Function assigns one element of one set to the other specific element of another set. The quotient of the fraction [tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex] is [tex]{\sqrt{13}-\sqrt{11}}[/tex].
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As the fraction is given to us,
[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex]
Rationalizing the fraction we will get,
[tex]=\dfrac{2}{\sqrt{13}+\sqrt{11}} \times \dfrac{{\sqrt{13}-\sqrt{11}}}{{\sqrt{13}-\sqrt{11}}}\\\\= \dfrac{2({\sqrt{13}-\sqrt{11}})}{(\sqrt{13})^2-(\sqrt{11})^2}\\\\= \dfrac{2({\sqrt{13}-\sqrt{11}})}{13-11}\\\\=\dfrac{2({\sqrt{13}-\sqrt{11}})}{2}[/tex]
Now, if we divide the numerator by the denominator to get the quotient we will get,
[tex]= \dfrac{2({\sqrt{13}-\sqrt{11}})}{2}\\\\={2({\sqrt{13}-\sqrt{11}})}\div 2\\\\={\sqrt{13}-\sqrt{11}}[/tex]
Hence, the quotient of the fraction [tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex] is [tex]{\sqrt{13}-\sqrt{11}}[/tex].
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The quotient of the given number start Fraction 2 over start root 13 end root start root 11 end root end Fraction.
[tex]\sqrt{13}-\sqrt{11}[/tex]
What is the quotient?Quotient is the resultant number which is obtained by dividing a number with another. Let a number a is divided by number b. Then the quotient of these two number will be,
[tex]q=\dfrac{a}{b}[/tex]
Here, (a, b) are the real numbers.
The number Start Fraction 2 Over Start Root 13 End Root Start Root 11 End Root End Fraction given can be written as,
[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex]
Let the quotient of this division is n. Therefore,
[tex]n=\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex]
By rationalizing the denominator, we get,
[tex]n=\dfrac{2}{\sqrt{13}+\sqrt{11}}\times\dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{13-11}\\\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{2}\\n=\sqrt{13}-\sqrt{11}[/tex]
Hence, the quotient of the given number start Fraction 2 Over Start Root 13 End Root Start Root 11 End Root End Fraction.
[tex]\sqrt{13}-\sqrt{11}[/tex]
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Consider the expression (1.0045)^4t that represents the interest earned on a money
market account, where t is the time In years. What is the approximate yearly interest rate? Round your percent to the nearest tenth. INCLUDE THE % SYMBOL IN YOUR ANSWER
The approximate yearly interest rate is 1.02%
Exponential equationsGiven the expression that represents the interest earned on a money given as (1.0045)^4t
In order to calculate the approximate yearly percent, we will substitute t = 1 into the expression as shown:
f(t) = (1.0045)^4t
f(1) = (1.0045)^4(1)
f(1) = (1.0045)^4
f(1) = 1.018
Hence the approximate yearly interest rate is 1.02%
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I would appreciate a lot if y’all help me!
Answer:
Deductive reasoning
Step-by-step explanation:
please help thank you
Answer:
goofy
Step-by-step explanation:
70200 NC)
Demarcus will be 21 years old when he graduates. It is mean weekly wage over his career is $1.258.00 what will his lifetime earnings be when he retires at the age of 62? (1 point)
$1371 532.00
$287779200
$3.572132.00
$4049344.00
Step-by-step explanation:
Her life term earnings will be 4049344.00 dollars
4. What is the value of b in the triangle shown below?
(1 point)
3b
24 in.?
b
0-4 in
04 in
0 =4 in
O no solution
Answer:
4 inches
Step-by-step explanation:
[tex]24 = \frac{1}{2} (b)(3b) \\ \\ \implies \: 24(2) = 3 {b}^{2} \\ \\ \implies \: 48 = 3 {b}^{2} \\ \\ \implies \: \frac{48}{3} = {b}^{2} \\ \\ \implies \: {b}^{2} = 16 \\ \\ \implies \: {b} = \pm\sqrt{16} \\ \\ \implies \: {b} = \pm \: 4 \\ \because \: b \: is \: side \: length \\ so \: its \: value \: cant \: be \: negative. \\ \implies \: b = 4 \: in[/tex]
What is the gradient of the graph shown?Give your answer in its simplest form.
