Which number produces a rational number when added to 1/4?

The answer is option B : 0.44

Step-by-step explanation:

When you add fractions, the answer is always rational.

A rational number is in the form of , where .

We also know ,

Rational number + irrational number = irrational number

Now is an irrational number and when we will add it to , it will produce irrational number.

Similarly, and 1.4142135.. will also produce irrational numbers.

So, we have been left with 0.44, which is the answer.

0.44 can be written as or or

When we add to any of the fraction, it will always produce a fraction or rational number.

= which is a rational number.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

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

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions