Answer:
Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero.
We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction. Notice that in order for a/b to be in simplest terms, both of a and b cannot be even. One or both must be odd. Otherwise, we could simplify a/b further.
From the equality √2 = a/b it follows that 2 = a2/b2, or a2 = 2 · b2. So the square of a is an even number since it is two times something.
From this we know that a itself is also an even number. Why? Because it can't be odd; if a itself was odd, then a · a would be odd too. Odd number times odd number is always odd. Check it if you don't believe me!
Okay, if a itself is an even number, then a is 2 times some other whole number. In symbols, a = 2k where k is this other number. We don't need to know what k is; it won't matter. Soon comes the contradiction.
If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:
2=(2k)2/b22=4k2/b22*b2=4k2b2=2k2
This means that b2 is even, from which follows again that b itself is even. And that is a contradiction!!!
WHY is that a contradiction? Because we started the whole process assuming that a/b was simplified to lowest terms, and now it turns out that a and b both would be even. We ended at a contradiction; thus our original assumption (that √2 is rational) is not correct. Therefore √2 cannot be rational.
(I copied this from the internet, but hope it helps!)
Answer:
Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero.
We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction. Notice that in order for a/b to be in simplest terms, both of a and b cannot be even. One or both must be odd. Otherwise, we could simplify a/b further.
From the equality √2 = a/b it follows that 2 = a2/b2, or a2 = 2 · b2. So the square of a is an even number since it is two times something.
From this we know that a itself is also an even number. Why? Because it can't be odd; if a itself was odd, then a · a would be odd too. Odd number times odd number is always odd. Check it if you don't believe me!
Okay, if a itself is an even number, then a is 2 times some other whole number. In symbols, a = 2k where k is this other number. We don't need to know what k is; it won't matter. Soon comes the contradiction.
If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:
2 = (2k)2/b2
2 = 4k2/b2
2*b2 = 4k2
b2 = 2k2
This means that b2 is even, from which follows again that b itself is even. And that is a contradiction!!!
WHY is that a contradiction? Because we started the whole process assuming that a/b was simplified to lowest terms, and now it turns out that a and b both would be even. We ended at a contradiction; thus our original assumption (that √2 is rational) is not correct. Therefore √2 cannot be rational.
Chloe bought 8/9 pounds of grapes. She used 1/3 of the grapes in a fruit salad and saved the rest. How many pounds of grapes were in the fruit salad?
Answer:
8/27 lb
Step-by-step explanation:
The salad has 1/3 of 8/9 lb.
1/3 * 8/9 = 8/27
Answer: 8/27 lb
Which of the following is a factor of 3x3-12x2 +X-4 ?
A. X+3
B. X+2
C. X-4
D.X-1
Answer:
B.x+2
Step-by-step explanation:
What is the slope of the line through (0, 5) and (-2, -1)
Answer:
3
Step-by-step explanation:
To find the slope of a line going through two points, (x₁, y₁) and (x₂, y₂), we can use the following formula: [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]. Note that it doesn't really matter which points we call (x₁, y₁) or (x₂, y₂).
Let's call (x₂, y₂) = (0, 5) and (x₁, y₁) = (-2, -1). Now, we can plug in the values for x, y₁, x₂, and y₂ into the formula.
We have:
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{5-(-1)}{0-(-2)} =\frac{5+1}{0+2} =\frac{6}{2} =3[/tex]
Therefore, the slope of the line is 3. Hope this helps!
What is √7/√11 in simplest radical form?
Answer:
[tex]\sqrt{77}[/tex]
Step-by-step explanation:
[tex]\sqrt{7} \sqrt{11}[/tex]
Apply radical rule: [tex]\sqrt{a} \sqrt{b} =\sqrt{a*b}[/tex]
[tex]\sqrt{7}\sqrt{11} =\sqrt{7*11}[/tex]
[tex]=\sqrt{7*11}[/tex]
Multiply the numbers: [tex]7*11=77[/tex]
[tex]=\sqrt{77}[/tex]
Kilo meters using decimal
a) 3550m
b) 10km 75m
c) 33km 6m
Answer:
a) 3.55 k.m
b) 10.75 k.m
c) 33.o6 k.m
Mr. Percuoco is working the fish bowl toss. He used 13.6 gallons of water to fill 40 fish bowls. If he put an equal amount of water in each one, how many gallons of water are in each fish bowl?
Answer:
0.34 gallons of water
Step-by-step explanation:
Mr Percuoco is working the fish bowl toss
He used 13.6 gallons of water to fill 40 fish bowls
Therefore the gallons of water in each fish bowl can be calculated as follows
= 13.6/40
= 0.34
Hence there are 0.34 gallons of water in each fish bowl
You decide to bake a cake for your sister's birthday, but you discover you don't have enough eggs. Before you go to the store, you set up a linear function to model the number of eggs you will have after your purchase, y=12x+2 . What does the represent in this function?
a. the number of eggs you need
b. the number of eggs the recipe calls for
c. the number of eggs you have at home
d. the number of eggs you will buy
Answer:
I think it will c because I have some eggs at home
Just need A and B, thanks
Hello! my name is unamorrameca, but but I wanted to fit in English so I got ameccamorra
I am from Peru and therefore I speak Spanish. from there I participate in brainly.lat and then I started to think that crazy, there are other platforms of different brainly languages so I looked in this language (English) and I found it :)
I hope to get along with everyone since this is something new for me, to be able to help people from Canada, USA
Well, I know that nobody asked me what I'm doing here. I just want to know more about you. said this I say goodbye.
