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3 years ago

Use Euler’s formula to answer question.

Mathematics

1 answer:

NeTakaya3 years ago

8 0

Answer: The correct option is (C) 38.

Step-by-step explanation: Given that a polyhedron has 20 vertices and 20 faces.

We are to find the number of edges of the polyhedron using Euler's formula.

<em><u>Euler's formula :</u></em>

For any polyhedron, the number of vertices and faces together is exactly two more than the number of edges.

Mathematically, V − E + F = 2, where V, E and F represents the number of vertices, number of edges and number of faces of the polyhedron.

For the given polyhedron, we have

number of vertices, V = 20,

number of faces, F = 20

and

number of edges, E = ?

Therefore, from Euler's formula

$V-E+F=2\\\\\Rightarrow 20-E+20=2\\\\\Rightarrow 40-E=2\\\\\Rightarrow E=40-2\\\\\Rightarrow E=38.$ .

Thus, the required number of edges of the given polyhedron is 38.

Option (C) is CORRECT.

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The ratio of the number of volleyball to the number of basketballs in the P.E room is 4:7 .there are 21 basketballs . How many v

densk [106]

Let volleyball be v and let basketball be b.

v : b = 4 : 7, b = 21

v : 21 = 4 : 7

v/21 = 4/7

7*v = 4*21

v = 4*21/7

v = 4*3

v = 12

Volleyballs are 12

Hope this helps.

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3 years ago

Car Wash A theater group is having a carwash fundraiser. The liquid soap costs $31 and is enough to wash 40 cars. Each car is ch

zheka24 [161]

Answer:

A) Independent variable is "c"

Dependent variable is "p"

B) Yes, it's a function

C) p = 7c - 31

D)domain of the function: 0 ≤ c ≤ 40

Range of the function: 0 ≤ p ≤ 249

Step-by-step explanation:

A) c is the total number of cars washed and p is the profit. The profit depends on the total number of cars washed. Hence, profit(p) is the dependent variable while "c" is independent variable

B) Yes it's a function because for each number of cars washed, there is a distinct value of profit made.

C) We are told that the liquid soap costs $31 and is enough to wash 40 cars. Each car is charged 7$.

$31 is cost to wash one car. Thus profit made per car is;

p = 7c - 31

D) The cost of $31 liquid soap is enough to only wash a maximum of 40 cars. This means the domain for the cars is from 0 cars to 40 cars

Thus;

domain of the function is 0 ≤ c ≤ 40

The profit function is given in answer C above as p = 7c - 31.

Now, if 0 cars are washed they will make zero profit but if 40 cars are washed then;

p = 7(40) - 31

p = 280 - 31

p = 249

Range of the function: 0 ≤ p ≤ 249

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3 years ago

Write the equation of the line given an x -intercept of 10 and y -intercept of 5.

Sergeu [11.5K]

Answer:

y = (-1/2)x + 5

Step-by-step explanation:

As we move from the y-intercept (0, 5) to the x-intercept (10,0), x increases by 10 units while y decreases by 5 units. Thus, the slope of this line is

m = rise / run = -5 / 10 = -1/2.

Since we know both the slope and the y-intercept of this line, let's use the slope-intercept form of the equation of a straight line: y = mx + b.

Substituting -1/2 for m and 5 for b, we get:

y = (-1/2)x + 5

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