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3 years ago

State if each triangle is acute, obtuse,or right using Pythagorean theorem converse.

Mathematics

1 answer:

shtirl [24]3 years ago

3 0

Answer:

Right triangle

Step-by-step explanation:

Properties for acute, obtuse or right triangle,

1). Given triangle will be a right triangle if,

Hypotenuse² = (Leg 1)² + (Leg 2)²

2). Triangle will be an acute triangle if,

(Largest side)² < (leg 1)² + (leg 2)²

3). Triangle will be an obtuse triangle if,

(Largest side)² > (leg 1)² + (leg 2)²

Now we apply these properties in the given triangle,

(Largest side)² = (√11105)²

= 11105

(leg 1)² = (76)²

= 5776

(leg 2)² = (73)²

= 5329

Since 11105 = 5776 + 5329 (First Property)

11105 = 11105

Therefore, given triangle is a right triangle.

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Choice number one:

$\displaystyle \frac{5}{10}\cdot \frac{4}{9}$ .

Step-by-step explanation:

Let $A$ be the event that the number on the first card is even.
Let $B$ be the event that the number on the second card is even.

The question is asking for the possibility that event $A$ and $B$ happen at the same time. However, whether $A$ occurs or not will influence the probability of $B$ . In other words, $A$ and $B$ are not independent. The probability that both $A$ and $B$ occur needs to be found as the product of

the probability that event $A$ occurs, and
the probability that event $B$ occurs given that event $A$ occurs.

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In case A occurs, there will only be four cards with even numbers out of the nine cards that are still in the bag. The conditional probability of getting a second card with an even number on it, given that the first card is even, will be:

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