits by the shopper in a month = 3.2

So, the residual for the shopper will be,

$520 = 275.3 + 90.7 (3.2)

$520 = 275.3 + 290.24

= -45.54

To know more about equation:

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PLS HELP (MARKING BRAINLIEST)

Answers

Answer:

there is a fraction calculator you can use

https://www.calculatorsoup.com/calculators/math/fractions.php

Step-by-step explanation:

Jenny wants to buy an MP3 player that costs $30.98. Write an equation so find how much change (x) she receive if she gives the cashier $40. *

Answers

Answer:

40.00-30.98=x

what is the slope of this line?

Answers

Answer:

-1/200

Step-by-step explanation:

To get from one point to the other you rise (go down in this case since the slope is negative) $1 every time you make 200 more scarves.

in the figure below, lines m and n are parallel. What is the value of x?

Answers

Answer:

x = 51

Step-by-step explanation:

It looks like alt int. angles (correct me if im wrong)

3x - 40 = 2x + 11

x = 51


What is the value of 7P3?
021
35
210
840

Answers

Answer:

210

Step-by-step explanation:

The answer for 7p3 is : 210. This can be solved in the following way: 7p3 is an expression for permutation which means the number of ways of arranging 3 items from a total of 7 items.

Hope This Help?

Please Mark Me Brainly!

Lorenzo's family is driving to the beach to go kayaking with sea otters. The beach is 85 miles from Lorenzo's house. They have already driven 63 miles. Help and plz put the equation

Answers

Answer: See explanation

Step-by-step explanation:

Your question isn't complete but I'm guessing that you want to find the equation to know the miles left for Lorenzo family to reach the beach.

The equation will be gotten by subtracting the distance that the family has driven already from the total distance from their house to the beach. This will be:

= 85 miles - 63 miles

= 22 miles

Felipe planted some seeds for a science project. One of his plants grew 6 1/2 inches in the first week, and then it grew 5 3/4 inches during the second week. How much did the plant grow during these two weeks? The answer should be written as a proper mixed number and should be simplified, if possible. *ill give brainliest*

Answers

Answer:

12 1/4

Step-by-step explanation:

3-4/5X-2/3–3/15+3/5divided by -3/2

Answers

Answer:

-2(6x-13)/15

Step-by-step explanation:

This is done by simplifying the expression as well as combining like terms

you rode a bicyde for 2 hours and travelled 43 km, calculate your average
speed.​

Answers

Answer:

22.5km per hour

Step-by-step explanation:

Pls Help!!!!! I will pick the brainiest answer as well. ;)

Answers

Answer:

49

Step-by-step explanation:

20+4=24 24+25=49

Help what is the value

Answers

Answer:

I love you 3566267840 and pas 123456

Find the zeroes of the quadratic polynomial 4x²-4x+1 and verify the relation between its zeroes and coefficients

Answers

Answer:

A) zeros are x = ½ or x = ½

B) >> sum of zeros = (-Coefficient of x)/(Coefficient of x²)

>> Product of the zeros = Constant term/Coefficient of x²

Step-by-step explanation:

To find the zeros, we will equate the polynomial to zero.

Thus;

4x² - 4x + 1 = 0

Using quadratic equation, we can find the zeros.

x = [-(-4) ± √((-4)² - (4 × 4 × 1))]/(2 × 4)

x = (4 ± 0)/8

x = 4/8 and x = 4/8

Thus, zeros are x = ½ or x = ½

Now, to find the relationships between its zeroes and coefficients;

Sum of zeroes = ½ + ½ = 1

This is equal to -b/a = -(-4)/4 = 1.

Thus;

sum of zeros = (-Coefficient of x)/(Coefficient of x²)

Product of zeros = ½ × ½ = ¼

c/a = 1/4

This is equal to the product of the zeros.

Thus;

Product of the zeros = Constant term/Coefficient of x²

4) Ari can swim 2 laps per minute. Which equation represents the number of laps,
n, that Ari travels in m minutes?
a n = 2m
b. m = 2n
c. n = 2 +m
d. n = 2 divided by m

Answers

It’s a, n=2m. ||||||||||||||||||||

What is the distance between points S and U if S is 2, 1 and U is 6, 8

Round to the nearest tenth of a unit.


A. 3.3 units

B. 6.4 units

C. 8.1 units

D. 12.0 units

Answers

The distance formula is:

D = sqrt((x2-x1)^2 + (y2-y1)^2)

D= sqrt ((6-2)^2 + (8-1)^2)

D = sqrt(4^2 + 7^2)

D = sqrt( 16 + 49)

D = sqrt(65)

D = 8.06

Rounded to the beat tenth = 8.1 units.

The answer is C. 8.1 units

Answer:

C

Step-by-step explanation:

S has coordinates (2 , 1) and U has coordinates (6, 8) . Computing the SU vector gives us (4 , 7)

taking the distance formula : sqrt(4^2 +7^2)

= sqrt(65) = 8.1 which is answer C

Division sum:
20 ➗ 2 =

Answers

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

20/2 = 10

Find the sum.
5y+2/xy^2 + 2x-4/4xy

Answers

[tex]\frac{5y+2}{xy^2}[/tex]+[tex]\frac{2x-4}{4xy}[/tex]=[tex]\frac{xy+8xy+4}{2xy^2}[/tex]

or just (xy+8y+4)/2xy^2 if u can't see the equation

The value of the expression using sum will be (8y + xy + 4) / (2xy²).

