Can someone please show me their working on these on how to work out?​

Can Someone Please Show Me Their Working On These On How To Work Out?

Answers

Answer 1

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 2

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


Related Questions

632 16/25 +32 3/10 answer in decimal

Answers

Answer:

664.94

Step-by-step explanation:

Give me brainlyest please

Answer:

664.94 is the answer to this question. I hope this helps.

After two consecutive years of 5% rates of return, what rate of return in the third year will produce a cumulative gain of 16%? ​

Answers

Using decimal multipliers, it is found that a rate of return of 5.2% in the third year will produce a cumulative gain of 16%.

The decimal multiplier for a increase of a% is given by:

[tex]M = \frac{100 + a}{100}[/tex]

In this problem, two increases of 5%, thus:

[tex]M = \frac{100 + 5}{100} = 1.05[/tex]

Another of x, that we want to find, and the result is a increase of 16%, thus:

[tex]M = \frac{100 + 16}{100} = 1.16[/tex]

The three increases(5%, 5% and x%) result in a increase of 16%, thus:

[tex]1.05(1.05)(x) = 1.16[/tex]

[tex]x = \frac{1.16}{(1.05)^2}[/tex]

[tex]x = 1.052[/tex]

1.052 - 1 = 0.052

A rate of return of 5.2% in the third year will produce a cumulative gain of 16%.

A similar problem is given at https://brainly.com/question/21806362

How can you compare data sets?

Answers

Answer:

Grapgical charts and data plots

Step-by-step explanation:

Graphically.

Spread.

Shape.

Unusual features.

Step-by-step explanation:

Hope it helps you!!

Classify each number as an integer or not -32/4 yes or no -27/9 yes or no 5/11 yes or no -73.27 yes or no -36 yes or no

Answers

Answers:

-32/4 = yes-27/9 = yes5/11 = no-73.27 = no-36 = yes

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

Explanation:

Use long division or a calculator to find that -32/4 turns into -8. This is an integer because it's a negative whole number.

The same goes for -27/9 because it turns into -3

The value -36 is also an integer as well

Something like 5/11 is not an integer because 5/11 = 0.4545 approximately which isn't a positive whole number. Integers are either positive or negative whole numbers, or 0.

For similar reasons, we can see that -73.27 isn't an integer either because it's not a negative whole number.

Georg invests $5000 for 14 years at a rate of 2% per year compound interest.
Calculate the interest he receives.

Answers

Answer:

[tex]\frac{1}{50}[/tex] or 0.02

Step-by-step explanation:

2% x 1 to give the answer

or

reduce it to faction like

[tex]\frac{2}{100}[/tex] = [tex]\frac{1}{50}[/tex]

Which is an equation of the line through the origin and (3,4)? Please help
A. y = 4/3x
B. y = 3/4x
C. y = 4x
D. y = 3x

Answers

B is the answers………..

The constant of proportionality can be found by finding the

Answers

Answer:

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.

The constant of proportionality can be found by finding the ratio of y to x after applying the concept of a proportional relationship.

What is a proportional relationship?

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

The statement is:

The constant of proportionality can be found by finding the

As we know, from the definition of the proportional relationship;  the relationship between two variables when the first variable increases.

Let x and y are in the proportional relationship

y ∝ x

y = kx

Here k is the constant of proportionality:

k = y/x

The constant of proportionality can be found by finding the ratio of y to x.

Thus, the constant of proportionality can be found by finding the ratio of y to x after applying the concept of a proportional relationship.

Learn more about the proportional here:

brainly.com/question/14263719

#SPJ2

Part A: The sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. How many ergs of radiant energy does the sun produce in 3.25 ⋅ 103 seconds? (5 points)

Part B: Which is the more reasonable measurement of the distance between the tracks on a railroad:
1.435 ⋅ 10−3 mm or 1.435 ⋅ 103 mm? Justify your answer. (5 points)

Answers

9514 1404 393

Answer:

  A) 1.3×10^37 ergs

  B) 1.435×10^3 mm

Step-by-step explanation:

A) The quantity is found by multiplying the rate by the time:

  (3.9×10^33 ergs/s)×(3.25×10^3 s) = 1.2675×10^37 ergs ≈ 1.3×10^37 ergs

The least-precise contributor to the calculation has 2 significant digits, so we need to round the result to 2 significant digits.

