is the sum of two rational numbers always rational

Answers

Answer 1

Answer:

in short, Yes they are always rational.

here's why...

E.g. suppose [tex]\frac{c}{d}[/tex] and [tex]\frac{a}{b}[/tex] are fractions, that means that a,b,c,d are all integers, and b and d are not zero. finding the sum the numerator, and denominator would also have to be integers. the denominator of the sum can't be zero since the denominators of the fractions were not zero, and would give [tex]\frac{ad+bc}{bd}[/tex] and since they are bound by addition (sum means addition) they must also be rational since eit would equal a bigger integer than initially had

Step-by-step explanation:


Related Questions

Mateo wants to buy a BMX bike to compete in his town's extreme sports contest. He set up a lemonade and cookie stand to raise the money. Mateo sold lemonade for $1 per cup and cookies for $3 each. He sold 40 cups of lemonade and 20 cookies. How much money did he make?

Answers

Answer:100$

Step-by-step explanation: you multiply 40x1 and 20x3

Select the correct answer.

Why do the hands on the clock form an angle?
OA.
The hands lie in the same circle.
OB.
The hands are two line segments that share the same endpoint.
Oc.
The hands are two line segments that are perpendicular to one another.
OD.
The hands lie in the same plane.

Answers

Answer:

Step-by-step explanation:

The hands are two line segments that share the same endpoint.

While driving to Aunt Pat’s house we filled up our tank of gas. We traveled 2/5 of the way. How much further do we have to travel?

Answers

Answer:

3/5

Step-by-step explanation:

Use the picture below to answer the question. The measure of angle 3 is 50 degrees. What is the measure of angle 6?

Answers

angle 6=50degrees
reason: alternate interior angles

Find the measures of the interior angles of the triangle,

Answers

Answer:

Angle B = 88

Angle C = 44

Step-by-step explanation:

X+48+(X-44)=180

Subtract 48 from both sides

X+48-48+(x-44)=180-48

X+(x-44)=132

2x-44+44=132+44

2x= 176

X=88

Angle A=48

Angle B =88

Angle C=44

(88-44)

88+44+48=180

Answer:

∠A = 48°

∠B = 48°

∠C = 84°

Explanation:

For C, it is parallel to A, so it would be the same sized angle. For context, all angles of a triangle add up to 180°, so you do; ∠A + ∠C and get 96°

Then you do, 180° - 96° to get 84°

So ∠C would be 84°

Given the graph below. What is the axis of symmetry (vertex)of the parabola?

Answers

Answer:

Answer:

safe speed for the larger radius track u= √2 v

Explanation:

The sum of the forces on either side is the same, the only difference is the radius of curvature and speed.

Also given that r_1= smaller radius

r_2= larger radius curve

r_2= 2r_1..............i

let u be the speed of larger radius curve

now, \sum F = \frac{mv^2}{r_1} =\frac{mu^2}{r_2}∑F=

r

1

mv

2

=

r

2

mu

2

................ii

form i and ii we can write

v^2= \frac{1}{2} u^2v

2

=

2

1

u

2

⇒u= √2 v

therefore, safe speed for the larger radius track u= √2 v

CAN SOMEONE HELP ME PLEASE ASAP!?

Answers

Answer:

45/10 =4.5

4.5 x 7 = 31.5

Hight = 31.5

Answer:

B.

Step-by-step explanation:

Since they are equal do.

45 divided by 10

which equals 4.5.

So the image is being reflected by a 4.5 times bigger scale.

So then you do,

7 x 4.5

which is 31.5.

Type the correct answer in the box.
3 units
2 units
2 units
The area of the figure is
square units.
Reset
Next
Plz help

Answers

Answer:

8 units

Step-by-step explanation:

Area of square = 2x3 = 6 units

Area of triangle = (2x2)/2 = 2 units

Total area = 6 +2 = 8 units

Answer:

As previous answer stated, 8 units

Step-by-step explanation:

You multiply one side of the square by another to get 6 units, then, add the units from the triangle

line has equation 3x + y = 15

Find the gradient of the line.

Answers

Answer:

  -3

Step-by-step explanation:

We can add -3x to put the equation into slope-intercept form.

  y = -3x +15

The gradient of the line (slope) is the coefficient of x: -3.

The gradient is -3.

Pleaseeeeee help
And THANK YOU

Answers

[tex] \: \: \: \: \: \: [/tex]

[tex]a.) \: \: \: \: \frac{36}{5} [/tex]

[tex]d.) \: \: \: \: - \frac{ 15}{2} [/tex]

refer to the attachment for explanationhope it helps

Answer:

A= 7 1/5

D=  -7 1/2

Step-by-step explanation:

Hope this helped!

