Which are rational and irrational? Thanks in advance :)

Here's why:

sqrt(49) = sqrt(7^2) = 7

We can write 7 as a ratio or fraction of two integers 7 = 7/1

This shows that 7 is rational, so that makes sqrt(49) rational as well.

An irrational number is one where we cannot write it as a fraction of two integers. An example of an irrational number would be pi. Another irrational number is sqrt(2).

Note: the denominator can never be zero.

Answer:

-30x^3+5x^2

Step-by-step explanation:

Answer:

bc= 12 :)

Step-by-step explanation:

Answer:

see below (I hope this helps!)

Step-by-step explanation:

To find the distance between two points, we can use the formula d = √(x₂ - x₁)² + (y₂ - y₁)² where d = distance and (x₁, y₁), (x₂, y₂) are the points. Therefore:

d = √(-6 - 2)² + (2 - (-6))²

= √(-4)² + (8)²

= √16 + 64

= √80 ≈ 8.944272

Answer:

$225

Step-by-step explanation:

Given that:

Principal = $6,000

Interest rate = 5%

Time = 1 year

Taxes paid = 25% on the interest earned

To find:

Money earned after paying taxes ?

Solution:

First of all, let us calculate the total interest earned:

Formula for Simple Interest is given as:

[tex]SI =\dfrac{PRT}{100}[/tex]

Where P is the principal

R is the rate of interest

T is the time taken

Putting the given values:

[tex]SI =\dfrac{6000 \times 5\times 1}{100} =\$300[/tex]

Now, it is given that 25% of the interest earned is given as taxes.

Taxes paid = 25% of $300

[tex]\Rightarrow \dfrac{25}{100} \times 300 =\$75[/tex]

Therefore, the money earned = Interest earned - Taxes paid

The money earned = $300 - $75 = $225

Answer:

The answer is C.

The steps are :

[tex] {T}^{2} = ( \frac{4 {\pi}^{2} }{GM} ) \times {r}^{3} [/tex]

[tex] {T}^{2} \div ( \frac{4 {\pi}^{2} }{GM}) = {r}^{3} [/tex]

[tex] {T}^{2} \times \frac{GM}{4 {\pi}^{2} } = {r}^{3} [/tex]

[tex] \frac{GM {T}^{2} }{4 {\pi}^{2} } = {r}^{3} [/tex]

[tex] \sqrt[3]{ \frac{GM {T}^{2} }{4 {\pi}^{2} } } = r[/tex]

[tex]r = \sqrt[3]{ \frac{GM {T}^{2} }{4 {\pi}^{2} } } [/tex]

Answer :

C

[tex]r = \sqrt[3]{ \frac{ {T}^{2}GM} {4 {\pi}^{2} } } [/tex]

Step-by-step-explanation :

[tex] {t}^{2} = ( \frac{4 {\pi}^{2} }{gm} ) {r}^{3} \\ {t}^{2} = \frac{4 {\pi}^{2} {r}^{3} }{gm} [/tex]

[tex] {t}^{2} gm = 4 {\pi}^{2} {r}^{3} \\ \frac{ {t}^{2} gm}{4 {\pi}^{2} } = \frac{4 {\pi}^{2} {r}^{3} }{4 {\pi}^{2} } [/tex]

[tex] {r}^{3} = \frac{ {t}^{2} gm}{4 {\pi}^{2} } [/tex]

[tex] \sqrt[3]{ \frac{ {t}^{2} gm}{4 {\pi}^{2} } } = \sqrt[3]{r} [/tex]

[tex]r = \sqrt[3]{ \frac{ {t}^{2} gm}{4 {\pi}^{2} } } [/tex]

Answer:

  B.  32

Step-by-step explanation:

The product of the lengths of segments to the near and far circle intercepts are the same, where the length is measured from the point where the secant and tangent meet. The tangent point counts as both circle intercepts, so we have ...

