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4 years ago

Which expressions are equivalent to (5⋅x)⋅3 ? Drag and drop the equivalent expressions into the box.

Mathematics

1 answer:

marysya [2.9K]4 years ago

3 0

<h2>Greetings!</h2>

Answer:

3⋅(5⋅x)

5⋅(x⋅3)

15x

Step-by-step explanation:

As the values are inside the brackets, it does not matter what side the (x3) is on, so 3⋅(5⋅x) is equivalent.

Multiplying the contents of the brackets in the third one (x * 3) by 5 gives the same value as 3 * (x * 5) so 5⋅(x⋅3) is also equivalent.

On multiplying the brackets out:

5 * x = 5x

5x * 3 = 15x

So 15x is also equivalent.

<h2>Hope this helps!</h2>

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Nadia says the hypotenuse of the right triangle has a length of 73 because the Pythagorean theorem states that (28+45)squared eq

Setler79 [48]

Answer: Her solution is incorrect. The hypotenuse is 53 units

Step-by-step explanation: The error occurred when she quoted the Pythagorean theorem. She added up both sides and squared them and made the answer equal to the square of the hypotenuse. She was supposed to have squared them first, before adding up.

The Pythagorean (or Pythagoras) theorem states that the sum of the squares of two sides of a right angled triangle equals the square of the hypotenuse of the triangle. That is, in triangle ABC, if the hypotenuse is given as line AC, the Pythagoras theorem states that

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse and AB and BC are the other two sides.

In Nadia’s solution, if the hypotenuse is given as 73, and the other two sides are 28 and 45, then the Pythagorean theorem properly expressed would be as follows;

73^2 = 28^2 + 45^2

5329 = 784 + 2025

5329 ≠ 2809

As we have determined, writing out the expression as

73^2 = (28 + 45)^2 is very incorrect as this is not the Pythagorean theorem and of course, the triangle cannot have 73 as its hypotenuse as we have determined by properly writing out the Pythagorean theorem.

The correct solution is as follows;

AC^2 = AB^2 + BC^2

AC^2 = 28^2 + 45^2

AC^2 = 784 + 2025

AC^2 = 2809

Add the square root sign to both sides of the equation

AC = 53

Therefore, the hypotenuse is 53 units

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3 years ago

Read 2 more answers

Can someone please explain how to solve this problem(31)

pogonyaev

Answer:

(-1.92, 1.08)

Step-by-step explanation:

The <em>incenter</em> is the center of the largest circle that can be inscribed in the triangle. That circle is called the <em>incircle</em>. The incenter is at the point of intersection of the angle bisectors. For a right triangle, the <em>inradius</em> (the radius of the incircle), is found from a simple formula:

r = (a + b - c)/2 . . . . . where c is the hypotenuse, and a and b are the legs

In your triangle, the inradius is ...

r = (5 + 3 -√(5² +3²))/2 = 4 -√8.5 ≈ 1.08452

Among other things, this means the coordinates of the incenter are about (1.08, 1.08) from the right angle vertex, so are about ...

incenter ≈ (-1.92, 1.08)

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