This is in mixed form btw

inproper fraction:

A= 36/5

D: -15/2

The probability of event A is 0. 48, the probability of event A and B is 0. 21, and the probability of events A or B is 0. 89. What is the probability of event B? 0. 09 0. 20 0. 27 0. 62.

Answers

Probabilities are used to determine the chances of an event

The probability of event B is 0.62

The probabilities are given as:

[tex]\mathbf{P(A) = 0.48}[/tex]

[tex]\mathbf{P(A\ and\ B) = 0.21}[/tex]

[tex]\mathbf{P(A\ or\ B) = 0.89}[/tex]

To calculate the probability of event B, we make use of the following formula

[tex]\mathbf{P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)}[/tex]

So, we have:

[tex]\mathbf{0.21 = 0.48 + P(B) - 0.89}[/tex]

Collect like terms

[tex]\mathbf{P(B)= -0.48 +0.21 + 0.89}[/tex]

[tex]\mathbf{P(B)= 0.62}[/tex]

Hence, the probability of event B is 0.62

Read more about probabilities at:

https://brainly.com/question/11234923

A BRANLIST PLEASE HELP MY HEAD HURTS ....MATH

Answers

Answer: I think it might be negative

Step-by-step explanation:

5/9 + n = 2/3

What does n equal?

A. 1/3

B: 1/9

C: 2/9

D: 4/9

Answers

Answer:

n = 1/9

Step-by-step explanation:

5/9 + n = 2/3=> 5/9 + n = 6/9=> n = 1/9

Conclusion:

Therefore, n = 1/9

Hoped this helped.

[tex]GeniusUser[/tex]

5/9 + n = 2/3


What does n equal?


A. 1/3


B: 1/9


C: 2/9


D: 4/9


Answer:

PLS HELP
First answer- (5,0) (10,0)
Second answer- (0,1//20) (0,20)

Answers

X-intercept mean y=0

2/5x+1/10(0)=2

2/5x=2

X= 5

X-intercept = (5,0)

Y-intercept means x= 0

2/5(0)+1/10y=2

1/10y=2

y=20

Y-intercept = (0,20)

Make
q the subject of p=6q +7

Answers

To make q the subject of provided equation p equal to 6q +7, rewrite the equation in terms of q as q=(p+7)/6.

How to write an equation in the subject of a variable?

To write an equation in the subject of a specified variable, isolate this variable at one side of the equation using the mathematical operations.

The expression given in the problem is,

[tex]p=6q +7[/tex]

This equation need to be written as the subject of q. Subtract 7 both side of the equation to do this,

[tex]p+7=6q +7-7\\p+7=6q[/tex]

Divide both side of equation with number 6.

[tex]\dfrac{p+7}{6}=q[/tex]

Rewrite the equation as,

[tex]q=\dfrac{p+7}{6}[/tex]

Thus, to make q the subject of provided equation p equal to 6q +7, rewrite the equation in terms of q as q=(p+7)/6.

Learn more about the unknown variable here;

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pls help .................

Answers

Answer:

Step-by-step explanation:

I'm guessing at this a bit.

The final score will depend on what is par for each hole and/or for the entire course.  The scores for the first four rounds were all negative.  That means Ko required fewer strokes to hit the hole than the number considered "par" for the course.

Let P stand for the Par of the course.  Then the score for each round would be:

P-3

P-4

P-7, and

P-2

The sum:  4P - 16 is her score for the first four rounds.  I have no clue if there are more than 4 rounds, but if there are, the equation would be:

For n rounds:

nP - ∑[tex]x_{n}[/tex]

where ∑[tex]x_{n}[/tex] is the sum of over/under pars for the n rounds.

Simplify the radical expression. Select all that apply. (There are two answers I believe) √−36
a. 6
b. -6i
c. 6i
d. -i√6
please dont send links, i will give you brainliest

Answers

Based on the graphs of f (x) and g(x), in which interval(s) are both functions increasing? Polynomial function f of x, which increases from the left and passes through the point negative 5 comma negative 4 and goes to a local maximum at negative 4 comma 0 and then goes back down through the point negative 3 comma negative 2 to a local minimum at the point negative 2 comma negative 4 and then goes back up through the point negative 1 comma 0 to the right, and a rational function g of x with one piece that increases from the left in quadrant 2 asymptotic to the line y equals 1 passing through the points negative 6 comma 2 and negative 3 comma 5 that is asymptotic to the line x equals negative 2 and then another piece that is asymptotic to the line x equals negative 2 and increases from the left in quadrant 3 passing through the point negative 1 comma negative 3 and 2 comma 0 that is asymptotic to the line y equals 1 (–°, °) (–°, –4) (–°, –4) ∪ (–2, °) (–°, –4) ∪ (2, °)

By showing your working clearly verify if x=19/20is the solution of the equation 2x-3/4=1/3x+5/6
need the answer asap

