The product of a rational number and an irrational number is an irrational
number.
The correctly completed proof is presented as follows;
To prove that 4·π is irrational, with the assumption that, 4·π = [tex]\displaystyle \frac{a}{b}[/tex], where b ≠ 0. Which by isolation of π gives π = [tex]\displaystyle \mathbf{ \frac{a}{4 \cdot b}}[/tex].
The right side of the equation is irrational, because the left side of the
equation is irrational, this is a contradiction.
Therefore, the assumption is wrong and the number 4·π is irrational.
Reasons:
The proof is presented as follows;
With the assumption that 4·π is rational, we have;
[tex]\displaystyle 4 \cdot \pi = \mathbf{\frac{a}{b}}[/tex]
Where;
b ≠ 0
Making π the subject of the above formula, by isolating, it, we have;
[tex]\displaystyle \pi = \mathbf{\frac{a}{4 \cdot b}}[/tex]
The right side of the equation is rational, however, the left side of the
equation π is irrational, which results in a contradiction, therefore, the
product 4·π is an irrational number.
Learn more about irrational numbers here:
https://brainly.com/question/1625874
Answer:
irrationalirrationalirrational
(b) Part B
How many solutions does the following the system of equations have?
Answer:
Its C.
Step-by-step explanation
:Took the test
will mark brainleist
Answer:
Figure a) 2
Figure B) 4
Figure c) 5
Step-by-step explanation:
Answer: A: has 1 line B has 2 and 3 has 5
Step-by-step explanation:
Please help!!! what are the 3 solutions of 0
what's 5+5+5+5+5+5? and then times 1 ?
Once the prompt in image is read answer choices are:
A. -0.9
B. -0.4
C. 0.4
D. 0.9
3 3/4 x 2/5 as a fraction
Answer:
13/20
Step-by-step explanation:
The value of 3(3/4) x 2/5 as a fraction is 3/2.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
3(3/4) x 2/5
= 15/4 x 2/5
= 3/2
Thus,
The value is 3/2.
Learn more about fractions here:
https://brainly.com/question/24370499
#SPJ2
Pls help ion know how to this jaunt
Answer: a very straight forward b 2 4 and 6 c 9
Step-by-step explanation:
View the lane below and calculate the slope
by using the slope formula
Answer:
slope = 4
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (3, 12) ← 2 points on the line
m = [tex]\frac{12-0}{3-0}[/tex] = [tex]\frac{12}{3}[/tex] = 4
Answer:
The slope of this line is 4.
Step-by-step explanation:
Pick any 2 points on the graph you want, just make sure they land perfectly on where the line meets the grid. I'll pick (1, 4) and (2, 8) here.
The slope formula is:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
where (x1, y1) and (x2, y2) are the first and second points you picked above. Now, all you need to do is plug those 2 points into the formula and solve.
[tex]m=\frac{8-4}{2-1}\\\\m=\frac{4}{1}\\\\m=4[/tex]
The slope of this line is 4.
What is the equation of the line that passes through the point (-6, -6) and has a
slope of -1/3?
Answer:
Step-by-step explanation:
Let's find an equation by starting with the slope intercept form:
y = mx + b
where m is the slope and b the y-intercept (the value of y when x=0).
We are given the slope, so:
y = -(1/3)x + b
Now we need to find a value for b that will force the line to go through point (-6,-6). We can determine by putting the point (-6,-6) into the equation and solving for b:
y = -(1/3)x + b
-6 = -(1/3)(-6) + b [Enter the point (-6,-6]
-6 = 2 + b
b = - 8
The equation becomes y = -(1/3)x - 8.
See the attachment.
can anyone help me pls ??
Answer:
A
Step-by-step explanation:
Volume of a cylinder= πr² *height.height=volume÷πr²height=250÷π(which in this case we are using 3.14)3²height=8.85=ARaisins and nuts were mixed in a bowl. If nuts made up five eighths of the mixture, what was the ratio of raisins to nuts
Answer:
3/8
Step-by-step explanation:
hope this helped
9. Find the slope of the line
that passes through the
following pairs of points.
a. (5, 4) and (-4,3)
B. (10, 8) and (9, 13)
Answer:
a]y= 0.11x + 3.44
b]y= 0.11x + 3.44
explanation:
y=mx+b form
(Look at the picture ) Consider the graph of the function f below.