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ [(5y + 2) / (xy²)] + [(2x - 4) / (4xy)]

Simplify the expression, then we have

⇒ [(5y + 2) / (xy²)] + [(2x - 4) / (4xy)]

⇒ [4(5y + 2) / (4xy²)] + [y(2x - 4) / (4xy²)]

⇒ [(20y + 8) / (4xy²)] + [(2xy - 4y) / (4xy²)]

⇒ (20y + 8 + 2xy - 4y) / (4xy²)

⇒ (16y + 2xy + 8) / (4xy²)

⇒ (8y + xy + 4) / (2xy²)

The value of the expression using sum will be (8y + xy + 4) / (2xy²).

More about the Algebra link is given below.

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what is the gcf (greatest common factor) of 9/45​

Answers

Answer:

9: 1,3,9

45: 1, 3, 5, 9, 15, and 45

Step-by-step explanation:

So the gcf is 9

Answer:

9

GCF of 9 and 45 is 9

Step-by-step explanation:

The greatest common factor of two numbers x and y is the greatest number that divides x and y leaving the remainder as 0

We can find the GCF of 9 and 45 by the following methods.

GCF of 9 and 45 by Listing the Common Factors Method

GCF of 9 and 45 by Prime Factorization Method

Help ASAP! use the second image attached to answer!

Answers

Answer:

only the circle graph

Step-by-step explanation:

Answer:

Only the graph

Step-by-step explanation:

Im not an expert or anything but the chart only shows numbers, which aren't useful, but the circle shows, under the 80-89, 44.4%, which is the useful one. hope that helps you

Which values for A and B will create infinitely many solutions for this system of equations? A x minus y = 8. 2 x + y = B.

Answers

Answer:

A = -2

B = -8

Step-by-step explanation:

A system of equations has infinitely many solutions when both equations are exactly the same equation, then both graphs intersect in infinitely many points, meaning that the system has infinitely many solutions.

Then if we have the equations:

A*x- y = 8

2*x + y = B

We want to find A and B such that both equations are exactly the same thing.

Notice that in the first one we have negative y, while in the second we have positive y.

Then A needs to be minus the coefficient that multiplies x in the other equation, this means that:

A = -2

And B needs to be minus the corresponding therm in the other equation, then B = -8.

Then the system becomes:

-2*x - y = 8

2*x + y = -8

We can see that one equation is -1 times the other, so if we write both of them as linear equations in the slope-intercept form, we get:

y = -8 - 2*x

y = -8 - 2*x

So both equations are exactly the same thing, meaning that we have infinitely many solutions.

Which would be the most appropriate way to estimate -6.1(0.22)

Answers

Answer: Answer is 1

Step-by-step explanation:

Calculate the area of the right - angled triangle with base of 18cm and height 6.5cm

Answers

Answer:

area = 58.5 cm²

Step-by-step explanation:

area = 18 x 6.5 x 0.5 = 58.5 cm²

Work out the mean for the data set below: 58002, 58003, 58002, 58003, 58003, 58005, 58003

Answers

Step-by-step explanation:

Mean x¯¯¯ 58003

Median x˜ 58003

Mode 58003

Range 3

Minimum 58002

Maximum 58005

Count n 7

Sum 406021

Quartiles Quartiles:

Q1 --> 58002

Q2 --> 58003

Q3 --> 58003

Interquartile

Range IQR 1

Outliers 58005

copy machine goes brr

Is the number 0.1875 rational or irrational

Answers

rational...............

-1/4n-7<5

Answers:
-48
-20
0
20
48

Answers

Answer: -1/4n-7<5 = -48

14. Given that log 2 = 0.3010 and log 3 = 0.4771 , how can we find log 6 ?
A. log6 = log2 x log3 = 0.3010 x 0.4771
B. log6 = log2 + log3 = 0.3010 + 0.4771
C. log6 = log2 – log3 = 0.3010 – 0.4771
D. log6 = log2 = log3 = 0.3010 = 0.4771

Answers

Answer:

B. log6 = log2 + log3 = 0.3010 + 0.4771

Step-by-step explanation:

log 2 = 0.3010

log 3 = 0.4771

log 6 = ?

6 = 3 * 2

log 6 = log (3 * 2)

According to log rules;

log (a * b) = log(a) + log (b)

This means;

log 6 = log 3 + log 2

Inserting the values they represent;

log 6 =  log 3 + log 2 =  0.4771  + 0.3010

Correct option:

B. log6 = log2 + log3 = 0.3010 + 0.4771

leroy is calculating the probability of rolling a regualr 6-sided die and flipping a coun. He wants to know the probability if rolling a 4, then landing on heads twice Find P(4 and H and H).

Answers

Answer:

To roll the 4 is 1/6 and landing heads twice is 1/4 and 1/6 x 1/4 and the probability of him doing that would be 0.04166666666% chance

Step-by-step explanation:

Solve each equation b+3.3=8.9 what is b?

Answers

the answer will be 5.6 !

you can get this by doing 8.9 - 3.3 ! remember you can apply this to all problems by turning division to multiplication, addition to subtraction, etc.

please mark brainliest if this was useful ♡

please helps
Which function represents this sequence?

A.
f(n) = 4 ∙ 2n-1

B.
f(n) = 4n-1

C.
f(n) = 2 ∙ 4n-1

D.
f(n) = 2n-1

Answers

Answer: A. f(n) = 4 ∙ 2n-1

Step-by-step explanation:

because the 1st term is 4 according to your image, and then you will have to multiply that by its common difference and using your table, to get from 4 to 8 then 8 to 16 you would multiply by 2, and you would finally multiply that by n or known as the number of terms and 1 making the equation. f(n) = 4 ∙ 2n-1 I hope this is very helpful for everyone.

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