Answers
Answer:
Step-by-step explanation:
abc = 1
We have to prove that,
[tex]\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1[/tex]
We take left hand side of the given equation and solve it,
[tex]\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}[/tex]
Since, abc = 1,
[tex]\frac{1}{c}=ab[/tex] and c = [tex]\frac{1}{ab}[/tex]
By substituting these values in the expression,
[tex]\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}[/tex]
[tex]=\frac{b}{b+ab+1}+\frac{1}{1+b+ab}+\frac{ab}{ab+1+b}[/tex]
[tex]=\frac{1+b+ab}{1+b+ab}[/tex]
[tex]=1[/tex]
Which equal to the right hand side of the equation.
Hence, [tex]\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1[/tex]
Related Questions
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Answers
Ok so all’s you have to do here is get rid of x by dividing-56 by 4 and then divide 8y by 4. That leaves you with x - 2y = 14
Write an equation in slope-intercept form of the line that passes through the given point and is
perpendicular to the graph of the given equation.
(5,0); y+1=2(x-3)
Answers
Answer:
[tex]y=\frac{-1}{2}x +\frac{5}{2}[/tex]
Step-by-step explanation:
Slope intercept form looks like y=mx+b
The slope (m) needs to be the opposite reciprocal of 2, because the line needs to be perpendicular the given line. Therefore, m = -1/2
We can write the equation in point-slope form first because we're given a point and now we have the slope. The equation would be [tex]y-0=\frac{-1}{2} (x-5)[/tex]
Rewriting, we get [tex]y=\frac{-1}{2}x +\frac{5}{2}[/tex]
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Answers
Answer:
A
Step-by-step explanation:
Answer:
A) y ≥ 350x + 17,000
Step-by-step explanation:
If 17,000 is the original, you won't multiply or divide it by x. But since it goes up by at least 350 each year you will multiply by x.
So to set it up, you will have 350x + 17,000, and since it's at least, you will have a great than or equal to sign (≥)
y ≥ 350x + 17,000
The graph shows the savings in Andre’s bank account.
1. What is the slope of the line?
Fill in the blank: The slope means that Andre is saving
__ per __
HELP ASAPP
Answers
Answer:
The slope is 1/5
Andre is saving 4 dollars per week.
Step-by-step explanation:
I will mark BRAINLIEST IF CORRECT
ignore what i selected please help me
Answers
Answer:
- 5/4
Step-by-step explanation:
Amazon bought a tv for $500, they marked up the price 20%, what was the
TV selling for? *
Answers
FIND X PLEASE i rllyyyy need help
Answers
Answer:
I think for 9. x is about 12
Sorry I am not sure for 11.
Step-by-step explanation:
Va rog rezolvati cu operatii.
Answers
Answer:
can you translate that to english
Step-by-step explanation:
the equation of the line a is given as y = -3/4 x -2. Suppose the line a is parallel to line b and lime t is perpendicular to line a. Point (0, 5) lines on both line b and line t.
Answers
Answer:
equation 'b': y = -3/4x + 5
equation 't': y = 4/3x - 2
Step-by-step explanation:
parallel lines must have the same slope
the slope of perpendicular lines must be opposite and reciprocal
What is the slope of the line?
Answers
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Answers
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Answers
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Bobby hit the wrong lever and as a result the factory produced way too many cheese puffs. If the factory managers decide to to give away 1/3 of 1/9 of a ton away as samples, what fraction of a ton did they give away? Make sure you answer is fully reduced.
Answers
Given:
The factory managers decide to to give away [tex]\dfrac{1}{3}[/tex] of [tex]\dfrac{1}{9}[/tex] of a ton away as samples.
To find:
what fraction of a ton did they give away?
Solution:
According to the question, the factory managers decide to to give away [tex]\dfrac{1}{3}[/tex] of [tex]\dfrac{1}{9}[/tex] of a ton away as samples. So,
[tex]\text{Samples}=\dfrac{1}{3}\left(\dfrac{1}{9}(1\text{ ton})\right)[/tex]
[tex]\text{Samples}=\dfrac{1}{3}\times \dfrac{1}{9}\times (1\text{ ton})[/tex]
[tex]\text{Samples}=\dfrac{1}{27}\times (1\text{ ton})[/tex]
[tex]\text{Samples}=\dfrac{1}{27}(1\text{ ton})[/tex]
So, samples is [tex]\dfrac{1}{27}[/tex] of a ton.
Therefore, they give away [tex]\dfrac{1}{27}[/tex] of a ton as samples.
The perimeter of a rectangle is 30 cm and its length is x cm. Find its area in terms of x. step by step explanation.
Answers
Answer:
The area of the rectangle in terms of 'x' = 13x
Step-by-step explanation:
Perimeter = 30 cmLength = x cmUsing the perimeter formula to find the width w.
