Your friend is absent from class and asks you to explain what a function is how would you explain

To rationalize essentially means to get rid of the radical.

The trick to all of these it to multiply the top and bottom by a radical that will turn the radical you have into the square root of a perfect square.

Part a: [tex]\dfrac{1}{2\sqrt{5}}[/tex]

One approach that will always work, but not be the smallest radical, is to just multiply by the radical that is already there.

In the case of [tex]\dfrac{1}{2\sqrt{5}}[/tex], you can multiply the top and bottom by [tex]\sqrt{5}[/tex], so you'll really do this:

     [tex]\dfrac{1}{2\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}} = \dfrac{1\cdot\sqrt{5}}{2\sqrt{5}\sqrt{5}}[/tex]

But in the bottom, [tex]\sqrt{5}\cdot\sqrt{5} = \sqrt{25}=5[/tex], so your work finishes out like this:

    [tex]\dfrac{1\cdot\sqrt{5}}{2\sqrt{5}\sqrt{5}} = \dfrac{\sqrt{5}}{2\sqrt{25}} = \dfrac{\sqrt{5}}{2\cdot5} = \dfrac{\sqrt{5}}{10}[/tex]

Part b: [tex]\dfrac{4}{5\sqrt{2}}[/tex]

In the case of [tex]\dfrac{4}{5\sqrt{2}}[/tex], you can multiply the top and bottom by [tex]\sqrt{2}[/tex], so you'll really do this:

     [tex]\dfrac{4}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]

But in the bottom, [tex]\sqrt{2}\cdot\sqrt{2} = \sqrt{4}=2[/tex], so your work finishes out like this:

    [tex]\dfrac{4}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{4\sqrt{2}}{5\sqrt{4}}=\dfrac{4\sqrt{2}}{5\cdot{2}}=\dfrac{4\sqrt{2}}{10}[/tex]

Sometimes the fraction can be reduced, so this should be reduced to [tex]\dfrac{2\sqrt{2}}{5}[/tex].

Looking at all the others, they'll follow this same approach and they will all reduce at the end.

Here's part c, for one more example.

Part c: [tex]\dfrac{3}{3\sqrt{2}}[/tex]

In the case of [tex]\dfrac{3}{3\sqrt{2}}[/tex], you can multiply the top and bottom by [tex]\sqrt{2}[/tex], but you should also reduce the initial fraction first.

     [tex]\dfrac{3}{3\sqrt{2}} = \dfrac{1}{1\cdot\sqrt{2}} = \dfrac{1}{\sqrt{2}}[/tex]

And now proceed with rationalizing:

    [tex]\dfrac{1}{\sqrt{2}} \cdot\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]

But in the bottom, [tex]\sqrt{2}\cdot\sqrt{2} = \sqrt{4}=2[/tex], so your work finishes out like this:

    [tex]\dfrac{1}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{1\cdot\sqrt{2}}{\sqrt{4}}=\dfrac{\sqrt{2}}{{2}}[/tex]

And you're done.

Hopefully that helps you finish the rest of those.

To check your answers, here is the answer key for the rest:

part d:[tex]\dfrac{2\sqrt{6}}{5}[/tex]

part e:[tex]\dfrac{4\sqrt{2}}{3}[/tex]

part f:[tex]\dfrac{4\sqrt{5}}{7}[/tex]

part g:[tex]\dfrac{5\sqrt{10}}{3}[/tex]

part d:[tex]\dfrac{5\sqrt{2}}{3}[/tex]

Answer:

Step-by-step explanation:

(a) 1/(2 sqrt5) x (sqrt 5)/(sqrt5) = (sqrt 5)/10

(b) 4/(5bsqrt2) x (sqrt2)/(sqrt2) = (4sqrt2)/10 = (2sqrt2)/5

(c) 3/(3 sqrt2) x (sqrt2)/(sqrt2) =(sqrt2)/2

(d) 12 /(5 sqrt6) x (sqrt6)/(sqrt6) = (12sqrt6)/30 = (2sqrt6)5

(e) 8/(3 sqrt2) x (sqrt2)/(sqrt2) = (8 sqrt2)/6 = (4 sqrt2)/3

(f) 20/(7 sqrt5) x (sqrt5)/(sqrt5) = (20 sqrt5)/35 = (4 sqrt5)/7

(g) 50/(3 sqrt10) x (sqrt10)(sqrt10) = (50 sqrt10)/30 = (5sqrt10)/3

(h) 10/(3 sqrt2) x (sqrt2)/(sqrt2) = (10 sqrt2)6 = (5 sqrt2)/3

Answer:

The answer is 620,910,000 I worked it out By the way:)

Answer:

620,910,000 - Number form

620.9M+ - Short form

Six hundred twenty million, nine hundred, and ten thousand - Word form

Step-by-step explanation:

1. If you want me to go in full detail, I'll just say that I used a bit of internet search for the word form because I'm dyslexic, but yet I'm here in brainly answering other people's questions.

2. Have a wonderful day to you too!!

Hope this helped! :^)

- ✨7272033Alt✨

Step-by-step explanation:

hi hi hi nice to meet you meet you

Answer:

Nia answerd 45% of the questions correctly.

Answer:

5

Step-by-step explanation:

I hope this helps

yea xxx

Answer:

(a) SSS

.........................

Answer:

[tex]\huge\boxed{\sf \frac{7}{40} }[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{1}{5} \times \frac{7}{8} \\\\= \frac{1 \times 7}{5 \times 8} \\\\= \frac{7}{40} \\\\Hence, this \ is \ the \ simplest \ form.\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

7/40

Step-by-step explanation:

7 cant go into 40 so it just stays as 7/40

Answer: Let "T" denote households with television

"I" denote households with internet

and "N" denote households with neither of these.

Since P(N) = 0.05 then it means P(TuI) = 0.95. We know from set theory that P(TuI) = P(T) + P(I) - P(TnI). Thus,

0.95 = 0.92 + 0.72 - P(TnI) ==> P(TnI) = 0.69. This means P(T/I) = P(T) - P(TnI) = 0.92 - 0.69 = 0.23, and P(I/T) = P(I) - P(TnI) = 0.72 - 0.69 = 0.03. So,

a)

House                 Probability

Nothing                0.05

Only television      0.23

Only internet         0.03

Both                   0.69

b) P(internet but no television) = P(only internet) = 0.03

c) P(internet | there is television) = (By Bayes' Rule) P(TnI) / P(T) = 0.69 / 0.95 = 0.726 (rounded to 3 decimal points)

d) P(internet | there is no television) = (By Bayes' Rule) P(I/T) / P(T') = 0.03 / 0.08 = 0.375

e) From (c) and (d) ==> In Canada, it is (0.726/0.375 ≈ 2 ) twice more likely that if there's television in the household, then there is internet.

Step-by-step explanation:

Answer:

.0833 or 83.3333

Step-by-step explanation:

1/12=.0833

The probability of number greater than [tex]12[/tex] is zero.

Probability is the ratio of number of favorable outcome to the total number of outcome.

We have,

Total number of outcome [tex]=12[/tex]

And number of greater than [tex]12[/tex]  [tex]=0[/tex]

So,

Probability [tex]=\frac{Number\ > \ 12}{Total\ number}[/tex]

                   [tex]=\frac{0}{12}[/tex]

Probability [tex]=0[/tex]

A probability of [tex]0[/tex] means that the event will not happen.

Hence, we can say that the probability of number of greater than [tex]12[/tex] is zero.

To know more about Probability click here

https://brainly.com/question/11234923

#SPJ3

Answer:

x = 32

(The answer should be 32 if we are solving for x)

Answer:

5/3

Step-by-step explanation:

We need to rewrite the equation in slope intercept form

y =mx +b where m is the slope

-3x-5y = 7

Add 3x to each side

-5y = 3x+7

Divide by -5

y = -3/5 x -7/5

The slope of this line is -3/5

Perpendicular lines  have slopes that are negative reciprocals

-1 / (-3/5)

5/3

The slope of the perpendicular line is 5/3

Answer:

(-1,0) (0,-2) (1,0)

Step-by-step explanation:

the function crosses the axis in this 3 points

Answer: X=4/2x+3

Step-by-step explanation:

I just know

Answer:

8 minutes, 30 seconds, by the look of the graph.