  30×30 = 18×(18 +x)

  900 = 324 +18x . . . . eliminate parentheses

  576 = 18x . . . . . . . . . subtract 324; next, divide by 18

  32 = x

Answer:

[tex] 16x^2 + 8x +1[/tex]

Step-by-step explanation:

[tex] 16x^2 + 8x +1 = (4x+1)^2 [/tex]

Answer:

[tex]2\frac{8}{15}[/tex]

Step-by-step explanation:

The calculation of average speed in kilometres per hour is shown below:-

As we know that

[tex]Speed = \frac{Distance}{Time}[/tex]

So, the average speed is

[tex]= 3\frac{1}{6} \div 1\frac{1}{4}[/tex]

Now we will convert into a mixed number i.e

[tex]3\frac{1}{6} = \frac{19}{6} \\\\ 1\frac{1}{4} = \frac{5}{4}\\\\ = \frac{19}{6} \div\frac{5}{4}\\\\ = \frac{19}{6} \times \frac{4}{5}[/tex]

Now the cross cancel common factor is 2

So,

[tex]= \frac{19}{2}\times \frac{2}{5} \\\\ = \frac{38}{15} \\\\ = 2\frac{8}{15}[/tex]

hence, the average speed is [tex]2\frac{8}{15}[/tex] in kilometers per hour

Therefore we simply applied the above formulas to determine the average speed that comes in kilometers per hour

Answer:

i) width = 3.75

length = 4.5

ii) 6.75m^2

iii) 78.75m^2

Step-by-step explanation:

11)

i) Bedroom 1

actual width = 2.5 × 1.5

= 3.75 m

actual length = 3 × 1.5

= 4.5m

ii) Kitchen

actual width = 1.5 × 1.5

= 2.25 m

actual length = 2 × 1.5

= 3 m

actual area = 2.25× 3

= 6 .75 m^2

iii) Apartment

actual width = 5 × 1.5

= 7.5 m

actual length = 7 × 1.5

= 10. 5 m

actual area = 7.5 * 10.5

= 78.75 m ^2

Answer:

[tex]x=-6[/tex]

Step-by-step explanation:

So we have the equation:

[tex]-34=7(x+8)+8x[/tex]

First, distribute the 7 into the (x+8) and simplify:

[tex]-34=7(x)+7(8)+8x\\-34=7x+56+8x[/tex]

Combine the like terms 7x and 8x by adding them together:

[tex]-34=56+15x[/tex]

Subtract 56 from both sides to isolate the x:

[tex]-34-56=15x+56-56\\15x=-90[/tex]

Divide both sides by 15 to get x:

[tex]x=-90/15=-6[/tex]

Answer:

49.6 liters

Step-by-step explanation:

Let the number of water that the smaller chest be x liters. If the smaller chest can hold 4/5 of the water that the large chest can hold, then:

The amount of water held by small chest (x) = 4/5 × amount of water that can be held by large chest

x = 4/5 × 62 liters = 49.6 liters

This means that the small chest can hold up to 49.6 liters of water

Smaller chest can hold 49.6 liters.

The smaller chest holds 4/5 the amount of water that the larger chest can hold which is 62 liters.

The amount the smaller chest can hold is therefore:

= Amount of water large chest can hold x proportion of large chest that small chest can hold

= 62 x 4/5

= 248/5

= 49.6 liters

The smaller chest can therefore hold 49.6 liters.

Find out more at https://brainly.com/question/17474612.