- una nueva aventura chida :,D
Answer:
Hi! Nice to meet you!
Step-by-step explanation:
P.S Can I have brainliest?
-18=7v+9-10v
slove for v.
Answer:
v=9
Step-by-step explanation:
-18 = 7v + 9 - 10v
combine like terms
-18 = -3v + 9
-9 -9
-27 = -3v
divide both sides by -3
9 = v
or
v = 9
Hope this helps!!!
X+y<-1jjjjjjjjjjhhhjjjjjj
Answer:
What's the problem?
Step-by-step explanation:
Makes NO sense
find the slope and the y-intercept of the line.
Answer:
Slope m = -5/4
y-intercept b = 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality Properties
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
[Standard Form] -5x - 4y = -12
Step 2: Rewrite
Add 5x to both sides: -4y = 5x - 12Divide -4 on both sides: y = -5/4x + 3Step 3: Identify
Break apart the function.
Slope m = -5/4
y-intercept b = 3
Use Simplex Method and Maximize 2x+3y =z
Hello!
Solve for x.
2x+3y=z
Step 1: Add -3y to both sides.
2x+3y+−3y=z+−3y
2x=−3y+z
Step 2: Divide both sides by 2.
2x/2=−3y+z/2
Answer:x= −3/2y+1/2zThank you for asking this question!
It would be greatly appreciated if you thanked me and marked me as the brainliest!
Have an amazing day.
If a = 3, find 7 – a
Answer:
4
Step-by-step explanation:
i need help with number 8
Answer:
Option (3)
Step-by-step explanation:
Given inequality is,
-2x + 8 < 12
By subtraction property of Order,
-2x + 8 - 8 < 12 - 8
-2x < 4
B division property of Order,
[tex]\frac{-2x}{(-2)}<\frac{4}{(-2)}[/tex]
x > -2
Since, there is no sign of equal to ( = ) in the given inequality, starting point on a number line will be a hollow point.
And an arrow starting from point x = -2 directing towards positive integers will represent the given inequality.
Option (3) will be the answer.
The length of a rectangle is 3 feet more than twice the width. Find its area if its perimeter is 7 1/3?
Plssss help me fast!!!!!!!!
Answer:
3+2w=l
2(l+w)=7 1/3
2(3+2w+w)= 7 1/3
6+6w= 7 1/3
-6 both sides
6w=1 1/3
/6 both sides
w=2/9
2/9*2=4/9+3=3 4/9
4/9*3 4/9= 1 43/81
1 43/81
in triangle ABC, the measure of angle Aequals 50 degrees. which is true about the measure of angle C?
Answer:
And....what are the options? or are we suppose to know answer that?
Answer:
could you add the options pls
Which Equation Represents a linear Function?!! PLS
Answer:
A because it has both the slope and the y-intercept
Solve the simultaneous equations:
y−2x=12
y+2x=4
x=
and y=
Answer:
y = 8
x = -2
Step-by-step explanation:
(If you are cancelling the y form the equation to find x first then subtract the equation as the signs are the same or else if you are cancelling the x first then add the equations as the signs are different)
y-12x=12 l cancelled the x from the equation to
y+2x=4 find y
+ + +
_____
2y = 16
y= 16/2
y=8
8 in eqn no 1
y-2x=12 replace the y with 8 and find x
8-2x=12
8-12=2x
-4=2x
-4/2=x
-2=x
What type of triangle is this?
A. Right
B. Equilateral
C. Isosceles
D. Scalene
Answer:
It's an Equilateral triangle
Step-by-step explanation:
This is because of the fact that all of its sides are equal
Answer:
Equilateral Triangle
Step-by-step explanation:
All sides are equal (60 degrees) so it is an equilateral triangle
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
4x + 10y = –20
Please help
Answer:
y=−2/5x−2
Step-by-step explanation:
Write in slope-intercept form, y = m x + b .
How can we get System B from System A?
Are they equal?
Answer:
No they aren't equal.....
Elena walked 12 miles. Then she walked 0.25 that distance. How far did she walk altogether? Select all that apply.
PLEASE HELP ASAP!!!!
If y=x+2 changed to y=x-1 how would it change
The teacher does not have to spend all $36. Write an inequality relating 36 and 9 (7 - x) representing this situation. (Copy/paste as needed: ≤ ﹤ ≥ ﹥)
Answer:
9(7-x) < 36Step-by-step explanation:
From the question, we are to relate the amount the teacher spent to the expression 9(7-x).
Since the teacher does not have to spend all the $36, this means that he spent amount less than $36 but not equal to $36. Hence the best inequality sign that relates both expression is a less than sign (<) as shown;
9(7-x) < 36
hence the required inequality is 9(7-x) < 36
It won't let me copy the question but I linked a screenshot of it.
Answer:
I can't see it to answer your question
Alan has forgotten his 4-digit PIN code.
He knows the first digit is 9 and the last digit is larger than 5.
How many different sets of 4 digits could it be?
Answer:
400 setsStep-by-step explanation:
First digit- 1 option (9)Second digit - 10 options (0 to 9)Third digit - 10 options (9 to 9)Fourth digit - 4 options (6, 7, 8, 9)Possible number of sets:
1*10*10*4 = 400Hard moments for me and the bois
Answer:
Angle 4,
Step-by-step explanation:
Partnership with angle 3, it'll make a 90 degree angle.
help!!!!!!!
The functions f(x) and g(x) are shown on the graph.
f(x) = x2
What is g(x)?
Answer:
-x²-2
Step-by-step explanation: