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3 years ago

A polyhedron (not regular) has 10 vertices and 5 faces. How many edges does it have?

Mathematics

1 answer:

Levart [38]3 years ago

3 0

Answer:

13 edges

Step-by-step explanation:

Euler's formula for polyhedra states that

F + V - E = 2 ( F is faces, V is vertices and E is edges ) , then

5 + 10 - E = 2

15 - E = 2 ( subtract 2 from both sides )

13 - E = 0 ( add E to both sides )

13 = E

The polyhedron has 13 edges

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Question 1.) Factor completely $12x^{4}+ 6x^{3}+18x^{2}$

Since $6$ divides all the three terms of the equation, so we take $6$ common out from the equation.

i.e., $6(2x^{4}+ 1x^{3}+3x^{2})$

Now, since $x^{2}$ divides all the three terms of the equation, so we take $x^{2}$ common out from the equation.

i.e., $6x^{2}(2x^{2}+ 1x+3)$

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$D = (1)^2 - 4(2)(3)\\ \ \ = 1- 24\\ \ \ = -23$

Since, the discriminant is less than zero. Therefore, the factored form of the given equation : $12x^{4}+ 6x^{3}+18x^{2}$ is : $6x^{2}(2x^{2}+ 1x+3)$

Question 2.) $7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}$

Since $7$ divides all the three terms of the equation, so we take $7$ common out from the equation.

i.e., $7(x^{3}y+ 2x^{2} y^{3} - x^{2}y^{2})$

Now, since $x^{2}y$ divides all the three terms of the equation, so we take $x^{2}y$ common out from the equation.

i.e., $7x^{2}y(x+ 2y^{2} - y)$

Therefore, the factored form of the given equation : $7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}$ is : $7x^{2}y(x+ 2y^{2} - y)$

Question 3.) What is the Greatest Common Factor of $x^{6}$ and $x^{3}$ ?

The Greatest Common Factor of two numbers is the biggest number which divides both the given numbers completely.

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Since, $x^{3}$ divides both the expressions completely and it is the biggest expression which divides both the expressions.

Therefore, $x^{3}$ is the Greatest Common Factor of $x^{6}$ and $x^{3}$

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4 years ago

Read 2 more answers

What's x ? find the indicated side of the right triangle

expeople1 [14]

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Answer: $\textsf{x = 6}$

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Given: $\textsf{The image provided with 2 angles and one side}$

Find: $\textsf{Solve for the unknown side of x}$

Solution: In order to determine the length of x we need to use some trigonometric functions. Using Soh Cah Toa we can see that we can either use 30 degrees or 60 degrees. We will stick to 60 and we can see that the opposite side is 3 and the hypotenuse is x meaning that we need to use sin. Plug in the values and solve for the unknown.

Plug in the values