Answer:

3 is right answer

Step-by-step explanation:

see in attached picture

hope it helped you:)

Answer:

Angle 1 = 39, Angle 2 = 78 , Angle 3 = 63

Step-by-step explanation:

78/2 = 39

(Angle 2/2 = Angle 1)

78 - 15 = 63

(Angle 2 - 15 = Angle 3)

39 + 78 + 63 = 180

(Angle 1 + Angle 2 + Angle 3 = 180)

Answer:

39°, 78°, 63°

Step-by-step explanation:

let ∠ 1 = x, then

∠ 2 = 2x ( twice the measure of ∠ 1 )

∠ 3 = 2x - 15 ( 15° less than ∠ 2 )

Sum the 3 angles and equate to 180

x + 2x + 2x - 15 = 180, that is

5x - 15 = 180 ( add 15 to both sides )

5x = 195 ( divide both sides by 5 )

x = 39

Thus

∠ 1 = 39°

∠ 2 = 2 × 39° = 78°

∠ 3 = 78° - 15 = 63°

Answer:

Step-by-step explanation:

If M is the midpoint of the segment AB, then AM+MB = AB. Given the following parameters;

AM=9x-5 and MB=15-x

Required parameter

segemnt AB

Substituting the given parameters into the given formula to get AB we will have;

AB = AM+MB

AB = 9x-5+15-x

collect like terms

AB = 9x-x-5+15

AB = 8x+10

Hence the length of segment AB is 8x+10

Answer:

  2

Step-by-step explanation:

If the number must be even, the units digit must be 8. That leaves 2 choices for the tens digit. The possible numbers are ...

  78

  98

There are 2 of them.

Answer: Only two: 78 and 98

Step-by-step explanation: 8 is the only even number available to put in the units place where even or odd is determined. With no repetition allowed, the only possibilities left are to switch positions of the 7 and 9 in the tens place.

Answer: 5

Step-by-step explanation:

  8-2b=-2

8-2b-8=-2-8

    -2b=-10

-2b/-2=-10/-2

       b=5

Answer:

y-3= 2(x-1)

Step-by-step explanation:

1. The equation of a line in point slope form is y-y1= m(x-x1)

2. m=slope and (x1,y1) is the point the line passes through

3. The point the line passes through is (1,3)

4, The slope is 2

5. Therefore the answer is y-3=2(x-1)

Answer:

y-3=2(x-1)

Step-by-step explanation:

Point slope form is y-y1=m(x-x1)

Now we just need to plug in what you have into this equation.

y-3=2(x-1) and this is the point slope form for this line.

Answer:

Perpendicular lines are 90 degrees on their central angle.

Step-by-step explanation:

1. Draw the line L with a meter-rule and a pencil.

2. extend the hand of the protractor beyond the radius of the line and bisect the line L, by placing the protractor pin on both ends of the line and marking up and down.

3. Join the points where the markings meet drawing a line through C which is the center of the line L.

Hello, please consider the following.

[tex]\begin{aligned}1280x^{11}-405x^7&=5x^7(256x^4-81)\\\\&= 5x^7(16^2(x^2)^2-9^2)\\\\&=5x^7(16x^2-9)(16x^2+9)\\\\&=5x^7((4x)^2-3^2)(16x^2+9)\\\\&\large \boxed{=5x^7(4x-3)(4x+3)(16x^2+9)}\end{aligned}[/tex]

So, the last one is the correct answer.

Thank you.

Answer:

(-3,-2)

Step-by-step explanation:

well, you take the difference between the midpoint and given endpoint and add it on in the other direction

Answer:

The possible values of k are 3 and -3

Step-by-step explanation:

Given

Points: (-3,k) and (2,0)

Distance between them = √34

Required

Determine the value of k

The distance between two points is calculated as thus;

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

Let

[tex](x_1,y_1) = (-3,k)[/tex]

[tex](x_2,y_2) = (2,0)[/tex]

Substitute these values in the given formula

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

Evaluate the brackets

[tex]Distance = \sqrt{-5^2 + k^2}[/tex]

[tex]Distance = \sqrt{25 + k^2}[/tex]

Recall that Distance = √34

So; we have

[tex]\sqrt{34} = \sqrt{25 + k^2}[/tex]

Take square of both sides

[tex]34 = 25 + k^2[/tex]

Collect Like Terms

[tex]k^2 = 34 - 25[/tex]

[tex]k^2 = 9[/tex]

Take square root of both sides

[tex]k = \±3[/tex]

Hence, the possible values of k are 3 and -3

Answer:

A

Step-by-step explanation:

The - in front of -x tells us that the line has to go down (slope -1), and the +2 tells us it will pass through (0,2).

