HELP NOW 15 POINTS AND BRAINLIEST Show an example where the product of two irrational numbers is a rational number.
Show an example where the product of two irrational numbers is an irrational number.

4+  2 and 2+  2

Step-by-step explanation:

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator and the denominator are whole numbers.  

On the other hand, all numbers that are not rational are considered irrational. An irrational number can be written as a decimal, but not as a fraction.

So, let us take two irrational numbers a=4+  2  and b=2+ 2  and we now calculate a−b as follows:  a−b=(4+  2  )−(2+  2)=4+  2 −2−  2 =2=  1 2

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Therefore, the difference of two irrational numbers a and b is 2 and from the above defination of rational numbers, we get that 2 is a rational number.

Hence, the difference of two irrational numbers 4+  2 and 2+  2  is a rational number.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

answer: 5

step-by-step explanation:

since, the range is the difference between the lowest and highest values of the given sample space.

and, here the sample space = { 3, 1, 0, 4, 1, 4, 2, 3, 0, 5, 0, 1, 1, 2, 0, 4, 1,4, 4 ,2 ,3 ,2 ,0 ,1 ,4 }

here, the highest value of the given sample = 5

and, the lowest value = 0

therefore, the range of the sample space = 5 - 0 = 5