An equation is shown: a×b=c. Let c be an irrational number. What can be said about a and b?
Please help
if c is a irrational number that means a or b is also an irrational number or both of them are irrational numbers but they are different then each other
i hope that will help
There are two possible answers:
'a' is irrational and b is rational, OR'a' is rational and b is irrationalYou can only pick one of those two cases. In short, exactly one of the 'a' or b is irrational and the other is rational. Both 'a' and b cannot be rational together, and they both cannot be irrational together.
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Explanation:
For a moment, let's say that 'a' and b are both rational numbers. This means they would be ratios of integers. So,
a = p/q
b = r/s
where p,q,r,s are integers. The denominators q & s cannot be zero.
Multiplying those rational numbers 'a' and b leads to
a*b = (p/q)*(r/s) = (p*r)/(q*s)
We get a result in the form of integer/integer. Recall that multiplying any two integers leads to some other integer. Since (p*r)/(q*s) is a ratio of integers, it is rational and that makes a*b = c to be rational. However, your teacher said that c is irrational which is the opposite of rational.
In short, if both 'a' and b are rational, then a*b = c is rational. This means we know for certain that both 'a' and b cannot be both rational for c to be irrational.
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Next, we'll consider 'a' and b to both be irrational. Is it possible to have a*b = c to be irrational as well? It depends.
If we have the following
a = sqrt(3)
b = sqrt(12)
then,
a*b = sqrt(3)*sqrt(12) = sqrt(3*12) = sqrt(36) = 6
Showing that a*b is rational because 6 = 6/1 is a ratio of integers. This is a bit strange considering how 'a' and b themselves were irrational, but they led to a rational product.
This doesn't always happen since something like
sqrt(3)*sqrt(5) = sqrt(3*5) = sqrt(15)
is irrational. So if both 'a' and b are irrational together, then a*b could be rational or it could be irrational. We would need more information about the values of 'a' and b.
Therefore, we know that we can rule out the case that 'a' and b are irrational together.
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Lastly, we'll consider the case when one of 'a' or b is rational while the other is irrational. The order doesn't matter. So we'll make 'a' to be irrational and b to be rational.
Since b is rational, this means b = p/q for some integers p,q where q is nonzero. The value of 'a' cannot be written as a ratio like this because it is irrational.
Multiplying any nonzero rational number with an irrational one always leads to an irrational result. If a*b was rational, then we could say
a*b = r/s
a*(p/q) = r/s
a = (r/s)*(q/p)
a = (r*q)/(s*p)
Showing that 'a' is rational, but this contradicts the fact we made 'a' to be irrational at the top of this section. Therefore, a*b is always irrational if exactly one of 'a' or b is irrational and the other is rational.
In other words, if,
'a' is rational and b is irrational, or'a' is irrational and b is rationalthen a*b = c is irrational
Persons taking a 30-hour review course to prepare for a standardized excam averago a score of 620 on that exam. Persons taking a 70-hour review course average a score of 809. Find a linear function, S(t), which fits this data, and which
expresses score as a function of time. Use this function to predict an average score for persons taking a 42-hour review course. Do not round until the final answer. Then round to the nearest tenth as needed.
Answer:
S(t) = 4.725t + 478.25
S(t) = 4.725(42)+478.25
S(t) = 676.7
Step-by-step explanation:
In the question, score is a function of time, that means time is the x-axis, while score is the y-axis.
Order the pairs to get:
(30,620) and (70, 809)
With these values, you use the the equation [tex]\frac{x2-x1}{y2-y1}[/tex] to get the slope m.
[tex]\frac{70-30}{809-620} = 4.725[/tex]
Use this equation and input any ordered pair to get the final function.
y-y1 = m(x-x1)
y-620 = 4.725x-141.75
y = 4.725x + 478.25
Replace x with t and y with S(t) to fit the x & y axis of the question.
What is the area of a circle with a radius of 6 inches?
Help asap
We know that,
→ Area of circle = πr²
→ Area of circle = π × (6)²
→ Area of circle = π × 36
→ Area of circle = 36π
Option C is correct.What is the area of a circle with a radius of 6 inches?
