Is it a , b, c, or d???

Which of the following statements is false?

kramer

Option D

The sum of two irrational numbers is always rational is false statement

<em><u>Solution:</u></em>

<h3><u>The sum of two rational numbers is always rational</u></h3>

"The sum of two rational numbers is rational."

So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number.

For example:

$\frac{1}{4} + \frac{1}{5} = \frac{9}{20}$

rational number + rational number = rational number

Hence this statement is true

<h3><u>The product of a non zero rational number and an irrational number is always irrational</u></h3>

If you multiply any irrational number by the rational number zero, the result will be zero, which is rational.

Any other situation, however, of a rational times an irrational will be irrational.

A better statement would be: "The product of a non-zero rational number and an irrational number is irrational."

So this statement is correct

<h3><u>The product of two rational numbers is always rational</u></h3>

The product of two rational numbers is always rational.

A number is said to be a rational number if it is of the form p/q,where p and q are integers and q ≠ 0

Any integer is a rational number because it can be written in p/q form.

Hence it is clear that product of two rational numbers is always rational.

So this statement is correct

<h3><u>The sum of two irrational numbers is always rational</u></h3>

"The sum of two irrational numbers is SOMETIMES irrational."

The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational.

Thus this statement is false

5 0

3 years ago

Find the circumference of a circle whose area is 24

zalisa [80]

The answer is: " 17.35 " .

__________________________________

→ The circumference of the circle is: " 17.35 units " .

__________________________________

The area, "A", of a circle:

A = $\pi$ * r² ;

Note: $\pi = 3.14$ .

The area of the circumference, "C", of a circle:

C = 2 $\pi$ r .

__________________________________________

Given:

A = 24 ;

Use the formula for the area, "A" of a circle, to find the radius, "r" .

Then, plug the value obtained for "r" into the formula for the circumference, "C" , of a circle:

C = 2 $\pi$ r l

To solve for the circumference, "C", of the circle.

________________

A = $\pi * r^{2}$ ;

24 = 3.14 * r² ;

↔ 3.14 * r² = 24 ;

Divide each side of the equation by "(3.14)" ;

[3.14 * r²] / 3.14 = (24) / (3.14) ;

to get:

→ r² = 7.64331210191 ;

Take the positive square root of each side of the equation;

to isolate "r" on one side of the equation; & to solve for the radius, "r" ;

→ ⁺√(r²) = ⁺√(7.64331210191) ;

to get:

→ r = 2.76281034802 ;

____________________________

Now, plug this "obtained value" for the radius, "r" into the equation for the formula for the circumference, "C" of a circle:

→ C = 2 $\pi$ * r ;

to solve for the circumference, "C", of the circle:

→ C = 2 * (3.14) * (2.76281034802) ;

= (6.28) * (2.76281034802) ;

= 17.3504489856 ;

→ round to: " 17.35 units" .

__________________________________

The answer is: " 17.35 " .

__________________________________

→ The circumference of the circle is: " 17.35 units " .

__________________________________

6 0

4 years ago

To the nearest hundredth, what is the length of line segment AB ?

sladkih [1.3K]

The answer is 5.83
Use the Pythagorean Theorem to calculate the 3rd side length.
a^2+b^2=c^2
3^2+5^2=c^2

8 0

3 years ago

Kyle is stringing a necklace with beads he puts black beads on 5/8 of the string and white beads on 1/4 of the string Kyle think

Alexeev081 [22]

Answer:Kyle’s claim is not reasonable

Step-by-step explanation:

Total length of the string of the necklace that Kyle covered with black beads is 5/8.

Total length of the string of the necklace that Kyle covered with white beads is 1/4.

Total length of the string of the necklace that Kyle covered with black beads and white beads is would be

1/4 + 5/8 = 7/8 = 0.875

Kyle thought that he will cover 6/12 of the string with beads. 6/12 = 0.5

It means that he covered more than 6/12. Kyle's claim was wrong

3 0

3 years ago

How do you create common denominator so you can compare fractions

Fofino [41]

Find a common denominator by multiplying the denominators together. Use that common denominator to create equivalent fractions. Then, compare the numerators to figure out which is bigger

7 0

3 years ago