Mathematics, 09.09.2020 18:01 hihihi129473838

Consider the following statements. Select all that are always true. - The sum of a rational number and a rational number is rational.
- The sum of a rational number and an irrational number is irrational.
- The sum of an irrational number and an irrational number is irrational. - The product of a rational number and a rational number is rational.
- The product of a rational number and an irrational number is irrational. - The product of an irrational number and an irrational number is irrational.

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Answer from: kayladgranger

A, B, D and E

Step-by-step explanation:

Given

Options A to F

Required

Determine which is true

Option A:

This is always true;

Take for instance the following rational numbers

$a = \frac{1}{2}$ $b = \frac{1}{3}$

$a + b = \frac{1}{2} + \frac{1}{3}$

$a + b = \frac{3 + 2}{6}$

$a + b = \frac{5}{6}$

This will always result in a rational number

Option B:

This is always true;

Take for instance the following rational number

a = 0.5

And the following irrational number

b = 3.142857

a + b =0.5+ 3.142857

a + b =3.642857

This will always result in an irrational number

Option C:

This is not always true;

1. Take for instance the following irrational numbers

a = 0.33333 b = 3.142857

a + b =0.33333 + 3.142857

a + b =3.476187

2. Take for instance the following irrational numbers

$a = 3 + \sqrt5$ $b = -\sqrt5$

$a + b = 3 + \sqrt5 - \sqrt5$

a + b = 3

From the above examples, this implies that the statement is not always true

This is always true;

Take for instance the following rational numbers

$a = \frac{1}{2}$ $b = \frac{1}{3}$

$a * b = \frac{1}{2} * \frac{1}{3}$

$a * b = \frac{1}{6}$

This will always result in a rational number

This is always true;

Take for instance the following rational number

a = 0.5

And the following irrational number

b = 3.142857

a * b =0.5 * 3.142857

a * b =1.5714285

This will always result in an irrational number

This is not always true;

1. Take for instance the following irrational numbers

a = 0.33333 b = 3.142857

a * b =0.33333 * 3.142857

a * b =1.04760852381

2. Take for instance the following irrational numbers

$a = 3 + \sqrt5$ b = 0

$a * b = (3 + \sqrt5) * 0$

a * b = 0

From the above examples, this implies that the statement is not always true

Answer from: Quest

80% of the cookies

step-by-step explanation:

Answer from: Quest

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

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Consider the following statements. Select all that are always true. - The sum of a rational number...

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