You can use the fact that is irrational to answer the questions below. You can also use other facts proven within this exercise. (a) Prove that is irrational. (b) Prove that is irrational. (c) Is it true that the sum of two positive irrational numbers is also irrational
Answers
Answer:
See Explanation for proofs
Step-by-step explanation:
Given
See attachment for complete question
Solving (a):
[tex]\frac{\sqrt{2}}{2}[/tex] is irrational
[tex]\sqrt{2} =1.41421356237.....[/tex]
So, we have:
[tex]\frac{\sqrt{2}}{2} = \frac{1.41421356237.....}{2}[/tex]
[tex]\frac{\sqrt{2}}{2} = 0.70710678118....[/tex]
[tex]0.70710678118....[/tex] can not be represented as a fraction of whole numbers.
Hence:
[tex]\frac{\sqrt{2}}{2}[/tex] is irrational
Solving (b):
[tex]\sqrt{2} -2[/tex] is irrational
[tex]\sqrt{2} =1.41421356237.....[/tex]
So, we have:
[tex]\sqrt{2} -2 = 1.41421356237..... - 2[/tex]
[tex]\sqrt{2} -2 = -0.58578643763.....[/tex]
[tex]-0.58578643763.....[/tex] can not be represented as a fraction of whole numbers.
Hence:
[tex]\sqrt{2} -2[/tex] is irrational
Solving (c):
The sum of two positive irrational number is always irrational
Proof Below
If a is irrational and b is also irrational,
then
[tex]a + b = irrational[/tex]
Take for instance:
[tex]a = \sqrt{2[/tex]
[tex]b = \sqrt{8[/tex]
[tex]a + b = \sqrt{2} + \sqrt{8[/tex]
[tex]a + b = \sqrt{2} + \sqrt{4*2[/tex]
[tex]a + b = \sqrt{2} + \sqrt{4}*\sqrt{2[/tex]
[tex]a + b = \sqrt{2} + 2\sqrt{2[/tex]
[tex]a + b = 3\sqrt{2[/tex]
[tex]3\sqrt{2[/tex] is irrational and this is true for the sum of every positive irrational numbers
Related Questions
Gina has two job offers as a dog walker. She wants to earn at least $75 each week. The first offer pays $15 each week plus $3 per dog walked. Let x represent the number of dogs walked.
Answers
Answer:
Step-by-step explanation:
15+3x≥75
3x≥75-15
3x≥60
x≥20
What is -2(5x -12)>54
Answers
Answer:
x < - 3 i guess I'm not sure
Answer:
x=13.6
Step-by-step explanation:
-2(5x-12)>54
5x-12>54+2
5x-12>56
5x>56+12
5x>68
x>68/5
x>13.6
Amy works at a surf shop at the beach during the summer. She is paid at a rate of $4 each hour, plus she
earns 7% commission on each sale that she makes,
Which equation correctly represents Amy's total income () in terms of (h) how many hours she works
and (s) how much she sells?
Answers
Answer:
4h+.07s
Step-by-step explanation:
four dollars per hour plus 7 percent of her sales
For the given data, the suitable equation which will correctly represent Amy's total income in terms of (h) and (s) that will represent sales is 4h+.07s.
What is the meaning of the term “equation”?A mathematical equation, states that two amounts or values are equal. Countable noun A scenario known as an equation is one in which two or more components must be taken into account in order to comprehend or understand the overall situation.
Identify the inquiry being made. Simple statements should be used to record the pertinent information. Assign symbols to values that are still unknown. Calculate the mathematical relationships between the assertions.
During the summer, Amy works at a beachside surf shop. She gets paid $4 per hour, plus she receives a 7% commission on every sale she closes. The proper formula is 4h+.07s.