N0.6
(4.6
6
(3.4)
21 8(2.2)
-6
-8
-4
-2
0
2
4
6
8
What is the value of f (4)?
1
A
B
3
С
6
D
14
Answer:
yes u picked C thats the correct answer
Step-by-step explanation:
You have 6 large candy bars you want to split each one into thirds.how many candy bar pieces will you then have
Answer:
18 lol
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
because you are getting a higher number of candy bars you can mutiply 6*3 to get 18
or you can do 3+3+3+3+3+3 or 6+6+6
Graph x≥2.
If you’re confused about the question pls don’t answer it just ask about it in the comment section
Answer:
The first graph is correct.
Step-by-step explanation:
Note that the equation states x ≥ 2. It includes the "equals" sign, so the graph line should include 2. This is indicated by the solid line, as opposed to the 4th graph, which shows it as a dashed line. The dashed line is correct for x>2, but not for x ≥ 2.
PLEASE HELP I NEED TO HAVE THIS DONE IN 30 MINUTES
Answer:
Yes it does. Because it's a linear graph, what Mena's it's a linear relationship, and linear relationships are proportional
WILL GIVE BRAINLIEST HELP ASAP
Step-by-step explanation:
I cannot draw here, but I can show and tell you how to find 2 points of the individual lines that you can then mark on the chart and draw the line through them.
1)
y = 7/2 x - 2
so, the first and easiest point is the y-intercept (where x = 0).
x = 0, therefore, y = -2
so, the first point is (0, -2)
for the second point : what value of x would eliminate the fraction and make this whole integer number calculations ?
well, x = 2 !
so,
y = 7/2 × 2 - 2 = 7 - 2 = 5
and our second point is (2, 5)
2)
y = -6x + 3
the same principles. first x = 0, therefore y = 3
the first point is (0, 3)
for the second point we can choose any integer x, as all the other terms are integer too.
let's pick x = 1
y = -6×1 + 3 = -6 + 3 = -3
so, the second point is (1, -3)
3)
y = -5
this just means that for every possible value of x the resulting y value is -5.
that means it is a horizontal line through y = -5 or (0, -5)
4)
y = 6/5 x + 1
the same principles. x = 0, therefore y = 1
the first point is (0, 1)
for the second point, again, what x eliminates the fraction and makes all an integer operation ?
well, x = 5.
y = 6/5 × 5 + 1 = 6 + 1 = 7
ok, 7 is off the chart, so let's use x = -5 instead.
y = 6/5 × -5 + 1 = -6 + 1 = -5
so, the second point on the chart is (-5, -5)
if we changed the –0.14 to a 2 in the equation, what would happen to the graph?
If -0.14 is changed to 2, the graph would become a positive graph, or it would be steeper, because it has a positive slope
The equation of the graph is given as:
[tex]y = -0.14x + 3[/tex]
The above equation is a linear equation, which is represented as:
[tex]y =mx + c[/tex]
Where m represents the slope of the linear equation.
By comparison, we have:
[tex]m = -0.14[/tex]
i.e. the slope of the equation [tex]y = -0.14x + 3[/tex] is -0.14
When -0.14 is replaced with 2, the equation becomes
[tex]y = 2x + 3[/tex]
And the slope of the new equation [tex]y = 2x + 3[/tex] is
[tex]m =2[/tex]
2 is greater than -0.14, and 2 is positive.
This means that the graph would become a positive graph, or it would be steeper, because it has a positive slope
Read more linear equations at:
https://brainly.com/question/19045223
_ ➗ 9 = 7
Find the missing number
Answer:
Hi the answer is x=63
x/9=7
multiply both sides by 9
(x/9)*(9)=(7)*(9)
therefore 63 is the missing number
**QUESTION**
Which of the statements about the y-axis are true?
**STATEMENTS**
I. The y-axis is a vertical number line that passes through the origin.
II. The y-axis intersects the x-axis at the point (0 , 0).
III. The y-axis is the first coordinate in an ordered pair that describes the vertical distance from the origin.
IV. The y-axis is a horizontal number line that passes through the origin.
**OPTIONS**
I and II
B.
I only
C.
IV only
D.
II and IV
Answer:
I.
II.
