Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The number $y$ is rational. Which statement about $y + 7$ is true? $\newline$ Choices: $\newline$ (A) $y + 7$ is rational. $\newline$ (B) $y + 7$ is irrational. $\newline$ (C) $y + 7$ 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 rational. Which statement about

y + 7

is true?

\newline

Choices:

\newline

(A)

y + 7

is rational.

\newline

(B)

y + 7

is irrational.

\newline

(C)

y + 7

can be rational or irrational, depending on the value of

y

.

Identify Number $7$ : Identify the nature of the number $7$ . $7$ is an integer, and all integers are rational numbers because they can be expressed as a ratio of integers ( $\frac{7}{1}$ in this case).
Combine with $y$ : Combine the rational number $y$ with the rational number $7$ . $\newline$ The sum of two rational numbers is always rational. This is because the sum of two ratios of integers is another ratio of integers, which by definition is a rational number.
Determine Truth: Determine the truth of the given statements based on the previous step. $\newline$ Since $y$ is rational and $7$ is rational, their sum $y + 7$ must also be rational. This means that statement (A) is true, while statements (B) and (C) are false.

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 1 month 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 2 months 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 10 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 26 days 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