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

Tell whether each pair of angle measurements are complementary, supplementary or neither.  36°,24°  18°,72°  96°,84°

Answers

Given:

The pairs of angles are:

36°,24°

18°,72°

96°,84°

To find:

Whether each pair of angle measurements are complementary, supplementary or neither.

Solution:

Two angles are complementary if there sum is 90 degrees.

Two angles are supplementary if there sum is 180 degrees.

For 36° and 24°,

[tex]36^\circ+24^\circ =60^\circ[/tex]

So, this pair is neither complementary not supplementary.

For 18° and 72°,

[tex]18^\circ+72^\circ =90^\circ[/tex]

So, this pair is complementary.

For 96° and 84°,

[tex]96^\circ+84^\circ =180^\circ[/tex]

So, this pair is supplementary.

I NEED THIS ASAP
For what value of q is the equation - 13(9 + 4) = 79 + 16 true?

Answers

Where is q????? Need more info!

Answer:

False

Step-by-step explanation:

ok so

9 + 4 = 13

-13 * 13 = -169

79 + 16 = 95

-165 does not equal 95

Hope this helps!!

A golf course has 18 holes. A guidebook provided to golfers includes useful information about each hole, as shown below. A 4-column table with 6 rows. Column 1 is labeled hole number with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled yards with entries 312, 530, 147, 350, 410, 185. Column 3 is labeled bunkers with entries 2, 5, 1, 0, 2, 1. Column 4 is labeled difficulty level with entries moderate, moderate, easy, moderate, hard, moderate. What are the individuals in this data set? holes yards bunkers difficulty levels

Answers

Answer:

Holes got it right :)

Step-by-step explanation:

Answer

difficulty levels

Step-by-step explanation:

took the test

sorry different question

Felipe calculated that he uses about 545 gallons of fuel each year. His car's owner's manual says that it is approved to use regular fuel. How much money can he save each year by switching from premium fuel, at $4.59 per gallon, to regular fuel at $4.18 per gallon?

$0.41

$2,501.55

$223.45

$2,278.10

$4,779.65

Answers

Answer:

$223.45

Step-by-step explanation:

premium fuel: 4.59 x 545

= 2501.55

regular fuel: 4.18 x 545

=2278.1

2501.55-2278.1 = 223.45

Find the area. The figure is not drawn to scale.

Answers

Answer:

A = 1/2 (13) ( 9 +9)

A = 1/2 (13) (18)

A = 117

What is the equation of the line that passes through the points (15,9) and (-2, 9)?
Oy - 9
11
Oy ----x+ 9
Oy=-17
Oy - 6x + 11

Answers

Answer:

c

Step-by-step explanation:

6x-18=51 solve for x​

Answers

move -18 to the other side
6x=51+18
6x=69
divide both sides by 6
6x divide by 6 and 69 divide by 6
x=11.5

Answer:

11.5

Step-by-step explanation:

add 18 to both sides

divide by 6

Hollis goes outside at 2:00. He spends 48 minutes riding his bike and playing with his dog. What time is it now? Write the time in two ways.

Answers

Answer:

2:48

Step-by-step explanation:

48 minutes passed and he went outside at 2:00 im not sure what they mean by write it in 2 ways though

Trigonometry math, help needed!!!

Find Q, R, and S. I think R is 123. I have provided a picture. Please put the right answer I would appreciate it.

Answers

Answer:

Step-by-step explanation:

PLEASE HELP DUE IN 30 MINUTES ILL GIVE You BRAINLY

Answers

Answer:

C

Step-by-step explanation:

Your answer is C this is just observation so no need for explanation

The radius of a circle is 6 meters. What is the area of a sector bounded by a 150 arc

Answers

Answer:

47.14 m²

Step-by-step explanation:

Recall that the central angle of a full circle is 2π radians or 360°.  The area of the sector bounded by a 150° arc is the fraction

150°

------- times the area of the full circle (πr²):

360°

(15/36)π(6m)² = 0.417(3.14)(36 m² = 47.14 m²

A scale drawing has a scale of 2 cm = 15 m. If the length of something on the drawing is 12 cm, what is the actual length?

Answers

Answer: 90

Step-by-step explanation:

Answer:

90m

Step-by-step explanation:

you have to cross multiply.

