Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The number $y$ is irrational. Which statement about $6 + y$ is true? $\newline$ Choices: $\newline$ (A) $6 + y$ is rational. $\newline$ (B) $6 + y$ is irrational. $\newline$ (C) $6 + y$ can be rational or irrational, depending on the value of $y$ .

View step-by-step help

View step-by-step help

Properties of operations on rational and irrational numbers

Full solution

Q. The number

y

is irrational. Which statement about

6 + y

is true?

\newline

Choices:

\newline

(A)

6 + y

is rational.

\newline

(B)

6 + y

is irrational.

\newline

(C)

6 + y

can be rational or irrational, depending on the value of

y

.

Identify Number $6$ : Identify the nature of the number $6$ . $6$ is a rational number because it can be expressed as a fraction of two integers ( $\frac{6}{1}$ ).
Consider Number $y$ : Consider the nature of the number $y$ . $y$ is given as an irrational number, which means it cannot be expressed as a fraction of two integers.
Analyze Sum: Analyze the sum of a rational and an irrational number. $\newline$ The sum of a rational number and an irrational number is always irrational. This is because if it were rational, then subtracting the rational number from both sides would leave an irrational number equal to a rational number, which is a contradiction.
Apply Rule: Apply this rule to the given numbers. $\newline$ Since $6$ is rational and $y$ is irrational, their sum $6 + y$ must be irrational.

More problems from Properties of operations on rational and irrational numbers

Question

Simplify. Write your answer as a proper or improper fraction in simplest form.

\newline

\frac{\frac{10}{9}}{\frac{1}{10}} = \frac{\square}{\square}

Posted 2 months ago

Question

a

b

be rational numbers, and let

b

be non-zero. Is

\frac{a}{b}

rational or irrational?

\newline

1

\newline

\newline

\newline

(C) It can be either rational or irrational

Posted 4 months ago

Question

a

be a non-zero rational number and

b

be an irrational number. Is

\frac{a}{b}

rational or irrational? Choose

1

\newline

\newline

\newline

(C) It can be either rational or irrational

Posted 4 months ago

Question

What is the slope of

y=6 x+2

Posted 4 months ago

Question

\frac{1}{5}+4 h=\frac{1}{3}

\newline

What is the value of

h

in the equation?

Posted 3 days ago

Question

\frac{2}{7} x+\frac{11}{7} x=\frac{3}{5}

\newline

Given the equation, what is the value of

13 x

Posted 21 days ago

Question

3 x+4(2-y)=5 x

\newline

2-y=6 x

\newline

Consider the given system of equations. If

(x, y)

is the solution to the system, then what is the value of

\frac{x}{y}

Posted 1 month ago

Question

y

-intercept of the graph of

y=3 x+7

Posted 4 months ago

Question

y=x+4

\newline

\frac{y+3}{4}=7 x^{2}-x+1

\newline

(a, b)

is a solution to the system of equations shown and

a>0

, what is the value of

a

Posted 4 months ago

Question

0

0939

Posted 2 months ago