Answer:
gradient = 1
Step-by-step explanation:
calculate the gradient using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
m = [tex]\frac{0-(-2)}{2-0}[/tex] = [tex]\frac{0+2}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
[tex]\longrightarrow[/tex]By observing the graph of the line , we can observes that it intersects x- axis at 2 and y -axis at -2 i.e., it passes through (2,0) and (0,-2) respectively.
[tex]\textsf{The gradient of a line passing through two}[/tex][tex]\sf{given \: points \:(x_1,y_1) \:and \:(x_2,y_2) \: is \:given \: by - }[/tex]
[tex]\green{ \underline { \boxed{ \sf{ Gradient =\frac{y_2-y_1}{x_2-x_1}}}}}[/tex]
Here,
[tex]\sf{x_1= 2}[/tex][tex]\sf{y_1=0}[/tex][tex]\sf{x_2=0}[/tex][tex]\sf{y_2= -2}[/tex]Putting Values:-
[tex]\begin{gathered}\\\implies\quad \bf Gradient =\frac{-2-0}{0-2} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \bf \frac{\cancel{-2}}{\cancel{-2}} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \bf 1 \\\end{gathered} [/tex]
>>The gradient of the graph shown is 1
* Hello I'm giving ALOT of points to the one who can answer this question with an ANSWER & a STEP-BY-STEP EXPLAINATION so that I can learn from this lesson. I'm truly more interested in learning than knowing a answer. If you dont do so I WILL take back my points :)*
The ages of two groups of karate students are shown in the following dot plots:
(Imported image)
The mean absolute deviation (MAD) for group A is 2.07 and the MAD for group B is 5.51. Which of the following observations can be made using these data?
1. Group A has greater variability in the data.
2. Group A has less variability in the data.
3. Group B has a lower range.
4. Group B has a lower mean.
Thank you so much for your help! Xx
Answer:
From the graph and data points, you can observe that Group B has a HIGHER range and has a greater variability. so it's NOT 1. 4. or 3. THEREFORE it's 2.
Explanation:
You start out by finding the mean (finding the sum of the data values and then dividing the sum by the number of data values)
and subtracting the first plot by the last in each graph.
(at least I think)
I've been through this topic. (it was a long time ago since I'm now in highschool so this might be different now as the grading curriculum has changed)
solve the inequality and tell weather it has infinite or no solutions
[tex]0.5x+8\ \textless \ 2x-4[/tex]
Owen measured a line to be 17.9 inches long. If the actual length of the line is 17.8 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
0.6%
Step-by-step explanation:
Percent Error = the absolute value of (actual value observed-expected value)/(expected value) x100%
(17.8-17.9)/(17.9) = -0.006
Absolute value is 0.006
0.006 times 100% equals 0.6%
The percent error of the measurement in the length is 10%.
What is percent error in measurement?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.Given is that Owen measured a line to be 17.9 inches long. The actual length of the line is 17.8 inches.
We can calculate the percentage error as -
%e = {(A.V. - E.V.)/(A.V.)} x 100
%e = (17.9 - 17.8) x 100
%e = 0.1 x 100
%e = 10%
Therefore, the percent error of the measurement in the length is 10%.
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The mean of 3 numbers is 4. 2 of the numbers are 1 and 9
What is the third number
Answer:
2
Step-by-step explanation:
[tex]\frac{a+b+c}3}= 4\\[/tex]
multiply both sides by 3
a+b+c=12
substitute the values we have
1+9+c=12
10+c=12
-10 -10
c=2
so the third number is 2
hope this helped you !
