The smallest non-zero real number by which √27 should be multiplied so as to get a rational number is:
[tex]a) \: \sqrt{3} \\ b) \: \frac{1}{ \sqrt{3} } \\ c) \sqrt{13} \\ d) \sqrt{27} [/tex]
I doubt between a) and b).
Please solve this and give me the accurate answer. Step-by-step solution needed. Spam free answer required.
Thank you in advance.​

Answers

Answer 1

Answer:

[tex]b)1/\sqrt{3}[/tex]

Step-by-step explanation:

Lets verify one-by-one:

a)

[tex]\sqrt{3} *\sqrt{27} =\sqrt{3*27} =\sqrt{81} = 9[/tex]

b)

[tex]1/\sqrt{3}*\sqrt{27} =\sqrt{1/3*27} =\sqrt{9} =3[/tex]

c)

[tex]\sqrt{13} *\sqrt{27} =\sqrt{13*27} =\sqrt{39*9} =3\sqrt{39}[/tex]

d)

[tex]\sqrt{27} *\sqrt{27} =(\sqrt{27})^2=27[/tex]

As we see in three cases we get rational number but the smallest one is 3, this indicates the answer is option b.


Related Questions

5/12 divided by 3 in fractions

Answers

Answer:

5/36

Step-by-step explanation:

First you need to find the "reciprocal" (the opposite, so the numbers switched around) of the second number, which is 3. In turn, the 3 would become 1/3. Then just multiply the two fractions which is 5/12 x 1/3 = 5/36.

Answer:

5/12 ÷3

Reciprocate

5/12× 1/3

=5/36

An experiment consists of drawing 1 card from a standard​ 52-card deck. What is the probability of drawing a club​?

Answers

Answer:

25%

Step-by-step explanation:

25%

there are 4 suits, and only 1 is of clubs

1/4 = 25%

As I was planting my sunflowers, I had to use 2 different sized flower pots. Now, some are very tall and others are not! Why would this be?


just wanted to know if you can answer

Answers

Answer:

Step-by-step explanation:

There are differents sizes of pots because there are different sizes of flowers and plants, some need more space to grow. :)

Answer:

When seedlings are a 3-6 inches tall, transplant to individual pots, with 1 plant per 8 inch pot. Larger pots (15-inch diameter) can have up to 3 plants.

Step-by-step explanation:

Find the average rate of change of k(x) = 3x between x = 4 and x = 4 + h, where h 0.
Simplify your answer. Your answer may be a number or an expression in terms of h.

Answers

Answer:

Step-by-step explanation:

8

The average rate of change of the function on [0,4] is 8.

Jessica had 289 dollars to spend on 7 books. After
buying them she had 16 dollars. How much did each book cost?

Answers

Answer:

39

Step-by-step explanation:

289-16= 273

273/7= 39

Hope this helps! :)

Answer:

$39

Step-by-step explanation:

let b = cost of each book

289 - 7b = 16

-7b = -273

b = 39

Which of the following is 3.761 written in expanded notation?

A) (3 x 1) + (7 x 110) + (6 x 1100) + (1 x 11000)
B) (3 x 1) + (7 x 110) + (6 x 110) + (1 x 1100)
C) (3 x 1) + (7 x 110) + (1 x 1100) + (6 x 11000)
D) (3 x 1) + (7 x 110) + (6 x 110) + (1 x 1100)


WORTH 40 POINTS

Answers

Answer:

To write a number in expanded form, divide it into digits and display the value of each one. As a result, 144 would be 100 + 40 + 4 = 144.

Step-by-step explanation:

Please help due today

Answers

Answer:

Step-by-step explanation:

Each boundary line equation is of the form ...

  y = mx + b

the value of m is the coefficient of x. The value of b is the constant. You find their values by matching the given relation to the form above, and identifying the matching parts.

  y ≤ 1/2x +2   ⇒   m = 1/2, b = 2

  y < -2x -3   ⇒   m = -2, b = -3

_____

The slope (m) in each case tells you how many units up (m>0) or down (m<0) the line will go for each unit to the right. The y-intercept (b) in each case gives you a starting point on the y-axis, making it easier to draw the line.