Answers

[tex]2x - \frac{3}{4} = \frac{1}{3} x + \frac{5}{6} \\ = > 2x - \frac{1}{3} x = \frac{5}{6} + \frac{3}{4} \\ = > \frac{6x - x}{3} = \frac{10 + 9}{12} \\ = > \frac{5x}{3} = \frac{19}{12} \\ = > x = \frac{19}{12} \times \frac{3}{5} \\ = > \frac{19}{20} \\ [/tex]

Therefore,

[tex]x = \frac{19}{20} [/tex]

verified.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Yes or no awnser pls

Answers

Answer:

No the question iant a function

Its very hard so brainly is very helpful

Answers

Answer: What question do you need help with?

Answer:

do u eat cat litter

Step-by-step explanation:

please help asap for brainlist

Answers

Answer:

Both graphs have a y-intercept of (0,1) and y=6^x is steeper

Step-by-step explanation:

Plug in 0 for x to find the y-intercept. THey would both be raised to the 0th power meaning both y's equal 1. So, they both have the y-intercept of (0,1).

y=6^x is steeper becuase when you graph it, you can see it is. Also of course 6 is higher than 3.

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There are 120 people in a school canteen.
Half of the people in the canteen are in year 11 students.
The number of year 11 students in the canteen is three times the number of year 10 students.
The rest of the people in the canteen are year 9 students.
the number of year 9 students : the number of year 10 students = n : 1
Work out the value of n.
You must show how you get your answer.

Answers

2:1

Step-by-step explanation:

List all variables

Total people=120

year 11 students=120/2=60

year 10 students=60/3=20

subtract year 10 and 11 students from the total to get the number of year 9 students

year 9 students=120-60-20

=40

year9:year10

40:20

2:1

Value of variable 'n' as per the given condition number of 9 year students : number of 10 year students = n:1 is equals to 2.

What is variable?

" A variable is defined as the quantity which represents the change in value  as per the given condition in a mathematical problem."

According to the question,

Total number of students in school = 120

As per the conditions given we have,

Number of 11 year students = [tex]\frac{120}{2}[/tex]

                                               = 60 people

Number of 11year students = 3 × ( Number of 10 year students)

Number of 10 year students = [tex]\frac{Number of 11 year students}{3}[/tex]

                                                   = [tex]\frac{60}{3}[/tex]

                                                   = 20 people

Number of (11year + 10year +  9year ) students  = 120  

⇒ 60 + 20 + Number of 9 year students =120                                        

Number of 9 year students = 120 - 80

                                                 = 40 people

Substitute the value in the given condition  to get the value of the variable we get,

Number of 9 year students : Number of 10 year students = n:1

⇒40 : 20 = n: 1

n = 2

Hence, value of variable 'n' as per the given condition number of 9 year students : number of 10 year students = n:1 is equals to 2.

Learn more about variable here

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If f(x) = 14
then what does f(-3) equal?

Answers

Answer:

27 I do believe so sorry if im wrong

Step-by-step explanation:


Anthony received $150 for his birthday this year. This was $10 less than half the amount he received last year.
How much money did Anthony receive for his birthday last year?

Answers

Answer

320

Step-by-step explanation

150 + 10 = 160

160 * 2 because it said than half the amount he received last year = 320!

Use difference tables to determine whether the data represents a linear or quadratic relationship.

Answers

Answer:

Its not linear

Step-by-step explanation: Linear means it travels in a perfect line

plz answer in (x,y). 15 POINTS!!!!!!!!

Answers

9x+3y=3/3
2x-3y=8/3

Add them
11x=11/3
X=11
X=3

Sub x in

What is the slope of a line that is parallel
and perpendicular to each line?

Answers

Answer:

m1.m2 = -1

Step-by-step explanation:

In the case of the parallel line, the slope of the two lines is parallel to each other.

Solve this system of equations using the Substitution Method. Don't forget to write your final answer as a coordinate point. You must show all your work.

3x + y = -2
y = 2x + 3

Answers

Step-by-step explanation:

substitute the value of y

3x+2x+3=-2 (collect like term)

5x=-2-3 (calculate the difference)

5x=-5 (both side over 5)

x=-1

i hop it helps you❤

If 8.4 million baby boomers out of a total 76 million baby
boomers have already retired, what percentage of this
group will retire in the next 20 years? Round to the
nearest whole percent.

Answers

Answer: Undefined: Needs more data

Step-by-step explanation: What is the timespan over which they have retired? Is this a direct relationship?

Evaluate the expression to find out how much she will pay if she drives 100 miles.
250 + 0.80m

Answers

We plug 100 miles into 0.80. 250 + 0.80(100) is 250 + 80. 250 + 80 is 330.
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