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
A normal population has a mean of 60 and a standard deviation of 12. You select a random sample of 9. Compute the probability the sample mean is : (a). Greater than 63. (b). Less than 56. (c). Between 56 and 63.
Answers
Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.2266 = 22.66% probability that the sample mean is greater than 63.
b) 0.1587 = 15.87% probability that the sample mean is less than 56.
c) 0.6147 = 61.47% probability that the sample mean is between 56 and 63.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 60, thus [tex]\mu = 60[/tex].Standard deviation of 12, thus [tex]\sigma = 12[/tex].Sample size of 9, thus [tex]n = 9, s = \frac{12}{\sqrt{9}} = 4[/tex].Item a:
This probability is 1 subtracted by the p-value of Z when X = 63, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{63 - 60}{4}[/tex]
[tex]Z = 0.75[/tex]
[tex]Z = 0.75[/tex] has a p-value of 0.7734.
1 - 0.7734 = 0.2266
0.2266 = 22.66% probability that the sample mean is greater than 63.
Item b:
This probability is the p-value of Z when X = 56, so:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{56 - 60}{4}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.1587 = 15.87% probability that the sample mean is less than 56.
Item c:
This probability is the p-value of Z when X = 63 subtracted by the p-value of Z when X = 56.
These p-values were found in the previous items, so:
0.7734 - 0.1587 = 0.6147
0.6147 = 61.47% probability that the sample mean is between 56 and 63.
A similar problem is given at https://brainly.com/question/24663213
What number is 28% of 45?
Answers
Answer:
12.6
Step-by-step explanation:
Hope it helps Brooo
Answer: 12.6
Step-by-step explanation:
28% × 45 = 12.6 => Divide 12.6 by 45And see if we get as a result: 28%
I hope this helps<33
2
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The numbers 7. 11, 12, 13, 14, 18, 21, 23, 27 and 29 are written on separate cards, and the cards are placed on a table with the numbers facing
down.
The probability of picking a card with an even number is?
Answers
Answer:
Answer=3/10
Step-by-step explanation:
even numbers=3
total cards=10
P=number of possible outcomes/total outcomes
=3/10
Answer:
you have a 3/10 probability of geting a even number bc
Step-by-step explanation:
there are ten numbers shown in the question and there are three even numbers out of ten so that is how you get you anewer
Which of the following satisfies 3x+1=4(mod9)
Answers
Answer:
X=1
Step-by-step explanation:
3x+1=4
3x=4-1
3x=3
x=1
step 1: find the factors of ac that add up to b. ac=6(−10)=−60 b=−11 the factors of −60 that add up to −11 are and . step 2: rewrite the trinomial with the x-term expanded, using the two factors from step 1. 6x2−11x−10 (6x2− )+( −10) step 3: group the first two and second two terms together, find the gcf and factor again. (2x−5)+ (2x−5
Answers
Answer:
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=6⋅−10=−60 and whose sum is b=−11
.
6x2+4x−15x−10
Factor out the greatest common factor from each group.
2x(3x+2)−5(3x+2)
Factor the polynomial by factoring out the greatest common factor, 3x+2
.
(3x+2)(2x−5)
Six more than a number is 17
Answers
The unknown number given from the expression Six more than a number is 17 is 11
How to solve linear equation?let
The unknown number = x
x + 6 = 17
subtract 6 from both sidesx = 17 - 6
x = 11
check:
x + 6 = 17
11 + 6 = 17
Learn more about equation:
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Last year 300 people attended a play with ticket price of $8. The school estimates that 20 fewer people attend for each $1 increase in price. What ticket price would give the greatest income?
Answers
Answer:
$12
Step-by-step explanation:
If we stuck with the price of $8, then we end with an income of $2400
Increasing it by $1 will decrease attendance by 20
8 x 300 = 2400
9 x 280 = 2520
10 x 260 = 2600
11 x 240 = 2640
12 x 220 = 2640
13 x 200 = 2600
We're starting to go down, so let's stop there
The ticket price of $11 or $12 appears to give the most income
I would stick with $12 since your still getting more money from one ticket
The price of a ticket stick at $12 since you still get more money from one ticket.
What ticket price would give the greatest income?Last year 300 people attended a play with a ticket price of $8.
The school estimates that 20 fewer people attend for each $1 increase in price.
If we keep the price at $8, we'll end up with a $2400 profit.
Increasing it by $1 will result in a 20 percent drop in attendance.
8 × 300 = 2400
9 × 280 = 2520
10 × 260 = 2600
11 × 240 = 2640
12 × 220 = 2640
13 x 200 = 2600
Let's come to a halt here since we're starting to descend.
The $11 or $12 ticket price looks to generate the most revenue.
I'd continue with $12 because you'll still make more money with one ticket.