One and two are the correct ones
Step-by-step explanation:
Y goes up and down
X is side to side
so
x comes first in an ordered pair.
(I remember that by saying, "You need to find the room before you can ride the elevator)
Multiply. Enter your answer as a simplified mixed number. -4(3/14)
Answer:
-53 /14
Step-by-step explanation:
Write as a single fraction in its simplest form.
[tex]\dfrac{4}{3x-5} + \dfrac{x+2}{x-1}\\\\\\=\dfrac{4(x-1) + (x+2)(3x-5)}{(3x-5)(x-1)}\\\\\\=\dfrac{4x-4 + 3x^2 -5x +6x -10}{(3x-5)(x-1)}\\\\\\=\dfrac{3x^2 +5x-14}{(3x-5)(x-1)}[/tex]
These are the coordinates of a
quadrilateral. Determine whether it is
also a trapezoid, parallelogram, or
neither.
J(5,5), K(8,6), L(9,9), M(6,8)
A. trapezoid
B. parallelogram
C. neither
Answer:
parallelogram is the answer
Answer:
Step-by-step explanation:
The quadrilateral is a parallelogram ( more precisely is the rhombus )
can i have some help :
Answer:
b<11=board is shorter then
b>11=more then 11 books
b<12=fewer then 12
b>12=taller then 12
Hope This Helps!!!
how to find the side of a triangle given one side and one angle calculator
Answer:
Check below :)
Step-by-step explanation:
If you are asked to find a side of a triangle using a given side and an angle. You should check if it is a right-angled triangle, if it is then you can use the SOH, CAH, TOA which uses the formulae as shown:
sinΘ= [tex]\frac{opposite}{hypotenuse}[/tex]
cosΘ= [tex]\frac{adjacent}{hypotenuse}[/tex]
tanΘ= [tex]\frac{opposite}{adjacent}[/tex]
(Search them online for detailed explanation about trigonometry on right-angled triangles)
If it is not right-angled triangles, you need to double-check if there is another side given or angle given to use the sine rule or cosine rule
Sine rule: 2 angles and opposite side/ 2 sides and opposite angle
Cosine rule: involves 3 sides and one angle
enter an algebraic expression for the word expression.
2 decreased by n
Answer:
2 - n
Step-by-step explanation:
2 decreased by n means n less than 2.
Answer:
Write each phrase as an algebraic expression. Phrase, Expression. nine increased by a number x, 9 + x. fourteen decreased by a number p, 14
Step-by-step explanation:
2-n Plz mark brainliest if correct
A ratio of a TV's width to its height is 16:9. If its width is 32 inches, what is the length of its diagonal? Give your answer to the nearest tenth of an inch.
Answer:
36.7
Step-by-step explanation:
Records show that Oliver is typically 10–30 minutes late for his shift at work. The distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve.
A uniform density curve is at y = StartFraction 1 Over 20 EndFraction.
Company policy requires employees to be less than 12 minutes late for work. What percentage of the time will Oliver meet company policy?
6.7%
10%
60%
90%
Based on the information given, the percentage of time that'll be required to meet the policy will be 10%.
From the complete information, the probability distribution will be:
= 1/(b - a) = 1/(30 - 10) = 1/20
Since the company policy requires employees to be less than 12 minutes late for work, the percentage of the time that Oliver will meet company policy will be:
= (12 - 10) × 1/20
= 2 × 1/20
= 1/10
= 10%
In conclusion, the correct option is 10%.
Learn more about percentage on:
https://brainly.com/question/24304697
5 |2x + 6| = 25 what is x
Step-by-step explanation:
මාපාංක සුලු කිරිම.
l xl means ± x .
then |2x+6| = ±(2x+6)
for positive no;
5 (2x+6) = 25
10x + 30 = 25
10x = -5
x = -1/2
for negative no;
5(-2x - 6) = 25
-10x - 30 = 25
-10x = 55
x = - 11/2
otherthan that I observed.
5 |2x + 6| means only consider about the positive number. i think it called as amplitude.
then you have to calculate by considering only considering plus value.
How ever in my openion is first method is correct. i have doubt about that. so you have to discuss your teacher dear. to find correct way.
Which of the following groups cannot represent the side lengths of a triangle.
A.49,20,17
B.7,11,16
C.9,13,21
D.30,9,27
Answer:
try B for an answer, hope it helps