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ahrayia [7]
3 years ago
5

The sum of a rational number and an even integer is rational. A) Always True B) Sometimes True C) Usually True D) Never True

Mathematics
1 answer:
SOVA2 [1]3 years ago
6 0
I think that the sum will always be a rational number
let's prove that


<span>any rational number can be represented as a/b where a and b are integers and b≠0

</span>and an integer is the counting numbers plus their negatives and 0
so like -4,-3,-2,-1,0,1,2,3,4....

<span>so, 2 rational numbers can be represented as

</span>a/b and c/d (where a,b,c,d are all integers and b≠0 and d≠0)

their sum is
a/b+c/d=
ad/bd+bc/bd=
(ad+bc)/bd

1. the numerator and denominator will be integers
2. that the denominator does not equal 0

alright
1.
we started with that they are all integers
ab+bc=?
if we multiply any 2 integers, we get an integer
<span>like 3*4=12 or -3*4=-12 or -3*-4=12, etc.
</span>even 0*4=0, that's an integer
the sum of any 2 integers is an integer
like 4+3=7, 3+(-4)=-1, 3+0=3, etc.
so we have established that the numerator is an integer

now the denominator
that is just a product of 2 integers so it is an integer


<span>2. we originally defined that b≠0 and d≠0 so we're good

</span>therefore, the sum of any 2 rational numbers will always be a rational number <span>is the correct answer.</span>
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For a segment of a radio show a disc jockey can play 10 records. If there are 12 records to select from in how many ways can the
sveta [45]

Answer:

<h2>66 different ways </h2>

Step-by-step explanation:

This is a combination question. Combination has to do with selection. For example if r objects are to be selected from n pool of oblects, this can be done in nCr number of ways.

nCr = n!/(n-r)r!

According to the question, if a radio show can only play 10 records out of 12 records available, this can be done in 12C10 number of ways.

12C10 = 12!/(12-10)!10!

= 12!/2!10!

= 12*11*10!/2*10!

= 12*11/2

= 6*11

= 66 different ways

7 0
3 years ago
The graph of a linear equation contains the points (3,11) and (-2,1) . Which point also lies on the graph.
Ainat [17]
The answer for this is b
6 0
3 years ago
A plumber charges a flat fee of $76 to visit a home and examine a clogged drain. The plumber charges an additional $24 per hour
prisoha [69]

Answer:

(a) 12 hours

(b) $220

Step-by-step explanation:

(a) First we plug in $364 for C

C=76+24h

364=76+24h

Subtract 76 from both sides

24h=288

Divide both sides by 24

h=12

She spent 12 hours fixing the drain

(b) First we plug 6 hours in for h

C=76+24(6)

Multiply it out

C=76+144

Add

C=220

It costs $220 for fixing a drain that takes 6 hours

5 0
2 years ago
REPOST*
xeze [42]

#1

  • -6-3-5

Hence inequality will be

\\ \sf\longmapsto -6\leqslant 5

#2.

  • 3<5

But we need inequality

\\ \sf\longmapsto 3\leqslant 5

#3

The inequality given by

\\ \sf\longmapsto -6\leqslant 3\leqslant 5

7 0
2 years ago
Read 2 more answers
Giving brainliest and max rating.
Yanka [14]

Given:

The cost of each carnival ticket is $5.

To find:

The equation, table of values and graph for the given problem.

Solution:

Let x be the number of tickets and y be the total money spent on tickets.

Cost of one ticket = $5

Cost of x tickets = $5x

So, total cost is

y=5x

The required equation is y=5x.

At x=1,

y=5(1)

y=5

At x=2,

y=5(2)

y=10

At x=3,

y=5(3)

y=15

The required table of values is

x       y

1        5

2      10

3      15

So, the required table of values is table A.

From the above table, it is clear that the graph passes through the point (1,5), (2,10) and (3,15). The graph B passes through these points.

So, the required graph is graph B.

Since the required answers are y=5x, table A, graph B, therefore the correct option is B.

8 0
3 years ago
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