You can find counterexamples to disprove this claim. We have positive integers that are perfect square numbers; when we take the square root of those numbers, we get an integer.

For example, the square root of 1 is 1, which is an integer. So if y = 1, then the denominator becomes an integer and thus we get a quotient of two integers (since x is also defined to be an integer), the definition of a rational number.

Example: x = 2, y = 1 ends up with $\frac{2}{\sqrt{1}} = \frac{2}{1}$ which is rational. This goes against the claim that $x/\sqrt{y}$ is always irrational for positive integers x and y.

Any integer y that is a perfect square will work to disprove this claim, e.g. y = 1, y = 4, y= 9, y = 16. So it is not always irrational.

4 0

3 years ago

9.) Write the following mixed number as an improper fraction. 7 3/5

VladimirAG [237]

7 3/5 = 7x5=35 +3 = 38/5

7 0

2 years ago

The product of 25 and the number of apples

GREYUIT [131]

"Product" means multiplication
Number of apples we will use the variable "a"

ANSWER: 25a

6 0

3 years ago

Determine the area of the figure

aliya0001 [1]

The area of the trapezoid is x+11 cm.

Given a trapezoid has one side of (x+6) cm, the other side is 5 cm, and the height is 2 cm.

A two-dimensional quadrilateral consisting of the sum of non-adjacent parallel sides and a suitable non-parallel side is denoted as a trapezoid.

Now we will use the formula to find the area of a trapezoid

Area = 1/2 × (base 1 + base 2) × height

Here base 1 = (x+6) cm, base 2 = 5cm and height = 2cm

Substituting the values into the formula, we get

Area = 1/2 × (x+6+5) × 2

Area = 1/2 × (x+11) × 2

Area = x+11

Thus, the area of the given figure when one side is x+6, the other side is 5 cm and the height is 2 cm is x+11 cm.

Learn more about the area of trapezium from here brainly.com/question/15815316

#SPJ1

8 0

2 years ago