Learn more about equation from here:
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identify the quadrilateral (help pls)
Answers
Answer:
A) would be a parallelogram B) would a rectangle C) would be a trapezoid and D) would be a square
Step-by-step explanation:
2 4/7 x 1 1/2 ayudapor favor
Answers
Answer:
3 6/7 is your correct answer
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\bold{Equation: 2\dfrac{4}{7}\times1\dfrac{1}{2}}[/tex]
[tex]\bold{2\dfrac{4}{7}=\dfrac{18}{7}}\\\\\\\bold{1\dfrac{1}{2}=\dfrac{3}{2}}[/tex]
[tex]\bold{New\ equation: \dfrac{18}{7}\times\dfrac{3}{2}}\\\bold{\dfrac{18\times3}{7\times2}}\\\bold{18\times3=54\leftarrow numerator}\\\bold{14\times2= 14\leftarrow denomination }\\\bold{= \dfrac{54}{14}}\\\bold{The\ GCF (Greatest\ Common \ Factor)\ of\ BOTH\ numbers(54\ \&\ 14)\ is\ 2.}}\\\bold{So, we\ DIVIDE\ both\ numbers\ by\ 2}\\\bold{\dfrac{54\div2}{14\div2}}\\\bold{54\div2=27\leftarrow numerator}\\\bold{\dfrac{14}{2}= 7\leftarrow denominator}\\\bold{= \dfrac{27}{7}}\\\bold{\dfrac{27}{7}= 3\dfrac{6}{7}}[/tex]
[tex]\boxed{\boxed{\bold{ANSWER: \dfrac{27}{7}=3\dfrac{6}{7}}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
69/85 in its simplified form. My you tube Riley Gaming
Answers
Answer: 4/5
Step-by-step explanation:
Answer: 69/85 is the simplified form. You can't simplify it.
Step-by-step explanation:
Giving brainliest I only have 1 try please give out correct answer:)
Answers
Which of the following proportions could be used to find x?
Answers
Answer:
X/2 = 6/ 1.5
Step-by-step explanation:
x/2 = 6/1.5
I hope this answer is correct
Answer:
x/2 = 6/1.5
Step-by-step explanation:
In the diagram, the measure of angle 5 is (10x - 9), and the measure of angle 7 is (9x)". What is the measure of angle
6, to the nearest degree?
1
A
13
516
8
What is the measure of angle 6, to the nearest degree?
Answers
Answer:
99/C
Step-by-step explanation:
I just did the test and it was right
Write 2847 correct to the nearest 100
Answers
Please help me ASAP......
Answers
Answer:
step 1. factor out a 35.
step 2. 35(3 + m).
find the 6the term in the sequence?
-1,4,-16,64
Answers
Answer:
-1,4,-16,64,-256,1024
Step-by-step explanation:
Each number is being multiplied by -4.
A fish tank has 12 angelfish .out of every 8 fish 3 are angelfish. how many fish are in the tank?
Answers
12 fishes are in the tank
A fish tank has 12 angelfish .out of every 8 fish 3 are angelfish. how many fish are in the tank?
Answer:
Step-by-step explanation:
12angelfish(8fish/3angelfish)=32 fish
Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.
Estimated Sales Volume =46.63+0.47(Advertising Expenditures)
If the company has a target sales volume of $275,000, how much should the sales manager allocate for advertising in the budget?
Answers
Answer:
$485890
Step-by-step explanation:
Given
Estimated Sales Volume =46.63+0.47(Advertising Expenditures)
Required
Find the allocated amount for advertising expenditure when target sales is $275000
Represent the sales volume with V and The advertising expenditure with a.
So, the expression is:
[tex]V = 46.63 + 0.47A[/tex]
Since the expression is in thousands, substitute 275 for V
[tex]275 = 46.63 + 0.47A[/tex]
Collect Like Terms
[tex]275 - 46.63 = 0.47A[/tex]
[tex]228.37= 0.47A[/tex]
Make A the subject
[tex]A = \frac{228.37}{0.47}[/tex]
[tex]A = 485.89[/tex]
Hence, $485890 should be allocated for advertising
What is the product of 3.6 x 4.2
Answers
Answer:
15. 12
Step-by-step explanation:
just multiply them
What is the slope of the line with the equation -5 - x = y?
O 5
O 1
O -1
O-5
Answers
Answer:
-1
Step-by-step explanation:
What ever number is in front of x that is the answer. If there is only a x then it means 1.
4. What equation represents the data table shown below?
х
0
-2
-4
-6
-8
у
8
12
16
20
24
y = -2x + 8
y = 14/8x +8
y=-1/2x + 8
y = 1/2x - 8
Answers
PLEASE HELP EASY I’ll mark BRAINLIEST
Answers
Answer:
A,B,C,D
Step-by-step explanation:
Answer:
Figure B is:
larger
same number of angles
angles with the same measures
same number of sides
y=7/x, x≠0 need the graph answer!!