The < part of each inequality symbol tells you the graph will be shaded below the boundary line. (Y-values in the solution set are less than those on the line.) The "or equal to" part of the first inequality symbol tells you the boundary line will be solid. (Y-values on that line are part of the solution set.) The lack of that in the second inequality tells you the boundary line will be dashed.

The graph is shown in the attachment.

A family needs to build fencing around their rectangular home and square swimming pool, depicted below

Answers

Answer:

160

Step-by-step explanation:

If the tires of a car have a diameter of 24 in., how many miles will the car travel when the tires make 16,000 revolutions

Answers

You just multiply by the two and however many meters miles or step is being taken

please help me i will give brainliest if you get the answer correct!!

Answers

the answer is the third option f(2)<g(2)

if we input in 2 in both equations for f(x) we get 48 and for g(x) we get 175

if a woman sells bitcoins for £42000 which is 12%more than she originally bought them for then calculate the original value of her bitcoins

Answers

164-73=18%
136-284=37
136%

Which of the following equations is steeper?
y=-2x+1
y=-5/4x+7
y=x-1
y=5x-1

Answers

Answer:

Option 4: y = 5x - 1

Step-by-step explanation:

The slope, or rate of change, represents the ratio of the vertical change (in y) to the horizontal change (in x) of points along the line. Thus, the slope is a means of measuring the steepness of a given line.

Generally speaking, slopes with higher values tend to have steeper lines.

Compare the slopes:

In comparing the slopes of the given options:

Option 1: slope = -2

Option 2: [tex]\LARGE\mathsf{slope = -\frac {5}{4}}[/tex] or 1.25

Option 3: slope = 1

Option 4: slope = 5

 

Option 4 has the highest slope of 5. Therefore, the graph of y = 5x - 1 has the steepest line.  

Attached is the graphed equations to prove that the graph of the equation in Option 4 has the steepest line.    

i need help i can’t understand how to solve it so pls help

Answers

Answer:  -4, 14, -22, 50

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

Work Shown:

1st term = -42nd term = -2*(1st term)+6 = -2*(-4)+6 = 143rd term = -2*(2nd term)+6 = -2*14+6 = -224th term = -2*(3rd term)+6 = -2*(-22)+6 = 50

The first four terms are: -4, 14, -22, 50

The idea is to start with the first term (-4) and use the template [tex]\text{nth term} = -2*(\text{previous term}) + 6[/tex] to generate each new term. We multiply the previous term by -2, then add on 6. This is exactly what the recursive equation [tex]a_n = -2(a_{n-1})+6[/tex] is indicating.

Find the equation of the line L.

Answers

Answer:

y = ([tex]-\frac{1}{2}[/tex])x + 4

Step-by-step explanation:

(x1,y1) = (0,4) ; (x2,y2) = (8,0)

The equation will look like y=mx+b

Slope m = [tex]\frac{rise}{run}[/tex] =  [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{0-4}{8-0}[/tex] = [tex]\frac{-4}{8}[/tex] = [tex]-\frac{1}{2}[/tex]

Next, substitute either x1y1 or x2y2 (it's gonna give the same answer anyways) and m to the equation y=mx+b to find b.

y=mx+b

0 = ([tex]-\frac{1}{2}[/tex])8 + b

0 = -4 +b

0+4 = -4 +4 +b

b=4

Then substitute b and m to the equation y=mx+b

y = mx + b

y = ([tex]-\frac{1}{2}[/tex])x + 4

algebra 2 is really difficult please help me no bogus answers please

Answers

#1

Discount is 40%=0.04x

So the function is

e(s(x))=0.04x

#2

[tex]\\ \tt\hookrightarrow( f\circ g)(x)[/tex]

[tex]\\ \tt\hookrightarrow f(x)g(x)[/tex]

