Answers
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
Related Questions
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)
could yall help me pls
Answers
Step-by-step explanation:
see the above attachment.
hence your answer is A.
hope this helps you .
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]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
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 m6
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:
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
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)
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
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
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
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.
NO LINKS!!
What's the Perimeter?
a. 2x+8
b. 2x+9
c. 3x+8
d. 3x+9
Answers
Answer:
A. 2x + 8Step-by-step explanation:
The perimeter is:
x + x sides3 + 1 + 4 = top and bottomTotal:
P = 2x + 8Correct choice is A
Answer:
A is correct
Step-by-step explanation:
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:
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:
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
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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:))
help for brainliest and good luck
Answers
18 is the correct answer
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
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]
How can you compare data sets?
Answers
Answer:
Grapgical charts and data plots
Step-by-step explanation:
Step-by-step explanation:
Hope it helps you!!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 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
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
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
ii. 3,000
iii. 200
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 :)
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.
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
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:
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
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