Answers
Answer:
so the first picture is it graphed without solving it and the second graph is the answer to it graphed
Step-by-step explanation:
"Triple a number is 18."
Show all work
Answers
Answer: 6
Step-by-step explanation:
3x = 18
Divide 18 by 3
x = 6
Simplify by dividing (-3/8) -5/9
Answers
Answer:
[tex]\frac{-27}{40}[/tex]
Step-by-step explanation:
[tex](\frac{-3}{8})[/tex]÷[tex]\frac{5}{9}[/tex]
[tex]\frac{-3}{8}[/tex]×[tex]\frac{9}{5}[/tex]
[tex]\frac{-27}{40}[/tex]
This hanger is in balance. There are two
labeled weights of 7 grams and 30 grams. The
four circles each have the same weight. What
is the weight of each circle, in grams?
Answers
Answer:
The weight of each circle is 2g
Factor each exspression. 16x + 40y
Answers
Answer: 8(2x+5y)
Step-by-step explanation:
16x+40y
=8(2x+5y)
Answer:
hut the F اا u ااck up (shut up)
shut the F اا u ااck up (shut up, yeah)
shut the F اا u ااck up (go)
shut the F اا u ااck up (go)
shut the F اا u ااck up (go)
shut the F اا u ااck up (shut up)
shut the F اا u ااck up (shut up)
shut the F اا u ااck up (shut up)
shut the F اا u ااck up (shut up)
shut the F اا u ااck up (hu, huh, yeah)
shut the F اا u ااck up (go)
shut the F اا u ااck up (go)
shut the F اا u ااck up (go)
shut the F اا u ااck up (shut up)
shut the F اا u ااck up (shut up)
shut the F اا u ااck up (shut up)
huh (daytrip took it to 10, hey)
Step-by-step explanation:
if someone could explain this to me :((
Answers
Answer:
A) (0,2)
Step-by-step explanation:
The Y-Intercept is where the line on the coordinate plane meets the y axis which in this case is 2
Answer:
A. (0, 2)
Step-by-step explanation:
So first things first, you will want to either put the line on a graph by hand or, in a graphing calculator, I recommend DESMOS
the table is a set of coordinates so
(-4, -18) (-2.5, -10.5) (-.4, 0) (0, 2) (2, 12)
Then you'll put these coordinates into a graph and the point you see touching the y-line is your answer, (0, 2)
hope this helps!!
Which of the following expressions is
equivalent to 12x + 8y?
Someone please help !!
Answers
Answer:
What are the options please ^^
Step-by-step explanation:
------------------------------------------------------------------------
Answer:
Step-by-step explanation:
Solve
Factor
12x+8y
Answer
4(3x+2y)
Which of the following fractions is closer to 0 than to 1
A. 2/10
B. 5/6
C.8/9
D. 4/9
E. 1/8
Answers
Because if you do the math
Answer:
it's E
Step-by-step explanation:
Because the 1 is closer to 0
You are making 100 mL of a saline solution in science class that has a strength of 50%.
You are going to mix some 40% saline solution with some 60% saline solution to do this.
How much of each should you add?
HELP HELP HELP HELP HELP HELP HELP HELP HELP HELP
Answers
Answer:
thisis your answer 100,000
Step-by-step explanation:
100
50
40
this is how you add it and you will get your answer
The equation Y+B=3(x-9) is written in point-slope form. What is the equation written in slope-intercept form?
Oy-x-3
O y-3x+9
O y-sx-9
O y-3x+3
Answers
Answer:
[tex]y = 3x - 27-b[/tex]
Step-by-step explanation:
Given
[tex]y + b = 3(x - 9)[/tex]
Required
Write in slope intercept
Open bracket
[tex]y + b = 3x - 27[/tex]
Collect Like Terms
[tex]y = 3x - 27-b[/tex]
Can someone help me on this?
Answers
43-30=13
The radius of a circle is 4 m. Find its area in terms of \piπ.
Answers
Answer:
50.3
Step-by-step explanation:
A=πr2=π·42≈50.26548