Step-by-step explanation:

At a distance of 10 inches, 1 minute has passed.

So multiply that by 8.5, and you have 85 inches travelled over 8 minutes, 30 seconds.

8mins and some 30secs according to the graph

Answer:

x=76

Step-by-step explanation:

#CarryOnLearning

Answer:x=76

Step-by-step explanation:

Distribute: -4(x-26)=-200       -4x + 104 - 104 = -200

Subtract 104 from both sides of the equation

-4x + 104-104 = -200-104

Simplify

Subtract the numbers

-4x +104-104=-200 - 104

-4x=-200 - 104

Subtract the numbers

-4x = -200 - 104

-4x = -304

-4x = -304

Solution

x=76

To find the answer, we will need to divide 3/5 by 2/3.

3/5 / 2/3

3/5 x 3/2

9 / 10

There are 9/10 groups of 2/3 in 3/5.

Hope this helps!! :)

500 = 400 + 50s. Therefore, Bart can buy 2 pairs of shoes.

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

Explanation:

s = number of pairs of shoes

50s = amount spent on shoes ($50 per pair)

50s+400 = total amount spent on shoes and uniforms

That expression is the same as 400+50s because we can add numbers in any order we want. Set this equal to the $500 he started with to get the equation 500 = 400 + 50s

We have enough info to determine the answer must be choice B

We can stop here if you wanted.

----------

Let's solve that equation for s

500 = 400 + 50s

400 + 50s = 500

50s = 500-400 .... subtract 400 from both sides

50s = 100

s = 100/50 .... divide both sides by 50

s = 2

This means he can buy 2 pairs of shoes.

Buying the shoes only will cost 50s = 50*2 = 100 dollars, which on top of the $400 for the uniforms, leads to a grand total of 400+50s = 400+100 = 500 dollars. This helps confirm we have the correct value for s.

Hi

Answer:

4+5+9+8+9=35

Step-by-step explanation:

nvm about that

Answer:

Below.

Step-by-step explanation:

4 + 5 + 9 + 8 + 9 = 35.

Answer:

Step-by-step explanation:

Answer:

watch me whipzdudbbd iv ex

Answer:

10

Step-by-step explanation:

press calculate

pls give brainliest

Answer: 10

Step-by-step explanation:

The sign √ means square root. Squaring is like multiplying a number by its own self again ( for example, x times x is equal to x squared). A square root is like dividing the square by its own self ( for example, √x^2 is equal to x ).

The square root of 100 is 10, since 10 squared is equal to 100.

Step-by-step explanation:

Don't mind me, just tryna get those points

Step-by-step explanation:

25+5=30

30+40=70

70+2=72

Answer:

800,000

Step-by-step explanation:

8 is in the hundred thousands, 1 is in the ten thousands, 1 is in the thousands, 5 is in the hundreds, 7 is in the tens, 0 is in the ones place

It rounds down as its nowhere near 900,000 which changes all its digits.

Answer:

area of triangle = 1/2×base×height

=1/2×20m×6m

= 20m×6m=120square metre

Answer: 41

Step-by-step explanation:

Answer:

well for the 10 it is a 4/52 chance and for face cards, 16/52

Step-by-step explanation:

Answer:

-2k + 6

Step-by-step explanation:

We start out with the expression -2k - (-5) + 1. We should first distribute the negative outside of (-5), which gets us to 5: -2k + 5 + 1. Now, we can combine like terms with 5 and 1 to get 6, giving us a final answer of -2k + 6. We can't simplify any further since there aren't any like terms.

If you have any questions or need clarification on anything, let me know!

Answer:

equivalent yan kasi pareho lang den nmn letters lng naiba