Which irrational number can be added to pi to get a sum that is rational?

The answer is:

The explanation for this exercise is shown below:

1. By definition, a rational number can be written as a fraction, whose numerator and denominator are integers. The irrational numbers can't be written as a fraction.

2. is an irrational number, because you can't write it as a fraction. The only way to get a rational number with the sum of and other irrational number shown in the image attached, is that this number added be , because and is a rational number.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9