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1 year ago

Using Euler’s formula, how many edges does a polyhedron with 20 faces and 12 vertices have?

Mathematics

1 answer:

astra-53 [7]1 year ago

3 0

Euler's formula for a polyhedron is given by:

$\begin{gathered} F+V=E+2 \\ \text{where,} \\ F=\text{faces} \\ V=\text{vertices} \\ E=\text{edges} \end{gathered}$

Make E, the subject of the formula:

$\begin{gathered} F+V=E+2 \\ E=F+V-2 \end{gathered}$

Put F = 20, V = 12, to obtain E,

$\begin{gathered} E=20+12-2 \\ E=30 \end{gathered}$

Therefore, there are 30 edges

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3.Which of these scatterplots shows no correlation?

Artemon [7]

This is an unanswerable question there are no graphs for us to look at.

But if the points are scattered randomly and you can’t make up if it’s going left to right or right to left then it’s no correlation.

4 0

3 years ago

Read 2 more answers

9/20

Stella [2.4K]

<u>Question:</u>

Find the number of real number solutions for the equation. x^2 + 5x + 7 = 0

<u>Answer:</u>

The number of real solutions for the equation $x^{2}+5 x+7=0$ is zero

<u>Solution:</u>

For a Quadratic Equation of form : $a x^{2}+b x+c=0$ ---- eqn 1

The solution is $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now , the given Quadratic Equation is $x^{2}+5 x+7=0$ ---- eqn 2

On comparing Equation (1) and Equation(2), we get

a = 1 , b = 5 and c = 7

In $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ , $b^2 - 4ac$ is called the discriminant of the quadratic equation

Its value determines the nature of roots

Now, here are the rules with discriminants:

1) D > 0; there are 2 real solutions in the equation

2) D = 0; there is 1 real solution in the equation

3) D < 0; there are no real solutions in the equation

Now let solve for given equation

$D= b^2 - 4ac\\\\D = 5^2 - 4(1)(7)\\\\D = 25 - 28 \\\\D = -3$

Since -3 is less than 0, this means that there are 0 real solutions in this equation.

4 0

3 years ago

11t - 6t = 45 solve the equation and enter the value of t below

Arada [10]

Answer:

$t = 9$

Step-by-step explanation:

$11t - 6t = 45$

$5t = 45$

$t = 9$

<h3>Hope it is helpful....</h3>

8 0

2 years ago

Read 2 more answers

the remains of an ancient ball court include a rectangular playing alley with a perimeter of about 48 M. the length of the alley

Firdavs [7]

Answer:

Length is 20 m and width is 4 m.

Step-by-step explanation:

Given:

Perimeter of the rectangular alley, $P=48\textrm{ m}$

Length is 5 times the width.

Let width be $x$ .

So, as per question,

Length, $l = 5x$

Now, perimeter of rectangle is given as:

$P=2(l+b)$

Plug in 48 for $P$ , $5x$ for $l$ and $x$ for b.

$48=2(5x+x)\\48=2(6x)\\48=12x\\x=\frac{48}{12}=4$

Therefore, width is 4 m.

Length is $5x=5\times 4=20$ m.

8 0

3 years ago

Suppose that, on a 3,000-mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 270 em

allsm [11]

Answer:

The number of empty seats each of these three airlines carried on its flight are as follows:

United Continental = 150 empty seats

American = 50 empty seats

Southwest = 70 empty seats

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question. See the attached pdf for the complete question.

The explanation of the answers is now provided as follows:

Let U, A and W represents number of empty seats of United Continental, American, and Southwest respectively. Therefore, we have:

U + A + W = 270 ………………………. (1)

Since United Continental had three times as many empty seats as American, this implies that:

U = 3A ………………………………… (2)

Substituting U = 3A into equation (1), we have:

3A +A + W = 270

4A + W = 270

W = 270 - 4A ………………………….. (3)

For the cost, we have:

3,000[((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100)] = $114,990

((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = $114,990 / 3,000

((14.90 / 100) * 3A) + (14.60A / 100) + (12.40W / 100) = 38.33

0.447A + 0.146A + 0124W = 38.33

0.593A + 0.124W = 38.33 ………………… (4)

Substituting W = 270 - 4A from equation (3) into (4) and solve for A, we have:

0.593A + 0.124(270 - 4A) = 38.33

0.593A + 33.48 - 0.496A = 38.33

0.593A - 0.496A = 38.33 - 33.48

0.097A = 4.84

A = 4.84 / 0.097

A = 49.8969072164948

Rounding to a whole number, we have:

A = 50

Substituting A = 50 into each of equations (2) and (3), we have:

U = 3 * 50 = 150

W = 270 - (4 * 50) = 70

Therefore, the number of empty seats each of these three airlines carried on its flight are as follows:

United Continental = 150 empty seats

American = 50 empty seats

Southwest = 70 empty seats

Download pdf

6 0

3 years ago