Then you can see that only graph A fits that description.

Hello!

Answer:

A

Step-by-step explanation:

if x=0 => y=2

if x=1 => y=1

This is A graph!

Answer:

20[tex]\sqrt{3}[/tex]

Step-by-step explanation:

The diagonal splits the square into 2 right triangles

Using Pythagoras' identity on one of the right triangles

With legs 10[tex]\sqrt{6}[/tex] and hypotenuse the diagonal d, then

d² = (10[tex]\sqrt{6}[/tex] )² + (10[tex]\sqrt{6}[/tex] )² = 600 + 600 = 1200 ( take square root of both sides )

d = [tex]\sqrt{1200}[/tex] = [tex]\sqrt{400(3)}[/tex] = [tex]\sqrt{400}[/tex] × [tex]\sqrt{3}[/tex] = 20[tex]\sqrt{3}[/tex]

Answer:

Since there are no common factors, the only common factor is 1

(●'◡'●)

Answer:

8 questions each for short answer questions and 8 questions of Multiple Choice Questions type.

A total of 16 questions.

Step-by-step explanation:

Given:

The number of multiple choice questions and number of short answer type questions are same.

Let it be equal to [tex]x[/tex].

Average Time taken to attempt multiple choice question = 2 minutes

Total time taken to attempt multiple choice question = 2[tex]\times x[/tex] minutes

Average Time taken to attempt short answer type question = 3.5 minutes

Total Time taken to attempt short answer type question = 3.5[tex]\times x[/tex]

Total time for test should be less than 45 minutes.

Therefore, the equation becomes:

[tex]2x+3.5x<45\\\Rightarrow 5.5x <45\\\Rightarrow x<8.18[/tex]

Hence, the value of [tex]\bold{x=8}[/tex]

Therefore, the answer is:

8 questions each for short answer questions and 8 questions of Multiple Choice Questions type.

A total of 16 questions.

Answer:

Step-by-step explanation:

2n+3.5n <45

Answer:

180/1000 or 18/100 0.18

Step-by-step explanation:

The repeating decimal 0.18 to a fraction is 2/11

From the question, we have the following parameters that can be used in our computation:

Number =  0.18

Express as fraction

So, we have

Number =  18/100

Subtract 1 from the denominator

Number =  18/99

Simplify

Number =  2/11

Hence, the fraction is 2/11

Read more about fraction at

brainly.com/question/31896427

#SPJ6

Answer:

C. [tex] 13.76 units^2 [/tex]

Step-by-step explanation:

Given:

∆ABC,

m<A = 66.28°

m<B = 31.09°

AB = 7.6

BC = 7.01

Required:

Area of ∆ABC

SOLUTION:

Area = ½*AB*BC*sin(B)

[tex] Area = \frac{1}{2}*7.6*7.01*sin(31.09) [/tex]

[tex] Area = \frac{1}{2}*7.6*7.01*sin(31.09) [/tex]

[tex] Area = 13.76 units^2 [/tex]

Answer:

B. [3, 5]

Step-by-step explanation:

The range of a graph are the y-values that are plotted on the vertical axis (y-axis). In order words, the range values, are the possible set of output values of that are plotted on the vertical axis on the graph.

"[ ]" is usually used to denote the possible set of values.

Therefore, the range of the given graph, as we can see from the y-axis, include values from 3 to 5. Therefore, the range of the graph is [3, 5].

Answer:

its negative :)

Step-by-step explanation:

..........

Answer:

The sum will be negative

Step-by-step explanation: Negative+Negative=Positive//Positive+Positive=Positive//Positive+Negative=Negative//Negative+Positive=Negative