Answer:-We know,
Formula of Area of circle is πr²Radius = 6 inches (Given)
So, Area of circle = π(6)² = 36π in²
The area of a circle with a radius of 6 inches is 36π in².
Hence, option (c) 36π in² is correct. [Answer]
[tex] \bf Hope \: it \: helps \: you [/tex] .Need answer with full work
Answer:
Step-by-step explanation:
x^2 - 17x - 60
(x - 20)(x + 3)
x^2 + 3x - 20x - 60
x^2 - 17x - 60
(x + 20) is not one of the factors
using F.O.I.L., it would have been
x^2 + 17x - 60
A researcher collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted speed limit was 25mph. The recorded speed of 20 randomly selected vehicles is given below: 2038243927402837293530313219331834213623 Calculate the sample mean, standard deviation, and the median of the above data. (Round to one decimal place
Answer:
[tex]\bar x =29.7[/tex]
[tex]\sigma = 6.81[/tex]
[tex]Median = 30.5[/tex]
Step-by-step explanation:
Given
[tex]Data:20,38,24,39,27,40,28,37,29,35,30,31,32,19,33,18,34,21,36,23[/tex]
[tex]n = 20[/tex]
Solving (a): The sample mean
This is calculated as:
[tex]\bar x =\frac{\sum x}{n}[/tex]
[tex]\bar x =\frac{20+38+24+39+27+40+28+37+29+35+30+31+32+19+33+18+34+21+36+23}{20}[/tex]
[tex]\bar x =\frac{594}{20}[/tex]
[tex]\bar x =29.7[/tex]
Solving (b): The standard deviation
This is calculated as;
[tex]\sigma = \sqrt{\frac{\sum(x-\bar x)^2}{n}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{928.2}{20}}[/tex]
[tex]\sigma = \sqrt{46.41}[/tex]
[tex]\sigma = 6.81[/tex]
Solving (c): The median
First, sort the data in ascending order
[tex]Sorted:18,19,20,21,23,24,27,28,29,30,31,32,33,34,35,36,37,38,39,40[/tex]
The position of the median is calculated as:
[tex]Median = \frac{n+1}{2}[/tex]
[tex]Median = \frac{20+1}{2}[/tex]
[tex]Median = \frac{21}{2}[/tex]
[tex]Median = 10.5th[/tex]
The 10.5th item represents the mean of the 10th and 11th item.
So, median is:
[tex]Median = \frac{30+31}{2}[/tex]
[tex]Median = \frac{61}{2}[/tex]
[tex]Median = 30.5[/tex]
plzzzzzzzzzzzzzzzzzzzzzzzzz help me this is a grade
Answer:
1.83
Step-by-step explanation:
Answer:
I'm not good with models and modeling but the answer will be 1.83.
If D = {1,3,5}, E={3,4,5}, F={1,5,10}
Find
a) ∪
b) ∩
c) ( ∩ )
d) ( ∪ ) ∩
e) ( ∩ )
Step-by-step explanation:
a)U={1,3,4,5}
b)={1,3,5}
What is the amount of simple interest saved on a savings deposit of $1,500 for 18 months at an interest rate of 6%?
Answer:
$135
Step-by-step explanation:
Given data
Principal= $1,500
Time= 18 months = 1.5 years
Rate= 6%
The formula for simple interest is given as
SI= PRT/100
Substiute
SI= 1500*6*1.5/100
SI= 13500/100
SI= $135
Hence the simple interest after 18months(1.5 years) is $135
Solve: 16 + x = 12 then you can get the brainiest.
its b i took a test .
Find the present worth ofRS.2040 due 4 years hence reckoning interest at 5%p.a.
Answer: 408
Step-by-step explanation:
The present worth of Rs 2040 is due 4 years hence reckoning interest at 5% per annum will be Rs 2448.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Simple interest has a constant principal amount, as opposed to compound interest, which multiplies the interest from the principal of previous years to calculate the interest of the subsequent year.
Given,
Principle amount = Rs 2040
Time period = 4 years
Rate of interest = 5 %
Simple interest = PRT/100
Simple interest = 2040 × 5 × 4/100 = Rs408
Present worth = Principle amount + Interest
Present worth = 2040 + 408
Present worth = Rs 2448.