[tex]\\ \tt\hookrightarrow (3x-1)(4x^2+9)[/tex]

[tex]\\ \tt\hookrightarrow 12x^3+27x-4x^2-9[/tex]

7.90×10^−2/1.0×10^−5

Answers

Answer:

[tex] \frac{7.90 \times {10}^{ - 2} }{1.0 \times {10}^{ - 5} } \\ = 7.9 \times {10}^{5 - 2} \\ = 7.9 \times {10}^{3} [/tex]

Given: Two distinct circles that are tangent to each other at a common point. How many tangent lines can be drawn that touch both circles?



3
1
2

Answers

there are only 3  tangent lines can be drawn that touch both circles

ok done. Thank to me :>

Help last day !!!!!!!!!!!!!!!

Answers

Answer:

The equation of the lines with the given point does not have a y-intercept of 4 but has a y-intercept of -4.

Step-by-step explanation:

y-intercept is 4

addition ordered pairs on the line are (2, -2), (4, 0), (6, 2), (8, 4)

Find the slope using two of the points: (2, -2), (4, 0).

Slope = (change in the y values)/(change in the x values0

Slope = [0 -(-2)]/ (4 - 2) =   2/ 2 = 1

Checking to see if the y-intercept is 4 substituting  slope (m) = 1 and (2, - 2)

      y = mx + b

     -2 = 1(2) + b

     -2 = 2 + b

  -2 - 2 = b

    -4 = b   so we know that the y-intercept is not 4 but it is -4.

Now write the equation of the line using a slope = 1 and y-intercept of -4

y = mx + b

y = x - 4

Next check the other points into the equation of the line to see if the equation is correct.

x = 2   did y = -2 ?    y = x - 4;   y = 2 - 4 ; y = -2     point (2, -2) works.

x  = 4   did y = 0?     y = x - 4;  y = 4 - 4;  y = 0       point (4,0)  works.

x = 6    did y = 2?     y = x - 4;  y = 6 - 4; y = 2         point (6, 2) works.

x = 8     did y = 4?     y = x - 4; y = 8 - 4;  y = 4        point (8, 4) works.

The area of a rectangle is 60 square inches.

The length is x – 3, and the width is x + 8.

Find the value of x, and the dimensions of the rectangle.

A=lw

Answers

X=7 because 7-3 = 4, 7+8= 15,15x4=60.

A piece of fabric 78.25cm long was cut from a 200cm long piece to make a shirt. What percent of the fabric was left behind?

Answers

Answer:

39.125 %

Step-by-step explanation:

you use the cross multiplication method:

200cm = 100%

78.25 = ???

78.25 × 100

——————— = 39.125%

200

if you are willing to check your answer:

39.125 × 200

———————–— = 78.25 cm

100

I HOPE THIS WOULD HELP!

PLZ HELPPP ME
Point B has coordinates ​(3​,2​). The​ x-coordinate of point A is 0 . The distance between point A and point B is 5 units. What are the possible coordinates of point​ A?

Answers

Answer:

A (0, - 2 ) or A (0, 6 )

Step-by-step explanation:

Using the distance formula

d = [tex]\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2 }[/tex]

with (x₁, y₁ ) = B(3, 2) and (x₂, y₂ ) = A(0, y )

AB = [tex]\sqrt{(0-3)^2+(y-2)^2}[/tex]

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

     = [tex]\sqrt{9+(y-2)^2}[/tex]

Given AB = 5 then equating gives

[tex]\sqrt{9+(y-2)^2}[/tex] = 5 ( square both sides )

9 + (y - 2)² = 25 ( subtract 9 from both sides )

(y - 2)² = 16 ( take square root of both sides )

y - 2 = ± [tex]\sqrt{16}[/tex] = ± 4 ( add 2 to both sides )

y = 2 ± 4

Then y = 2 - 4 = - 2 or y = 2 + 4 = 6

Possible coordinates of point A are

A (0, - 2 ) or A (0, 6 )

What is the solution to -4(8 - 3x) >_6x -8?