__

B) A fine human hair is more than 40×10^-3 mm in diameter, so the distance 1.435×10^-3 mm is completely unreasonable for railroad track spacing. The space between rails is closer to 1.4 meters. So 1.435×10^3 mm is a better measurement.

6
LA
3
2
1
-6
-5
-4
-3
-2
- 1
1
2
3
4
- 1
N-
-2
What is the slope of line segment AB?
A
NIN
B)
3
4
o
4
3
D
IN

Answers

Answer:)

Step-by-step explanation:

Can someone help me please

Answers

Answer:

181.25 square feet

1/6 quart water

1/18 cup milk

1/3 beef bouillon cube, and 2/3 a large carrot

Step-by-step explanation:

Name the jelly like fluid that the other organelles float around in a cell. O Cytoplasm O Cell Membrane O Chloroplast​

Answers

Step-by-step explanation:

[tex] \bf \underline\red{Question}[/tex]

Name the jelly like fluid that the other organelles float around in a cell?

[tex] \bf \underline\red{Answer}[/tex]

Cytoplasm.

Answer:

cytoplasm

step by step explanation

Hi, this is multiplication with decimals, help!

Answers

Answer:

Sean paid 0.25 more cents than Cal.

Step-by-step explanation:

Cal's problem: 2.4 * 2.55 = 6.12

Sean's problem: 2.6 * 2.45 = 6.37

Answer:

I think 0.25

Step-by-step explanation:

Multipled 2.4 and 2.55 then multipled 2.6 and 2.45. I got 6.12 and 6.37 Then subtracted them and got 0.25

NO LINKS!!

What's the Perimeter?

a. 2x+8
b. 2x+9
c. 3x+8
d. 3x+9​

Answers

Answer:

A. 2x + 8

Step-by-step explanation:

The perimeter is:

x + x sides3 + 1 + 4 = top and bottom

Total:

P = 2x + 8

Correct choice is A

Answer:

A is correct

Step-by-step explanation:

Which equation represents a proportional relationship?
A) y=5
B) x=3
C) y=2x+3
D) y=1/4x

Answers

Answer:

c! I had the same one in my class I'm pretty sure I was right

(can you make me brainleist I need to level up)

help for brainliest and good luck

Answers

18 is the correct answer

The answer is 28
4(x+7) is congruent to 6x-28 meaning they’re equal
4x+28=6x-28
Subtract 28 on both sides
4x=6x-56
Subtract 6x on both sides
-2x=-56
Divide by -2
x=28
Those are also Corresponding Angles

Find the length of the side of a square whose area is equal to the area of a rectangle with side measures 4.9 m and 1.6 m​

Answers

Given :

Area of square equals to the area of rectangle of sides 4.9m and 1.6m .

To find :-

The side of the square .

Solution :-

As we know ,

Area = side² 4.9 * 1.6 = a²a = √ 49/10 * 16/10 a = 7/10 * 4/10 a = 28/100 a = 0.28 m

c. The number of men in a community is 2,400. If the ratio of women to men in the community is 5:4,
find
i. The total number of people in the community.
ii. The number of women in the community.
iii. How many more women are there than men if 400 men joined the community.

Answers

i. 5,400
ii. 3,000
iii. 200
Total number of parts the population is divided into: 5+4=9.

We know that 2,400 relates to the 4 parts of the ratio, so one part is 2,400 : 4 = 600.

i) So, in total, there are 600 (measure for one part) * 9 (total number of parts) = 5400 people in the community

ii) There are 5 parts in the women’s community. So, total number of women: 5 * 600 = 3000

iii) There we’re originally 5400 - 3000 = 2400 men in the community. If 400 more join, there will be 2400+400 = 2800 men.

So, there are still 3000 women and now 2800 men, so the difference between these is 3000-2800= 200.

There are 200 more women than men if 400 men joined the community.