Hence present worth of the amount of Rs2040 in 4 years will be Rs 2448.
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Solve for x.
Greatly appreciate all efforts :)
Answer:
x = 11
Step-by-step explanation:
ΔLKM is an equilateral because a triangle with all 3 sides that are congruent is an equilateral triangle.
Angles in an equilateral triangle are all 60°.
Thus, ∠L = 60°.
=> 3x + 27 = 60
=> 3x = 33
=> x = 11
[tex]x=11[/tex]
Step-by-step explanation:
Given :-[tex]∠L=(3x+27)°[/tex]
ToFind:-Value of x.
We know that:-[tex]∠L= ∠K= ∠M=(3x+27)°[/tex]
[All sides of triangle are equal]
According to question:-[tex]∠L+ ∠K+ ∠M= 180°[/tex]
[Sum of all of triangle is 180°]
[tex]=>3x+27°+3x+27°+3x+27°=180°[/tex]
[tex]=>9x+81 =180°[/tex]
[tex]=>9x=180°-81[/tex]
[tex]=>9x=99[/tex]
[tex]=>x=\frac{99}{9}[/tex]
[tex]=>x=11[/tex]
The value of x is 11.a new school bought pencils for all of the classrooms. there are 7 pencils in each package, and each box of pencils contains 7 packages. Each classroom gets 4 boxes. How many pencils are there in 3 classrooms?
Answer:
588 pencils
Step-by-step explanation:
3 classroom times 4 boxes
12 boxes in total
12 boxes times 7
84 packages
7 pencils in each package
84 x 7
588 pencils
brainliest?
NEED ANSWER ASAP WILL GIVE BRAINLIEST FOR CORRECT ANSWER
given
[tex]y = - 67.9x + 679[/tex]
Substitute x into equation to find y.
[tex]y = - 67.9(2) + 679 \\ = - 135.8 + 679 \\ = 543.2miles[/tex]
Thao says she can find the answer to 8 x 90 by halving the 8 and doubling the 90 again and again until she gets down to 1 x 720. Is she correct?
Prove your answer.
Answer:
Yes
Step-by-step explanation:
4*180
2*360
1*720
8*90 = 720
Yes, halving the denominator and doubling the numerator gives the same results so she is correct.
What is numerator and denominator?In such a fraction, the value that appears above the horizontal line is referred to as the numerator.
It shows how many parts have been taken out of the whole. The numerical number that comes before the sum of all the factors is the denominator of a fraction.
Let's consider a multiplication a × b
If we do half of a and double of b
Then,
a/2 × 2b = a × b
Again,
(a/2)/2 × 2(2b) = a × b
So it will remain the same.
So similarly 8 x 90 will also remain the same.
Hence "Yes, halving the denominator and doubling the numerator gives the same results so she is correct".
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A circle with a diameter of 10 has its center in the first quadrant. The lines y = -3 and x = -1 are tangent to the circle. Write an equation of the circle.
Answer:
34
Step-by-step explanation:
Answer:
(h,k)=(-1,-3)
radius =10/2=5 unit
equation of the circle
(x-h)² +(y-k)²=r²
(x+1)²+(y+3)²=25 is a required equation..
5. In the morning, Kevin's cat eats 1/2 of a can of cat food. In the afternoon, the cat eats 1/4 of a can of food. In the evening, the cat eats 4/5 of a can of food. Which is the most reasonable estimate for the amount of food the cat eats throughout the day: 1 can, 2 cans, or 3 cans?
In just lazy so thanks people who are helping me
Answer:
2 cans
Step-by-step explanation:
1/2 + 1/4 + 4/5 = 1.55
2 is the best answer since we know the cat eats more than 1 and a half cans so the closest thing would be 2 cans
x + 2 1/2 = 10 what does x equal
Answer:
x = 7 1/2
Step-by-step explanation:
x + 2 1/2 = 10
subtract 2 1/2 from both sides of the equation:
x = 7 1/2
Answer:
x=15/2
Step-by-step explanation:
x+2 1/2=10
x+2×2+1/2=10
x+4+1/2=10
x+5/2=10
x=10-5/2
x=15/2
decimal form: 7.5
Question 12 (5 points)
Which statement represents the transitive property of equality?