More about the greatest income link is given below.
https://brainly.com/question/9453332
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I will give Brainliest :)
Answers
Answer:
Step-by-step explanation:
PLEASE HELP
answer both of the questions in the photo please
Answers
Answer:
-6
11
Step-by-step explanation:
-6n-5=31
-6n=36
n=-6
-28=-3n+5
3n=5+28
3n=33
n=11
What’s a reasonable domain for V(x)=x(11-2x)(17-2x)
Answers
Answer:
(-∞ , ∞) -∞ < x < ∞
Step-by-step explanation:
function has no domain constraint
The domain of the expression is all real numbers except where the expression is undefined.
The given function is v(x)=x(11-2x)(17-2x).
What is domain and range of the function?The B and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:
Domain = the set of all x-coordinates = {1, 2, 3, 4}
Range = the set of all y-coordinates = {2, 3}
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:(−∞,∞)
Set-Builder Notation:{x| x∈ R}
Therefore, the domain of the expression is all real numbers except where the expression is undefined.
To learn more about the domain and range visit:
brainly.com/question/28135761.
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At the bus station, buses depart a rate if 3 every 10 minutes. At the rate, how many buses would you expect to depart in one one hour?
A. 6
B. 15
C. 18
D. 30
Answers
Answer:
C.18
Step-by-step explanation:
at the rate 18 buses would have departed
Which is the graph of the following equation?
|x| = 2
Answers
Answer:
A
Step-by-step explanation:
|x|= negative and positive with the lines
Bro this my 10th time asking this pls. Someone help me giving brainlist :(
Answers
What is the measure of <1
1. 80
2. 40
3. 160
Answers
8) What is the area of a polygon with vertices
A(-2,4), B(4,4), C(7,0) and D(-5,0)?
(A) 48
(B) 42.5
(C) 36
(D) 24
Answers
Answer:
[C] 36.
Step-by-step explanation:
the given polygon is trapezoid, where its bases are AB and CD.
The required area can be calculated using the formula: A=0.5(AB+CD)*h, where h - height of the ABCD.
The lengths are: AB=6; CD=12; h=4, then the required area:
A=0.5(6+12)*4=36
5551-525152+62626626×552526
solve it.
Answers
Answer:
=34602838637675
Step-by-step explanation:
=−519601+(62626626)(552526)
=−519601+34602839157276
=34602838637675
Needs to show work.
1. Refer to the equation 2x − 6y = 12.
(a) Write the equation in Slope Intercept Form.
Answers
Answer:
y = 1/3x - 2
Step-by-step explanation:
2x − 6y = 12
-6y = -2x + 12
y = 1/3x - 2
the cylinder has radius 4√3 and hight h. the total surface area of the cylinder is 56π√6. find the exact value of h giving the answer in the form a√2 + b√3 where a and b are both integers.
Answers
The area of the cylinder is a function of its height (h) and radius, ([tex]\mathbf{4\sqrt 3}[/tex])
The exact value of h is: [tex]\mathbf{7\sqrt 2- 4\sqrt 3}[/tex]
The given parameters are:
[tex]\mathbf{Area =56\pi\sqrt 6}[/tex]
[tex]\mathbf{r=4\sqrt 3}[/tex]
The surface area of a cylinder is calculated as:
[tex]\mathbf{Area = 2\pi rh + 2\pi r^2}[/tex]
Substitute values for Area
[tex]\mathbf{56\pi\sqrt 6= 2\pi rh + 2\pi r^2}[/tex]
Divide through by pi
[tex]\mathbf{56\sqrt 6= 2 rh + 2r^2}[/tex]
Substitute value for r
[tex]\mathbf{56\sqrt 6= 2 (4\sqrt 3)h + 2(4\sqrt 3)^2}[/tex]
[tex]\mathbf{56\sqrt 6= 8h\sqrt 3 + 2\times 48}[/tex]
[tex]\mathbf{56\sqrt 6= 8h\sqrt 3 + 96}[/tex]
Collect like terms
[tex]\mathbf{8h\sqrt 3 = 56\sqrt 6- 96}[/tex]
Make h the subject
[tex]\mathbf{h = \frac{56\sqrt 6}{8\sqrt 3}- \frac{96}{8\sqrt 3}}[/tex]
[tex]\mathbf{h = 7\sqrt 2- \frac{12}{\sqrt 3}}[/tex]
Rationalize
[tex]\mathbf{h = 7\sqrt 2- \frac{12\sqrt 3}{3}}[/tex]
[tex]\mathbf{h = 7\sqrt 2- 4\sqrt 3}[/tex]
Hence, the exact value of h is: [tex]\mathbf{7\sqrt 2- 4\sqrt 3}[/tex]
Read more about surface areas t:
https://brainly.com/question/25131428
2/3 : 2/6 as a unit rate
Answers
Answer:
3/1
Step-by-step explanation:
evaluate the expression (2.5)^3
Answers
please mark this answer as brainlist
The value of the expression is 15.625.
