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3 years ago

Give a counterexample for the statement all square roots are irrational numbers explain your reasoning

2 answers:

7 0

Statement: ALL square roots are irrational numbers.

Irrational is defined as a non-terminating real number.

✓4 = 2

2 is a terminating real number.

Therefore, 2 is rational.

The square root of 4 results in 2.

Therefore the square root of 4 results in a rational number.

Hence not all square roots result in irrational numbers.

user100 [1]3 years ago

3 0

Square root of 16 = 4....that is rational....so this is ur counter example.

The square root of a perfect square will produce a rational number. If u were to find the square root of a number that is not a perfect square, then that would produce an irrational number.

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How many even 4-digit numbers can be formed from the digits 1, 4, 5, 8, and 9 with no repetitions allowed?

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3 years ago

Find the height of the triangle

Marianna [84]

Answer:

The height is 12 cm

Step-by-step explanation:

Hi there!

We are given a triangle with the 3 sides marked as 15, 20, and 25 and we want to find the height of it (marked as x in the problem).

This problem can seem a bit difficult, but let's see if the triangle is a right triangle first off.

One way to figure out if it is a right triangle is to apply the converse of the Pythagorean theorem.

Let's label the sides, where a is the shortest side, b is the second shortest side, and c is the longest side:

a=15

b=20

c=25

Now square a and b, then add the result together. If it's the same as c squared, then the triangle is a right triangle

15²+20²=25²

225+400=625

625=625

So we can safely say that the triangle is a right triangle

This makes the problem way easier, as there are 2 ways to find the area of a right triangle:

The first way is to multiply the legs (the sides that make up the right angle) together, then divide the result by 2

The other way is to multiply the height and the hypotenuse (the side OPPOSITE to the right angle) together, and then divide the result by 2

First, we need to figure out which sides are the legs, and which side is the hypotenuse

By the triangle inequality theorem, the hypotenuse of a right triangle is the longest side, which means that the 25 cm side is the hypotenuse, and that leaves 15 cm and the 20 cm sides as the legs

So let's find the area of the triangle using the legs

A= $\frac{15*20}{2}$ = $\frac{300}{2}$ =150

So the area of the triangle is 150 cm²

However, as mentioned above, we can also find the area of the triangle by multiplying the hypotenuse by the base, then dividing the result by 2

Which means that the area is also:

A= $\frac{25x}{2}$ cm²

As these both equal the area of the triangle, we can set them equal to each other. This is possible via a property known as transitivity (if a=b and b=c, then a=c)

$\frac{25x}{2}=150$

Multiply both sides by 2

25x=300

Divide both sides by 25

x=12 cm

So the height of the triangle is 12 cm

Hope this helps!

4 0

3 years ago

A 26-foot ladder is placed against a house and reaches the 24-foot roof. If you want to find the distance between the base of th

NemiM [27]

Answer:

x = 10 ft

Step-by-step explanation: INCOMPLETE QUESTION (WE DON´T HAVE IMAGENS OF TRIANGLE TO CHOOSE FROM)

A triangle is a three sides poligon, and in fact we have quite a big number of different shapes. All we need is that three differents segments of lines ( AB , AC, BC ) cut each other by pairs, to get a triangle

When a triangle has a right angle, that means when two of the segmets that form the triangle are perpendicular, we have a right triangle.

In our case the wall of the house and the ground form a right angle therefore we are in presence of a right triangle.

In a right triangle the opposite side to the 90⁰ angle is call hypotenuse, and the other two sides legs, there is a very important relation between the sides known as Pytagoras Theorem, in terms of equation that theorem establishes:

c² = a² + b² where c is the hypotenuse and a and b the legs, according to that any question about dimensions could be solve if we know two of the parameter of the triangle, in this particular case the question should be "to find the length of the third side.

The opposite side to the ∠90⁰ is the ladder ( 26 ft ) and the top point in the wall is 24 ft from the ground so we can compute the other leg ( side between the wall and the bottom of the ladder)

(26)² = (24)² + x²

x² = (26)² - (24)² ⇒ x = √ (26)² - (24)² x = √ 676 - 576 ft

x = √100 ft

x = 10 ft

To solve this type of problem

1.-Look for a right triangle

2.-Identify the hypotenuse

3.-Apply Pytagoras theorem

4 0

3 years ago

If a polynomial has four terms, 3x3 + 5x + 6x2 + 10, which factoring method can be considered? perfect-square trinomial differen

sergey [27]

Answer:

Step-by-step explanation:

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3 years ago

Read 2 more answers

Which of the following is the value of the expression 3y + 5(x - 8) when x = 11 and y = -2

Sholpan [36]

Answer:

9 Is the answer.

Step-by-step explanation:

So you have to substitute these values in to the equation and solve.

3(-2) +5(11-8)

-6+5(3)

-6+15

6 0

3 years ago