1) multiply (12 * 15) and multiply 2 * X)

2) you get 180 = 2x

3) to get X alone divide 180 by 2 and you will get 90meters

Will give brainiest to correct answer with explanation

1. on Thursday, John drove 3x - 6 miles. On Friday, he drove 2x - 8 miles. What is
the difference in miles driven?

Answers

Answer:

The answer is 1x+(-14)

Step-by-step explanation:

Step 1: Write the expression(3x-6)-(2x-8)

Step 2: Do KCC to the whole expression (keep change change)

(3x-6)+(-2x+-8)

Step 3: Rewrite with the like terms together.

(-2x+3x)+(-6+-8)

Step 4: Combine the like terms

1x+(-14)

I NEED HELP ASAP PLS DONT GIVE RANDOM ANSWERS OR LINK I WILL GIVE YOU BRAINLIEST......... thanks :)

Answers

Answer:

D

Step-by-step explanation:

The volume (V) of a cone is calculated as

V = [tex]\frac{1}{3}[/tex] πr²h ( r is the radius and h the height )

Here V = 226 and r = 12 ÷ 2 = 6 , then

[tex]\frac{1}{3}[/tex]π × 6²h = 226 ( multiply both sides by 3 to clear the fraction )

3.14 × 36h = 678

113.04h = 678 ( divide both sides by 113.04 )

h = [tex]\frac{678}{113.04}[/tex] ≈ 6 m ( to the nearest metre )

Solve these simultaneous equations:
6x + 8y = 36 6x + 5y = 27

Answers

Answer:

Y = 3

X = 2

Step-by-step explanation:

(6x2) = 12

(8x3) = 24

12 + 24 = 36

(6x2) = 12

(5x3) = 15

12 + 15 = 27

Solve for x.parallelogram
Plz show steps so I can learn

Answers

Answer:

in a parallelogram .......the sum.of adjacent angles is 180

11x-10+80=180

11x=110

x=10

A television channel broadcasts a baseball game every day. Yesterday's broadcast showed the game for 2 5/6 hours and commercials for 2/3 hour. At this rate, how many hours does the television channel show a game for every hour it shows commercials during its broadcasts?

Answers

Answer:

4.25 hours

Step-by-step explanation:

Given that :

Game broadcast time = 2 5/6 hours = 17/6 hours

Commercials time = 2/3 hours

2/3 hours of commercials = 17/6 of game broadcast

1 hour of commercials = x hours of game broadcast

Cross multiply ;

(2/3)x = 17/6

2x * 6 = 17 * 3

12x = 51

x = 51 / 12

x = 4.25

For every hour it shows commercials, game is broadcasted for 4.25 hours

How many 1/5 cup servings are in 5 cups of cereal?

I need the answer ASAP!

I'll give brainliest!

Answers

Answer:

there are 25 1/5 cups

Step-by-step explanation:

25/5=5

hope this helps

Answer:

25 servings

Step-by-step explanation:

to fill one cup, 5 servings would have to be, um... served.

for 5 cups, it would have to be 5 cups in each of the 5 cups, so 5 * 5, which makes 25 servings

(p.s., pls mark me brainliest, and have a great day!)

Please I need help
I need the equation of the graph below

Answers

Answer:

0x 57=63

Step-by-step explanation:

Which equation represents a circle that contains the point (-5, 3) and has a center at (-2, 1)? Distance formula: vaa -02 (x - 1)2 + ( + 2)2 = 25 (x + 2)2 + (-1)=5 O (* + 2) + (-1) - 25 (x-1) + ( + 2) = 5

Answers

Given:

The center of the circle = (-2,1).

Circle passes through the point (-5,3).

To find:

The equation of the circle.

Solution:

Radius is the distance between the center of the circle and any point on the circle. So, radius of the circle is the distance between the points (-2,1) and (-5,3).

[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]r=\sqrt{(-5-(-2))^2+(3-1)^2}[/tex]

[tex]r=\sqrt{(-5+2)^2+(2)^2}[/tex]

[tex]r=\sqrt{(-3)^2+(2)^2}[/tex]

On further simplification, we get

[tex]r=\sqrt{9+4}[/tex]

[tex]r=\sqrt{13}[/tex]

The standard form of a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where, (h,k) is the center of the circle and r is the radius of the circle.

Substitute h=-2, k=1 and [tex]r=\sqrt{13}[/tex].

[tex](x-(-2))^2+(y-1)^2=(\sqrt{13})^2[/tex]

[tex](x+2)^2+(y-1)^2=13[/tex]

Therefore, the equation of the circle is [tex](x+2)^2+(y-1)^2=13[/tex].

