In order to figure what type of triangle this is out, we need to start by plotting the given points. That will help us visualize the triangle better and see if our conclusions make sense. (See attached picture).

Once we got the triangle, the strategy to follow is to use the distance between two points formula to see what the measurement of each side of the triangle is. This will help us determine if 2, 3 or none of the sides of the tirangle are the same.

The distance formula is the following:

$distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

so now we can find the desired distances, let's start with the distance between P and Q:

$|PQ|=\sqrt{(-4-0)^{2}+(9-8)^{2}}$

which yields:

$|PQ|=\sqrt{17}$

next, let's find the distance between P and R:

$|PR|=\sqrt{(-4-(-3))^{2}+(9-5)^{2}}$

which yields:

$|PR|=\sqrt{17}$

and finally the distance between Q and R:

$|QR|=\sqrt{(0-(-3))^{2}+(8-5)^{2}}$

which yields:

$|QR|=3\sqrt{2}$

As you may see from the result, only two of the three sides are the same, |PQ| and |PR|, so this will be an Isosceles triangle.

6 0

3 years ago

Annie has $18.00 to spend at the grocery store. She is going to buy bags of nuts that cost $5.70 each and one box of cookies tha

Tcecarenko [31]

Answer: She can buy up to 2 bags of nuts

Step-by-step explanation:

Hi, to answer this question we have to write an inequality:

The product of the number of bags of nuts bought (n) and the price per bag (5.70); plus the price of one box of cookies (4.25) must be less or equal to Annie's money (18).

5.70n +4.25 ≤18

Solving for x:

5.70n ≤18 -4.25

5.70n ≤13.75

n ≤13.75/5.70

n ≤2.41

n ≤2 (rounded)

She can buy up to 2 bags of nuts

8 0

3 years ago

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