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Nadya [2.5K]
2 years ago
10

How many sunsets of at least one element does a set of six elements have

Mathematics
1 answer:
Lesechka [4]2 years ago
7 0

Answer:

63

Step-by-step explanation:

Given:

a set of six elements  

The solution would be like this for this specific problem:

number of subsets of n elements = 2^n

(2^6) - 1

= 64 – 1

= 63

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2 years ago
the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle
inna [77]

Answer:

2m

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

A = \frac{1}{2}bh

They give us the area as 6m^2, so let's include it in the equation.

6 = \frac{1}{2}bh

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that h = b-4

So replace h in the equation with b-4.

You will now get:

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Now we can work towards solving. Let's get simplifying.

12 = b(b-4)\\12 = b^2 - 4b\\

bring everything to one side so we can make a quadratic and factor:

0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2

We get that b=6.

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that h = b - 4, so to find h, we just sub in our b value into that.

h = (6) - 4 = 2

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