[tex]P=2(l+w)[/tex]
[tex]P = 2l + 2w[/tex]
[tex]2w = P-2l[/tex]
Dividing both sides by 2
[tex]w\:=\:\frac{P}{2}-2[/tex]
as P = 30 cm
[tex]w\:=\:\frac{30}{2}-2[/tex]
[tex]w\:=\:15-2[/tex]
[tex]w = 13[/tex] cm
Using the formula of the rectangle area
[tex]A = wl[/tex]
substitute w = 13 and l = x in the formula
[tex]A=13\times \:x[/tex]
[tex]A = 13x[/tex]
Therefore, the area of the rectangle in terms of 'x' = 13x
PLEASE HELP ME!! An eagle eats 6 pounds of food every 8 days.How long does it take the eagle to eat 90 pounds of food
Answers
Answer:
15 days
Step-by-step explanation:
8 days equals 48 pounds of foods. 48 times 2 will be 96 and that equals 16 days. Subtract 6 from 96 and you get 90 but you have to subtract a day as well.
Answer:
120 days
Step-by-step explanation:
6/8 = 0.75 meaning the eagle eats 0.75 pounds of food every day.
90/0.75=120 days
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Solve the following equation. Then place the correct number in the box provided.
x+6-5=8-2
Answers
Good luck tho
What is the constant rate of change between the values of x and y in the table?
Answers
The answer is -3/2. ( I used the formula y/x)
A 5-m ladder is resting against a wall. The
base of the ladder is 2 m along the ground
from the base of the wall. What angle does
the base of the ladder make with the ground?
Express your answer to the nearest tenth of a
degree.
Answers
Jordan is makinga garden
with an area of x^2 2+13x+
30 square feet and a length
of x +3 feet. Find an
expression for the width of
Jordan's garden
Answers
Answer:
( x + 10 )
Step-by-step explanation:
→ Divide x² + 13x + 30 by x + 3
( x + 3 ) ( x + 10 )
An equation of a line through (11, 12) which is perpendicular to the line y=3x+1 has slope: ____Blank____
and y -intercept at
____Blank____
Answers
Answer:
the slope is 3 and 1 and the y intercept is 1 and 1
Step-by-step explanation:
During a nature walk Jill identified 20 species of animals and plants she said that 1/3 of the species she identified were animals can this be correct?
Answers
if a person weighs 120 on earth and 106 on Venus how much would a person weighing 180 on earth weigh on venus
Answers
Answer:
166
Step-by-step explanation
If you subtract 106 from 120 you get 14 so then you take that and you subtract 14 from 180 hope this helps
Answer:
166
Step-by-step explanation:
hope this helps
Please can y'all help me asp
flying with the wind a plane went 396km/h. Flying into the wind the plane only went 350 km/h. Find the speed of the wind and the speed of the plane in still air.
Answers
Answer:
/
Step-by-step explanation:
(Driver's Ed) Once in an intersection,
A) You may not make any lane change
B) You must be in the center lane to turn
C) You may make any lane changes you desire
D) You can change your mind about turning
Answers
P(x)=-3+4x when x=-2,0, and 5
Answers
-3 + 4(-2)
-3 - 8
-11
-3 + 4(0)
-3 + 0
-3
-3 + 4(5)
-3 + 20
17
Write the slope perpendicular to y=-5/4x+1
Answers
Answer:
the slope is -4/5
Step-by-step explanation:
to find a perpendicular slope, you take the opposite of the reciprocal of the slope, if I remember correctly.
Which expressions are equivalent to square root 1188x^5? Check all that apply
Answers
Answer: a,c,f
Step-by-step explanation:
Mary is planning her birthday party. She's inviting 7 friends and wants to buy party favors. The favors she wants come in packages of 3. How many packages will she need to buy in order to have enough party favors for all of her guests? *
Answers
Answer:
3 packages
Step-by-step explanation:
each package has 3
if she buys 1, she has 3 party favors
buys 2, has 6
buys 3, has 9
she can't buy 2 packages, then one friend doesn't get a party favor. so she will have to buy 3 packages, use 7, leave 2 extra.
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Mary should buy 3 packages to have enough for all the friends.
What is words problem?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given that, Mary is planning her birthday party. She's inviting 7 friends and wants to buy party favours. The favours she wants to come in packages of 3.
Since, Each package has 3 favours
if she buys 1, she has 3 party favours
If buys 2, has 6
And, if buys 3, has 9
she can't buy 2 packages, then one friend doesn't get a party favour.
So, she will have to buy 3 packages, use 7, leave 2 extra.
Hence, she will need 3 packages.
For more references on word problems, click;
https://brainly.com/question/2610134
#SPJ6
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Answers
Answer:
2x = y
Step-by-step explanation:
As you can see in the table, y = 2x, this is proven by the fact that if you divide any value in the y of the table by 2 you will get its corresponding x value, proving that 2x = y is the function that is used to represent this table's value.
Answer:
2x = y
Step-by-step explanation:
If x = 10
2x = y
2 * 10 = y
20 = y
Adam has 10 blocks numbered 1 through 10. Which describes the probability of randomly choosing a block that has an even number?
Answers
Answer:
[tex]\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given that:
10 number of blocks which have numbers from 1 through 10.
To find:
Probability of randomly choosing a block that has an even number.
Solution:
The given set of numbers is: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
There are a total of 5 Even numbers are {2, 4, 6, 8, 10}.
And There are a total of 5 Odd number are {1, 3, 5, 7, 9}.
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, Event E is randomly choosing an even number.
Number of favorable cases = 5
Total number of cases = 10
Therefore, the required probability is:
[tex]P(E) = \dfrac{5}{10}\\\Rightarrow P(E) = \dfrac{1}{2}[/tex]