O x >_-4/3
O x<_-4/3
O x>_4
Ox<_4

Answers

The answer is x greater than or equal to 4
First I distributed the -4
Then I isolated all of the x on one side
Then I divided everything by 6 to get the value (greater than or equal to) of one x

sorry last one!!
3 × x[tex]x^{2}[/tex] × y × 4z × x × 2y × z

Answers

[tex]\red{\bold{Answer:}}[/tex]

z1 Multiplied by z1 = z(1 + 1) = z2

[tex]\color{skyblue}{\boxed{\tt{Final\:Answer}}}[/tex]

= (3•2³x3y2z²)

help please!!!!!!!!!​

Answers

Answer:

c

Step-by-step explanation:

my mom had a abortion when i was 6

Sofi stores water for her turtle tank in a container with a maximum
capacity of 64 ounces. The container is filled with 4 8 ounces less than
its maximum capacity
PART A
PARTE
Sofi accidentally spills 5% of the container's Sofi needs to add 16 ounces of water to
maximum capacity on the counter. To what her turtle tank. What percentage of the
percent of its capacity is the container
remaining water in the container does she
now filled?
need to use? Explain.
67.5%
12.5%
87 99
95%

Answers

A) If Sofi accidentally spills 5% of the container's maximum capacity on the counter, the container is now filled to 87.5% of its capacity.

B) If Sofi needs to add 16 ounces of water to her turtle tank, she needs to use 28.57% of the remaining water in the container.

Given that Sofi stores water for her turtle tank in a container with a maximum capacity of 64 ounces and the container is filled with 4.8 ounces less than its maximum capacity, to determine A) if Sofi accidentally spills 5% of the container's maximum capacity on the counter, to what percent of its capacity is the container now filled, and B) if Sofi needs to add 16 ounces of water to her turtle tank, what percentage of the remaining water in the container does she need to use, the following calculations must be made:

A)

64 = 100 (64 - 4.8) - (64 x 0.05) = X 64 = 100 56 = X 56 x 100/64 = X 87.5 = X

Therefore, if Sofi accidentally spills 5% of the container's maximum capacity on the counter, the container is now filled to 87.5% of its capacity.

B)

56 = 100 16 = X 16 x 100/56 = X 28.57 = X

Therefore, if Sofi needs to add 16 ounces of water to her turtle tank, she needs to use 28.57% of the remaining water in the container.

Learn more in https://brainly.com/question/17592236

Answer:

A=87.5%   b=28.57

Step-by-step explanation:

ADVICE PLEASE LOOK AT THIS VERY HELPFUL

PART                           percent

--------- over =          ----------------- over   Cross multiply and then divide by 100  

WHOLE                       100%

The distance from the post office to a supermarket is 0.5 km. What is the distance in meters?
Enter your answer in the space provided.

The distance from the post office to the supermarket is
meters.

Answers

Answer:

The answer is 500 meters

Step-by-step explanation:

I got it right

Please mark me as brainly!

Please leave a 5 star review

Have a good dat!

:)

Multiply as indicated. Write the product in standard form.
(2+i)^2

Answers

Answer:

3 + 4i

Step-by-step explanation:

i need help on this pls

Answers

Answer:

the answer is 15 bc 30-15=15

Step-by-step explanation:

Answer:11?

Step-by-step explanation:30 buldogs

                                             pirates 10 plus star 9 19 in 30 wwhats left

Sam earns $.75 for each call he makes for a telemarketing service. He hopes to make at least $100 each day. Write an inequality to represents the number of calls he must make each day. (Let c equal the number of calls. )

Answers

0.75c < or equal to 100

I’ll mark the brainiest

Answers

Answer: 122°

Step-by-step explanation:

Because angles on a straight line are supplementary (add up to 180°), then:

m∠2 = 180° - 58°

        = 122°

122
Supplementary angles
180-58=122
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