Use the following long division.

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

What number is needed to complete the pattern below 66 73 13 21 52 _1020

Dimas [21]

<span>Answer 61 73-66= 7 21-13 = 8 ?? -52= 9 20-10 = 10 ??=61</span>

6 0

3 years ago

At one store, Julia saved $10 with a coupon for 40% off her total purchase. At another store, the $29 she spent on books is

barxatty [35]

Let "a" and "b" represent the values of the first and second purchases, respectively.
0.40*(original price of "a") = $10
(original price of "a") = $10/0.40 = $25.00 . . . . divide by 0.40 and evaluate
a = (original price of "a") - $10 . . . . . . Julia paid the price after the discount
a = $25.00 -10.00 = $15.00

At the other store,
$29 = 0.58b
$29/0.58 = b = $50 . . . . . . . divide by the coefficient of b and evaluate

Then Julia's total spending is
a + b = $15.00 +50.00 = $65.00

Julia spent $65 in all at the two stores.

6 0

3 years ago

In his freshman year, Mario earned a C in algebra, a B in English, an A in science, and a C- in geography. As a sophomore, he ea

Leya [2.2K]

from what I know

A=4

B=3

C=2

and a plus adds 0.33 and a minus minuses 0.33

question wants us to find yearly average or average per 1 year

since these grades span over 2 years, we must divide the total average by 2

averagefresh=sum of fresh grades/4 grades per year

averagesoph=sum of soph grades/4 grades per year

yearlyaverage=(averagefresh+averagesoph)/2

freshman:

(C)+(B)+(A)+(C-)=2+3+4+(2-0.33)=10.67

sophomore:

(B+)+(A-)+(C+)+(B-)=(3+0.33)+(4-0.33)+(2+0.33)+(3-0.33)=12

averagefresh=10.67/4=2.6675

averagesoph=12/4=3

yearlyaverage=(2.6675+3)/2=2.83375

so it's about a $B^{-}$ average

7 0

3 years ago

Bruce has 150$ and saves 20$ each week. Katie has 200$ and saves 10$ each week. After how many weeks will they have the same amo

NNADVOKAT [17]

None because they will have spent it all on lawsuits

4 0

3 years ago