Hope that’s helpful :)

YO I NEED HELP

A forest owned by the Jumbo Lumber Corporation contains 4,498 trees. If Jumbo Lumber cuts down 57 trees every day, which function can be used to find the number of trees, n, left in the forest after t days?
A.
n(t) = (4,498-57)t
B.
n(t) = 4,498 + 57t
C.
n(t) = 4,498t - 57
D.
n(t) = 4,498 - 57t

Answers

Answer:

D

Step-by-step explanation:

Edmentum:))

how many fifths are there in 4 wholes? (see the illustrate given)​

Answers

Answer:

To divide two fractions, flip the second fraction and change the operation from division to multiplication. Therefore, there are 20 fifths in four wholes

(A)

The lines represented by the equations y=-\frac{5}{2}x+7y=− 2 5 ​ x+7 and y-\frac{2}{5}x=-4y− 5 2 ​ x=−4 are

Answers

Answer:

bxjfjxucjkkdndjkjhkjjnn

solve. −3.1=−3.5x−4.6

Answers

Answer:

x = 0.428571 repeating

Step-by-step explanation:

Answer:

-0.428571 repeating

Step-by-step explanation:

add 4.6 both sides

1.5 = -3.5x

divide -3.5 both sides

-0.428571 repeating

SOLVE THIS AND EXPLAIN STEP BY STEP PLEASE!!!!

Answers

Answer:0=0

Step-by-step explanation:2(4x + 3) = 17x+3-9x +3 1st we will distribute. 2 times 4x gives you 8x and 2 times 3 gives you 6. Now the equation is 8x + 6 = 17x+3-9x+3.Now we're gonna add 3 + 3 gives you 6. Now the equation is 8x +6 = 17x+6-9x Now we're gonna combine like terms. So now we'll put together 17x - 9x which give you 8x. Now the equation is 8x +6 = 8x +6. Now where gonna subtract 6 from both sides. 8x = 8x and if I simplify it we'll get 0=0 which is the final answer

How simplify -8/3 devided by -2/6

Answers

Answer:

The answer is 8

Step-by-step explanation:

-8/3 divided by -1x2 / 3x2

-8/3 divded by -1/3

-8/3 x 3 / 3 x -1 = -8/-1 =  8 x -1 + 0 / -1

= 8

So your answer is 8

Please mark Brainliest I answered First

no links please

Suppose you took out a $120,000 loan to go to med school. Your loan has a 6.9% APR to be paid in 30 years. You make monthly payments of $790.32 – to date, you have made 180 payments. What is the total amount you have left to pay if you simply make payments for the next 180 months?​

Answers

The total amount left to pay is $ 745,945.74.

Supposing you took out a $ 120,000 loan to go to med school. Your loan has a 6.9% APR to be paid in 30 years, and you make monthly payments of $ 790.32, and to date, you have made 180 payments, to determine what is the total amount you have left to pay if you simply make payments for the next 180 months the following calculation must be performed:

(120,000 x 1,069 ^ 30) - (790.32 x 180) = X (120,000 x 7.40) - 142,257.6 = X 888,203.34 - 142,257.6 = X 745,945.74 = X

Therefore, the total amount left to pay is $ 745,945.74.

Learn more in https://brainly.com/question/8846837

Which phrase has the same meaning as 12y - 2?
-
O A. Subtract the sum of 12 and y from 2.
O B. Subtract 2 from the sum of 12 and y.
O C. Subtract the product of 12 and y from 2.
D. Subtract 2 from the product of 12 and y.

Answers

D, 12y is also 12 • y and when there is an answer to a multiplication problem, it’s a product. and that minus 2 is subtracting.
B is your answer. You subtract 2 from the sum of 12y

please solve it.......​

Answers

Answer:

dy/dx = - (y/x)^4

Step-by-step explanation:

We are given the equation:

[tex] \displaystyle \large{ \frac{1}{ {x}^{3} } + \frac{1}{ {y}^{3} } = {a}^{3} }[/tex]

Recall important differential formulas such as:

[tex] \displaystyle \large{ \frac{d}{dx} (f(x) + g(x)) = \frac{d}{dx} f(x) + \frac{d}{dx} g(x)} \\ \displaystyle \large{ \frac{d}{dx} k = 0 \: \: \tt(k \: \: is \: \: a \: \: constant.)}[/tex]

Above is a basic property of differential. Looking at the equation above, differentiate both sides with respect to x. (dy/dx)

[tex] \displaystyle \large{ \frac{d}{dx}( \frac{1}{ {x}^{3} } + \frac{1}{ {y}^{3} } )= \frac{d}{dx} {a}^{3} }[/tex]

Apply the distribution property in.

