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Rom4ik [11]
3 years ago
8

In the equilateral triangle XYZ, X is located at (-5, -9) and Z is located at (1, -17). What is the perimeter of Triangle XYZ? a

30 units b 10 units c 25 units d 5 units
Mathematics
1 answer:
mario62 [17]3 years ago
3 0

Answer:

Option a. 30 units

Step-by-step explanation:

we know that

An equilateral triangle has three equal sides

so

XY=YZ=XZ

The perimeter of triangle XYZ is equal to

P=XY+YZ+XZ

P=3XZ

<u><em>Find the distance XZ</em></u>

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have

X is located at (-5, -9) and Z is located at (1, -17)

substitute the values in the formula

XZ=\sqrt{(-17+9)^{2}+(1+5)^{2}}

XZ=\sqrt{(-8)^{2}+(6)^{2}}

XZ=\sqrt{100}

XZ=10\ units

Find the perimeter

P=3(10)=30\ units

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Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what
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<em>The complete exercise with the answer options is as follows:</em>

Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.

Type of Crust Number Sold

Thin crust            364

Thick crust             240

Stuffed crust             176

Pan style            260

Based on this information, of the next 3000 pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.

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692 thick crust pizzas

Step-by-step explanation:

With the data given in the exercise, we must first find the total number of pizzas, then we must find the proportion between the thick crust pizzas and the total number of pizzas, finally we must propose a rule of three to find the new proportion of crust pizzas thick on a total of 3000 pizzas.

Type of Crust Number Sold

Thin crust            364

Thick crust             240

Stuffed crust             176

Pan style            260

total pizzas  : 1040

Now we must calculate for 3000 pizzas how much would be the total of thick crust pizzas.For that we must use the relationship found, that is, in 1040 pizzas there are 240 thick crust pizzas

1040→240

3000→x

x= \frac{3000x240}{1040} = 692

Now we have a new proportion that out of 3000 pizzas there are a total of 692 thick crust pizzas

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