The table shows values of a function f(x) what is the average rate of change of f(x) over the interval from x=4 to x=9
Answer:
18/5
Step-by-step explanation:
it's just slope formula
(14- -4)/(9-4)
(14+4)/5
18/5
Anthony resells shoes that he purchases. He bought a pair for $210, and then applied a 43% markup. How much will the shoes be sold for?
Explain how to solve the equation.
g/4=24
Part 1
Select the correct choice below and fill in the answer box within your choice.
(Type a whole number.)
A.Divide both sides by
B.Subtract from both sides.
C.Multiply both sides by
D.Add to both sides.
Answer:
C. Multiply both sides by 4.
Step-by-step explanation:
You are isolating the variable, g, and so you will do the opposite of all operations that occurs with the variable, g.
Note the equal sign, what you do to one side, you would do to the other. Isolate the variable, g, by multiplying 4 to both sides of the equation:
[tex]\frac{g}{4} * 4 = 24 * 4[/tex]
[tex]g = 24 * 4[/tex]
[tex]g = 96[/tex]
~
The first to answer will be named brainlest
Answer:
Id say 1st and 3rd answer.
Step-by-step explanation:
Answer:
First Third and Fourth Statements are true.
Step-by-step explanation:
Is (6, 1) a solution to the equation y = 5x?
Answer:
False, but depends on…
Step-by-step explanation:
If you are dealing with x and y-intercepts, or slopes, then no. The answers wouldn't be in the given format. If you're looking for a coincidence, then it could be a solution. Hope this helps!
The equation f = v + at represent the final velocity of an object f with an initial velocity v and an acceleration rate a overtime t. which is an equivalent equation solved for t
Answer:
t = f-v/a (First choice)
Explanation:
step by step:
1) f = v + at
2) f - v = v - v + at
3) f - v = at
4) f - v / a = at / a
5) f - v / a = t
6) t = f - v / a
mZ3 = 37. Find mZ1.
1
4
2
3
Answer:
37⁰
Step-by-step explanation:
Angles 3 and 1 are vertical angles. Therefore it is congruent.
Wanda rides her bike 5 hours a week. How many hours does she ride in 4 weeks?
Answer:
20
Step-by-step explanation:
We can put the rate of hours a week as 5. Since in this case hours will substitute for distance, and distance=speed*time, then the amount of hours will be 5*4=20.
edit: mistyped
Answer:
20 hours
Step-by-step explanation:
Given the following question:
5 hours per week
How many hours does she ride in 4 weeks?
We know the amount of hours Wanda rides per week, so this is a simple multiplication problem.
[tex]5h\times4w[/tex]
[tex]5\times4=20[/tex]
[tex]=20[/tex]
Wanda rides her bike for "20 hours" in 4 weeks.
Hope this helps.
Please Help! Explain too!
Answer:
A Because probability cannot be of - sign it ranges from o-1
Pleaseee someone plizzz help me on this one ✊✊✊
Answer:ok so u have to help
Step-by-step explanation:
Get moneyy. Answer this.
Answer:
60
Step-by-step explanation:
all the outer angles have to add up to 360
1. In the computer lab, there
are 14 desktops and 16
laptops. Approximately what
percent of the computers are
laptops?
Answer:
53.3333333%
Step-by-step explanation:
Given the following question:
14 desktops
16 laptops
14 + 16 = 30
To find the answer use the formula to calculate percentages.
[tex]\frac{16}{30}\times100[/tex]
[tex]16\div30=0.533333333[/tex]
[tex]0.533333333\times100=53.3333333[/tex]
[tex]=53.3333333[/tex]
16 of 30 as a percentage is "53.3333333%."
Hope this helps.
POINTS AND BRAINLY
PLEASE HELP MEEEE
Answer:
the answer would be A a pure sound
Answer:
I think it is A pure Sound
Step-by-step explanation:
The Panthers baseball team needs new equipment. They plan to purchase bats that cost $60 each and gloves that cost $25 each. The number of bats they will purchase is half the number of gloves they will purchase. If they have $700, how many of each can they buy?