[tex] \displaystyle \large{ \frac{d}{dx} \frac{1}{ {x}^{3} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = \frac{d}{dx} {a}^{3} }[/tex]

We treat x^3 and y^3 as function to one another, this type of differential will be called implicit once another variable of function is involved f(x,y).

But we treat a^3 as a constant so we just put 0.

[tex] \displaystyle \large{ \frac{d}{dx} \frac{1}{ {x}^{3} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 }[/tex]

Recall the quotient rules for the numerator = 1.

[tex] \displaystyle \large{ \frac{d}{dx} (\frac{1}{f(x)}) = -\frac{ \frac{d}{dx} (f(x))}{ {(f(x))}^{2} } }[/tex]

Thus:

[tex] \displaystyle \large{ - \frac{ \frac{d}{dy} ( {x}^{3} )}{ ({x}^{3})^{2} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 } \\ \displaystyle \large{- \frac{ 3 {x}^{2} }{ {x}^{6} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 }[/tex]

Make sure to recall power rules for differential and exponent laws.

From 3x^2 / x^6.

[tex] \displaystyle \large{ - \frac{ 3 }{ {x}^{4} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 }[/tex]

Now what do we do with 1/y^3? We just differentiate it normally but we multiply with dy/dx once we differentiate the y function.

[tex] \displaystyle \large{- \frac{ 3 }{ {x}^{4} } -\frac{ \frac{d}{dx}( {y}^{3}) }{ ({y}^{3})^{2} } = 0 } \\ \displaystyle \large{ -\frac{ 3 }{ {x}^{4} } - \frac{ 3 {y}^{2} }{ {y}^{6}} = 0 } \\ \displaystyle \large{ - \frac{ 3 }{ {x}^{4} } - \frac{ 3 }{ {y}^{4}} \frac{dy}{dx} = 0 }[/tex]

Solve for dy/dx, add both sides by 3/x^4.

[tex] \displaystyle \large{ - \frac{ 3 }{ {x}^{4} } + \frac{3}{ {x}^{4} } - \frac{ 3 }{ {y}^{4}} \frac{dy}{dx} = 0 + \frac{3}{ {x}^{4} } } \\ \displaystyle \large{ - \frac{ 3 }{ {y}^{4}} \frac{dy}{dx} = \frac{3}{ {x}^{4} } } \\ [/tex]

Divide both sides by - 3/y^4.

[tex] \displaystyle \large{ \frac{- \frac{3}{ {y}^{4} } \frac{dy}{dx} }{ - \frac{3}{ {y}^{4} } } = \frac{ \frac{3}{ {x}^{4} } }{ - \frac{3}{ {y}^{4} } } } \\ \displaystyle \large{ \frac{dy}{dx} = \frac{3}{ {x}^{4} } \times (-\frac{ {y}^{4} }{3} )} \\ \displaystyle \large{ \frac{dy}{dx} = \frac{1}{ {x}^{4} } \times (- \frac{ {y}^{4} }{1}) } \\ \displaystyle \large{ \frac{dy}{dx} = - \frac{ {y}^{4} }{ {x}^{4} } } \\ \displaystyle \large{ \frac{dy}{dx} = - ( { \frac{y}{x} })^{4}}[/tex]

PLZ ANSWER WILL GIVE BRAINLYEST!!!!
What are the x and y-intercepts of the line described by the equation?

3x−9y=10.8
Question 2 options:

x-intercept = 1.2

y-intercept = -3.6


x-intercept = -1.2

y-intercept = 3.6


x-intercept = -3.6

y-intercept = 1.2


x-intercept = 3.6

y-intercept = -1.2

Answers

Answer:

x-intercept = 3.6

y-intercept = -1.2

Step-by-step explanation:

could yall help me pls

Answers

Step-by-step explanation:

see the above attachment.

hence your answer is A.

hope this helps you .

15. A skier descends at a rate of 6 feet per second. What is the change in
elevation after one minute? *
Your answer
help

Answers

Answer:

After one minute they would've descended 360 feet

Step-by-step explanation:

The least common multiple of the numbers 15, 12, 8

Answers

Answer: LCM of 8, 12, and 15 is 120.

Step-by-step explanation:

I hope this helps!

Answer:

2 and 1

Step-by-step explanation:

1 is the best which can go into

8 15 and 12

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