OA) If m ZA= mB, then m
B) If x = y, then y = x.
OC) If WX = XY, then XY = WX.
OD) If WX = XY and XY = YZ, then WX = YZ.
Answer:
D) If WX = XY and XY = YZ, then WX = YZ.
Step-by-step explanation:
The transitive property states that if a=b and b=c, then a=c. So, if two different values equal to the same, separate value, then they are also congruent. The answer choice, d, represents this idea because WX and YZ both equal XY and are shown to be equal.
Answer:
OD) If WX = XY and XY = YZ, then WX = YZ.
Step-by-step explanation:I took the test
Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
r = 4 cm
2.5 cm
3 cm
3 cm
[? ]%
Round to the nearest tenth of a percent.
PLEASE
Answer:
38.8%
Step-by-step explanation:
This is a very famous computer solution called the Monte Carlo Method. It's like throwing darts at an enlarged diagram. You will always be inside the circle.
The red triangle has an area = 1/2 h * b
The red triangle has an area = 1/2 * (2.5 + 4) * (3 + 3)
The red triangle area = 1/2 6.5 * 6
The red triangle area = 19.5
The area of the circle = pi * r^2
pi = 3.14
r = 4
The area of the circle = 3.14 * 4^2
The area of the circle = 50.24
% = (19.5/50.25) * 100
% = 38.8%
3
13
1
3
Area
-
in?
6
N
1
1
2
3
2
1
6.
2
3
4
5
6
7
8
Enter
Answer:
IF THERE IS A LINK DON'T CLICK ON IT
Step-by-step explanation:
IT IS A COMPUTER TABLET AND PHONE VIRUS
Jose is going hiking for 5 days. He packed 8 bags of trail mix to eat along the way.
Jose wants to eat all the trail mix without having any left over. He also wants to eat
the same amount every day. Use division to help Jose calculate how much he can
eat every day
Answer:
1.6
Step-by-step explanation:
since it is 5 days and you are splitting the traik mix
divided the amount of trail mix by the day
Answer:
The answer is D
Step-by-step explanation:
What type of angles are <5 and <6?
A. Vertical angles
B. Alternate exterior angles
C. Supplementary angles
D. Alternate interior angles
Answer:
C
Step-by-step explanation:
Supplementary angles because their sum is 180 degrees
NO WEBSITES ALLOWED (especially bitly)
Answer:
top right is an acute angle the top left is an obtuse angle and the bottom right is a right angle and I'm not to sure what the bottom right is
Answer:
Bottom right is a right
Step-by-step explanation:
and since it has no matching sides it would be a Isosceles
SOMEONE HELP PLEASE NEED ANSWER ASAP!!!
Answer:
3
Step-by-step explanation:
=12/4
the common ratio =3
Find the quotient of 10x4 / 5x2.
Plzzzz answer fast..
Answer:
D) LM=12; QP=8
Step-by-step explanation:
12/18=(x-1)/(x+3)
cross multiply
12x+36=18x-18
36+18=18x-12x
54=6x
9=x
LM = x+3 = 9+3 = 12
QP = x-1 = 9-1 = 8
The coordinates of G are
The coordinates of vertex G are (2,0). I did this.
f(x)=
2x
2
−x−15
−4x+12
Answer:
f(x) = -x -3
Step-by-step explanation:
PLS HELP FAST ITS THE LAST DAY TO DO THIS TEST NO LINKSSSS
An electrician charges $40 per hour plus an initial service fee of $75. He charges a customer $195 for 3 hours of work.
When this linear relationship is graphed, which value represents the slope?
A. 3
B. 40
C. 75
D. 195
Answer:
40 because every hour he charges 40 dollas so its 40x+75=y
Step-by-step explanation:
The slope is 40 because every hour he charges 40 dollars so its 40x+75=y
We have given that,
An electrician charges $40 per hour plus an initial service fee of $75. He charges a customer $195 for 3 hours of work.
We have to determine,
When this linear relationship is graphed, which value represents the slope.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as a rising overrun.
The slope is 40 because every hour he charges 40 dollars so its 40x+75=y
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