Answer:
Therefore, they can buy
6.36 bats and 12.72gloves
Step-by-step explanation:
Let us represent:
The number of bats purchased = b
The number of gloves purchased = g
We are told in the question that:
The number of bats they will purchase is half the number of gloves
b = 1/2g
b = g/2
g = 2b
The teams plan to purchase bats that cost $60 each and gloves that cost $25 each. they will purchase. If they have $700, how many of each can they buy?
Hence:
$60 × b + $25 × g = $700
= 60b + 25g = 700
We substitute 2b for g
60b + 25(2b) = 700
60b + 50b = 700
110b = 700
b = 700/110
b = 6.3636363636
b = 6.36 bats
Therefore, the number of bats they can buy = 6.36 bats
Remember:
g = 2b
b = 6.36
Hence,
g = 2 × 6.36
g =12.72
Therefore, the number of gloves = 12.72 gloves
Find the total amount given the original price, tax rate and tip rate. Round to the nearest hundredth if necessary.
Original price: $90.34
Tax rate: 3.5%
Tip: 20%
Enter the correct answer in the box.
Answer:
$111.5699. Round to hundredths $111.57
Step-by-step explanation:
First identify the %
20% =.20 20/100= .20
3.5% = .035 3.5/100= .035
Then Find the tax rate and tip
Tax Rate .035 × 90.34
= $3.1619 (tax rate)
Tip. is .20× 90.34
= $18.068 (tip)
Final Add all it up tax rate+ tip + original price
$90.34. Don't forget to line up your demicals
$3.1619. or use a calculator
+ $18.068
Total = $111.5699
round to the nearest hundredth
$111.57 is your total
A vanilla thickshake is $2 more than a fruit juice. If 3 vanilla thinkshakes and 5 fruit juices cost $30, determine their individual price.
Answer:
vanilla=$5 and fruit juice=$3
Step-by-step explanation:
let $x and $y denote the cost of vanilla thickshake and fruit juice respectively.
Now,
$x=$y+2$ (Given)-----(i)
3×$x + 5×$y =30
3×($y+$2)+5×$y=30 (From equation i )
3×$y +$6 + 5×$y = 30
8×$y + $6 = $30
8×$y= $24
.: $y =$3
Then,
From i
$x =$y+$2
=$3+$2
#$5
i will give brainliest
Find n.
35n/35 = 700/35
Answer:
20
Step-by-step explanation:
[tex]\frac{35n}{35} =\frac{700}{35} \\[/tex]
multiply both sides by 35
[tex]35*\frac{35n}{35} = 700 * 35\\35n = 700[/tex]
divide both sides by 35
[tex]n = 20[/tex]
Answer:
N = 20
Step-by-step explanation:
Move all terms to the left
35n/35-(700/35)=0
Add all of the numbers together, and all of the variables
35n/35-20=0
Multiply all of the terms by the denominator
35n-20*35=0
Add all of the numbers together, and all of the variables
35n-700=0
Move all of the terms containing N to the left, all other terms to the right
35n=700
n=700/35
n=20
A book costs $10 at one book store. About how much more does the book cost when the book store increases its prices 18%?
$11.80
Step-by-step explanation:
Find value of x with the steps please
Answer:
x=7°
Step-by-step explanation:
The figure is a triangle.
1. Triangles's angles add up to 180°.
2. We know that 1 angle measures 104°, so the remaining 2 angles add up to 76°. It is an isosceles triangle, so both of the remaining 2 angles have equal measures.
3. 76÷2=38°.
4. 9x-25°=38°
5. 63°-25°=38°
6. 9x=63°
7. x=7°
Step by step explanation above. Hope it is correct!
How long is the altitude of a right triangle that separates the hypotenuse into lengths 6 and 25?
a. 5^6
b. 150
c. 4^5
d. 10^5
Answer: A
Step-by-step explanation: