1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ioda
3 years ago
14

Definition: A fraction a/b is reduced if a and b are relatively prime.

Mathematics
1 answer:
Mariulka [41]3 years ago
3 0

Answer:

it is true

Step-by-step explanation:

We can demonstrate this by contradiction.

First choosing a random rational and assuming that exist two ways to represent this rational. Call that rational x, a, b and a', b ' the couples of relatively prime to express x.

Then we have

x=x\\\frac{a}{b}=\frac{a'}{b'}

Isolating a:

a=\frac{a'b}{b'}

a is an integer and a' is a relatively prime with b', for this reason b has to be a factor of b'. Suppose this factorization b'=nb, replacing it:

a=\frac{a'nb'}{b'}=a'n

But now we have that n is a factor of a and is a factor of b, it means that a and b are not relatively prime, that is a contradiction with our premises. The sentence is true.

And referring to the positive denominator. If we want to express a positive rational the denominator and numerator will be both positive and if is a negative one we choose a positive denominator and a negative numerator.

You might be interested in
What divides each median into two sections at a 2:1 ratio? Question 6 options: a) circumcenter b) incenter c) centroid d) orthoc
allochka39001 [22]

Answer:

C. Centroid

Step-by-step explanation:

The circumcenter is the center of a triangle's circumcircle (circumscribed circle over triangle). It can be found as the intersection of the perpendicular bisectors.

The incenter is the center of the incircle (inscribed circle into a triangle) of a triangle. The incenter can be constructed as the intersection of angle bisectors.

Centroid is the point where the three medians of the triangle intersect.

The intersection of the three altitudes of a triangle is called the orthocenter.

Since three medians intersect at point which divides each median into 2:1 ratio, the answer is centroid.

6 0
3 years ago
Read 2 more answers
PLEASE HELP NEED DONE FAST!!!
Natalija [7]

Answer:1/2

Step-by-step explanation:

5 0
3 years ago
If the equation of the line y = 2x - 6 is changed to y = -2x - 6, how is the graph changed?
-Dominant- [34]

Answer:

from sloping up to sloping down ⇒ answer D

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

* Now lets solve the problem

∵ The equation of the line is y = 2x - 6

∵ The equation is changed to y = -2x - 6

- If the both signs of x and the number are changed means the

 equation is multiplied by -1

∴ The line is reflected across the x-axis

- If the sign of x only is changed

∴ The line is reflected across the y-axis

- From the equation 2x changed to -2x, but -6 not changed

∴ The sign of x only changed

∴ The line is reflected across the y-axis

* The graph is reflected across the y-axis

∴ from sloping up to sloping down

4 0
3 years ago
Read 2 more answers
Highschool level trigonometry!!! Need help knowing step by step how to find answer!
Goshia [24]

Answer:

\theta \approx 82.34^\circ

Step-by-step explanation:

Please refer to the attached diagram. (Apologies if the shading or resolution is a bit off.)

So, we want to find θ.

Since we formed a right triangle, we can use right triangle ratios.

We know the measure of the adjacent side to θ and the hypotenuse.

Therefore, we will use the cosine ratio:

\displaystyle \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}

The adjacent side is 2 and the hypotenuse is 15. By substitution:

\displaystyle \cos(\theta)=\frac{2}{15}

Now, we will take the inverse cosine of both sides. So:

\displaystyle \theta=\cos^{-1}\Big(\frac{2}{15}\Big)

Use a calculator. Hence:

\theta \approx 82.34^\circ

The angle between the ground and the ladder is about 82.34°.

5 0
3 years ago
What's the ratio of 75 to 80?
oksano4ka [1.4K]

Answer:

75:80   OR    15:16

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Find the sum to the equation of:
    11·1 answer
  • Vince had c CDs until he won 21 more in a contest. Write an expression that shows how many CDs Vince has now.
    5·1 answer
  • Find the coordinates of the midpoint of a segment with endpoints at (-11,34) and (47,0).​
    6·1 answer
  • Please help me?
    6·2 answers
  • Cylinder A:diameter=7in., height=12 in<br> cylinder B:diameter=12 in.,height=7 in
    6·1 answer
  • LMN is a right triangle.<br><br> A= True<br> B= False
    9·1 answer
  • Write the following equation in slope intercept form:<br> 10x + 2y = 24
    14·1 answer
  • PLSS HELP IF YOU TURLY KNOW THISS :)
    5·2 answers
  • Find the largest prime divisor of $15^6 - 7^6$.
    11·1 answer
  • 9 burgers and 1 doughnut cost $31.30. 3 doughnuts and 6 burgers cost $26.70. Find the cost of 2 burgers.​
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!