We have,
Expression:
(2.5)³
The base is 2.5 and the power is 3.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
This can be written as,
= 2.5 x 2.5 x 2.5
Convert the decimals into fractions.
= 25/10 x 25/10 x 25/10
Simplify the fractions.
= 15.625
Thus,
The value of the expression is 15.625.
Learn more about expressions here:
https://brainly.com/question/3118662
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5 3/4 as an improper fraction
Answers
Answer:
23/4
Step-by-step explanation:
Answer:
A mixed number is an addition of its whole and fractional parts.
[tex]5 \frac{3}{4} [/tex]
Add:
[tex]5 \: and \: \frac{3}{4} [/tex]
To write 5 as a fraction with a common denominator, multiply by
[tex] \frac{4}{4} [/tex]
Combine:
[tex]5 \: and \: \frac{4}{4} [/tex]
Combine the numerators over the common denominator.
[tex] \frac{5.4 + 3}{4} [/tex]
Simplify the numerator.
Multiply 5 by 4.
Add 20 and 3.
[tex] \frac{23}{4} [/tex]
Step-by-step explanation:
Thanks!!!!!!
A family bought a total of 13 tickets to a magic show, some adult and some child. The family paid a total of $85
Adult tickets are $15 each and child tickets are $5 each.
Let x represent adult tickets and y represent child tickets.
Write an equation to model the total amount of money that they spent.
Answers
Answer:
250 $3 tickets and 100 $2 tickets were sold.
Step-by-step explanation:
The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?
Solution:
Step 1: Set up a table with quantity and value.
quantityvaluetotal$3 tickets$2 ticketstogether
Step 2: Fill in the table with information from the question.
The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?
Let x = number of $3 tickets
Let y = number of $2 tickets
Total = quantity × value
quantityvaluetotal$3 ticketsx33x$2 ticketsy22ytogether350950
Step 3: Add down each column to get the equations
x + y = 350 (equation 1)
3x + 2y = 950 (equation 2)
Use Substitution Method
Isolate variable x in equation 1
x = 350 – y (equation 3)
Substitute equation 3 into equation 2
3(350 – y) + 2y = 950
1050 – 3y + 2y = 950
3y – 2y = 1050 – 950
y = 100
Substitute y = 100 into equation 1
x + 100 = 350
x = 250
GIVING BRAINLIEST AND 20 points!
Please answer this question I will give you brainliest if you answer
WITH A STEP BY STEP explanation
Sorry for the caps but just want to make it clear if u want brainliest you gatta do that
Answers
Answer:
The answer is 27
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2(3y+6+3)=196−16
(2)(3y)+(2)(6)+(2)(3)=196+−16(Distribute)
6y+12+6=196+−16
(6y)+(12+6)=(196+−16)(Combine Like Terms)
6y+18=180
6y+18=180
Step 2: Subtract 18 from both sides.
6y+18−18=180−18
6y=162
Step 3: Divide both sides by 6.
6y
/6
=
162
/6
y=27
I just need mental help at this point
Answers
Answer:
1:2
Step-by-step explanation:
QRS is double the size of TUV
Find the value of x.
Answers
calculate the formula of the triangle and then use pythagoras thereom to solve the values according to their sides
Don't forget to thank me later
We can find this out by doing 8/12 which is simplified to 2/3.
We can check this is correct because 12 x 2/3 gives us 8.
So now we do 15 x 2/3 = 10
This means x - 4 = 10
x = 14
HELppppppppppppppppp
Answers
9514 1404 393
Answer:
40 -8p -3w$4Step-by-step explanation:
Ms. Liu will have to pay 8p for p bags of popcorn, and 3w for w bottles of water. The amount she will have left will be these amounts subtracted from $40.
40 -8p -3w . . . . represents the money remaining
For p=3 and w=4, this evaluates to ...
40 -8(3) -3(4) = 40 -24 -12 = 4
Ms. Liu will have $4 left after her purchase.
Please answer this
Hope you get along
I report What to answer
Answers
What the hel you expect us to do all that for 5 kids points? Go ask you mom to do that for you. If you're asking US to do that, then it has to be 40 or 50 points.
help pls. i’ll give brainliest
Answers
Answer:
last 2 I think
Step-by-step explanation:
okokokokokipullup
Help me please help me help please
Answers
Answer:
4
Step-by-step explanation:
-4/-1 = 4
HELP HELP EASY
Use a calculator to approximate cos 43° and round to
four decimal places.
Answers
Answer:
0.731353701619170483287543608275622403378...
Step-by-step explanation:
cos((43 π)/180)
UwU
It's verified you can trust
0.7315Is what you needed