Use the long division method to find the result when 4x^3+18x^2+22x+54x 3 +18x 2 +22x+5 is divided by 2x+52x+5.

Answers

Answer:

2x² + 4x + 1

Step-by-step explanation:

Given the question :

4x^3+18x^2+22x+5 divided by 2x+ 5

Dividend = 4x^3+18x^2+22x+5

Divisor = 2x + 5

In other to ensure question is answered clearly and reasonably, the solution Using long division haa been worked out and attached as a picture

The opposite sides of a parallelogram are _____?

Answers

Answer:

parallel

Step-by-step explanation:

Answer:

A parallelogram is a quadrilateral

Her why:

whose opposite sides are parallel. The opposite angles of a parallelogram are equal. The opposite sides of a parallelogram are equal.

PLEASEEEEEEEE HELPPPPPPP

Answers

It would be the 4th one

What value of x make the equation 24-(3x - 9)-6= -2(4x - 10+ 5x + 7 true?

Answers

Answer:

x = 0

Step-by-step explanation:

24 - (3x - 9) - 6 = -2(4x - 10) + 5x + 7

solve the brackets by using the distribute property:

1(3x - 9) = 3x - 9

-2(2x - 10) = -8x + 20

rewrite the equation:

24 - 3x - 9 - 6 = -8x + 20 + 5x + 7

combine like therms:

27 - 3x = -3x + 27

subtract 27 from both sides:

27 - 3x - 27 = -3x + 27 - 27

- 3x = -3x

add x to both sides of the equation:

-3x + 3x = -3x + 3x

x = x or 0 = 0

to check, substitute 0 for x

24 - (3(0) - 9) - 6 = -2(4(0) - 10) + 5(0) + 7

anything times 0 is 0

24 - (0 - 9) - 6 = -2(0 - 10) + 0 + 7

solve:

24 + 9 - 6 = 0 + 20 + 0 + 7

27 = 27

Two of the sides of a triangle are 7 inches
and 8 inches. If the third side is a whole
number of inches, what is its greatest
possible measure?

Answers

Answer:

11 inches

Step-by-step explanation:

7^2+8^2=c^2

49+64=c^2

113=c^2

square root both side

c=10.63014581

round up and get c=11

hope this helped :)

Use substitution to solve the following system of equations.
x + 2y = 13
3x - 5y = 6

Answers

Answer:

{1} x + 2y = 13

{2} 3x - 5y = 6

x = 13 - 2y

substituting into {2}

3x -5y = 6

3( 13 - 2y) - 5y = 6

39 - 6y -5y = 6

-11y = 6 -39

y = -33 /-11

 ( minus and minus cuts in fraction, so the answer will come in positive)

y = 3

now , substituting into {1}

x + 2(3) = 13

x = 13 -6

x = 7

so,

the solution are:-

x = 7

y = 3

I hope this helps a little bit.

A tennis ball is launched from a catapult from the ground with an initial velocity of 26fps. What is the maximum height of the ball? When will it attain this height? Use H=-16T2+26T

Answers

Answer:

10.5618feet, 0.8125sec

Step-by-step explanation:

Given the height reached by the catapult expressed by the equation H=-16T^2+26T

At the maximum height, the velocity of the object is zero, hence;

v = dh/dt = 0

-32t + 26 = 0

-32t = -26

t = 26/32

t = 0.8125secs

Hence it will attain the maximum height after 0.8125second

Substitute t = 0.8125s into the expression to get the maximum height

H=-16t^2+26t

H = -16(0.8125)^2 + 26(0.8125)

H = -16(0.6602) + 21.125

H = -10.5632+21.125

H = 10.5618

hence the maximum height reached by the ball is 10.5618feet

A package of sliced cheese weighs 2 1/4 pounds and costs $18. If 3 slices weigh a total of 2 ounces, how much do the 3 slices cost?

Answers

10 slices will cost 10 dollars

whats the mode of $6.00 $6.00 $6.00 $6.00 $5.00 $7.00 $4.00 $7.00​

Answers

Answer:

4.00,5.00,6.00,6.00,6.00,6.00,7.00,7.00

Step-by-step explanation:

Mean  5.875

Median  6

Mode 6.00

Isaac received 125 for his birthday. He spent 65 on a new video game. How much money, x, how much does issac have

Answers

Answer: $60

Step-by-step explanation:

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