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The Euler's formula relates the vertices, faces and the edges of a polyhedron.

The correct option is (e) [tex]V = 6[/tex]    [tex]E = 10[/tex]    [tex]F = 6[/tex]     [tex]6- 10 + 6 = 2[/tex]

First, we count the number of faces. This is the flat parts of the shape.

The attached shape has 6 flat surfaces.

So:

[tex]F = 6[/tex]

Next, we count the number of edges. This is where two faces meet.

The attached shape has 10 edges;

So:

[tex]E = 10[/tex]

Lastly, we count the number of vertices. This is where two edges meet.

The attached shape has 6 vertices.

So:

[tex]V = 6[/tex]

Using Euler's formula, we have:

[tex]V - E + F = 2[/tex]

Substitute values for V, E and F

[tex]6- 10 + 6 = 2[/tex]

[tex]2 = 2[/tex]

Hence, the polyhedron has 6 vertices, 10 edges and 6 faces

Read more vertices, edges, and faces at:

https://brainly.com/question/23347978

Answer:

- 5i

Step-by-step explanation:

sqrt(-100) / -sqrt(4)

We know that  sqrt(a) / sqrt(b) = sqrt(a/b)

- sqrt(-100/4)

- sqrt(-25)

We know that sqrt(ab) = sqrt(a) sqrt(b)

- sqrt(25) sqrt(-1)

We know sqrt(-1) = i

Taking the principle value of sqrt(25)

- 5i

Answer:

Binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2.

Answer:

B

Step-by-step explanation:

The slope is zero is the answer

Answer:

B

Step-by-step explanation:

Answer:

The bigger angle is 144 degrees and the smaller one is 36 degrees

Answer:

Answer

5.0/5

2

poojamaurya21

Virtuoso

133 answers

14.9K people helped

Answer:

): "x2" was replaced by "x^2". 4 more similar replacement(s).

Step by step solution :

Step 1 :

Step 2 :

Pulling out like terms :

2.1 Pull out like factors :

x6 - x5 + x4 - x3 + x2 - x =

x • (x5 - x4 + x3 - x2 + x - 1)

2.2 Factor x5 - x4 + x3 - x2 + x - 1

Try to factor this 6-term polynomial into (2-term) • (3-term)

Begin by splitting the 6-term into two 3-term polynomials:

-x2 + x - 1 and x5 - x4 + x3

Next simplify each 3-term polynomial by pulling out like terms:

-1 • (x2 - x + 1) and x3 • (x2 - x + 1)

Note that the two simplified polynomials have x2 - x + 1 in common

Now adding the two simplified polynomials we get

(x3 - 1) • (x2 - x + 1)

Answer:

the larger one is 183

Step-by-step explanation:

[tex]x + y = 262 \\ x - y = 104 \\ y = 262 - x \\ x - (262 - x) = 104 \\ x - 262 + x = 104 \\ 2x = 104 + 262 \\ 2x = 366 \\ x = 183 \\ y = 262 - 183 \\ y = 79[/tex]

Answer:

29 feet

Step-by-step explanation:

14 × 3 = 42

100 - 42 = 58

58 ÷ 2 = 29

One of the longer chains is 29 feet long.

Hope this helps.

Answer:

The answers are all bolded below. If you can, please read the explanation so you can pass a test if asked.

Step-by-step explanation:

First, the quadratic equation we are starting with is -x^2 + 10x + 9.5

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For the first part, it's asking for how high it is when it starts, commonly, we use 0 as the start point so if we plug 0 into the quadratic equation, we have 9.5. The height is 9.5 feet at start.

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For the second part I'm assuming it's asking for either a minimum or a maximum and because the equation has a -x^2, that means the parabola has a maximum. You can tell by -x^2 being negative, if it was x^2 (positive) it would have a minimum.  

The maximum is found using the vertex formula(because the vertex is the max or min), -b/2a, where a is -1, b is 10, and c is 9.5 found in the equation because the quadratic is in standard form ax^2 + bx + c. This gives a vertex of 5.

We plug 5 back in the equation to get (5, 34.5).

5 is the x-coordinate so it is 5 feet horizontally and 34.5 feet high

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For the last part it's asking for a root, or when the parabola touches the x axis/the ground.

-x^2 + 10x + 9.5

You would use the quadratic formula but I'm too lazy so I just put it into a calculator.

That gives roots of around x=−0.87367 and x=10.8737.

You can't have a negative root so you're left with x= 10.8737, rounding to the tenth decimal place, 10.9.

I think that's correct, could be wrong, if it is wrong just follow the steps and it should be fine.

Answer:

0.85y

Step-by-step explanation:

Cost of the wrist watch = $y

Present percentage = 100%

Percentage Loss = 15%

Selling price = (Present percentage - Percentage Loss) * Cost of the wrist watch

= (100% - 15%) * y

= 85% * y

= 85/100 * y

= 0.85 * y

= 0.85y

Selling price = 0.85y

9 in 8956 = 900

9 in 95675 = 90000

9 = 9 in 124569

9 in 68795 = 90

90000 = 9 in 2549652.........

hope it helps...

Part (i)

We start with five dots to make the pattern in figure 1.

In figure 2, we add on 1 dot to each arm of the X shape. So that means we've added 4 dots total going from 5 to 5+4 = 9 dots.

In figure 3, there are 9+4 = 13 dots

So the pattern is simply "add 4" to get the next term. Again, this is because we add one dot per arm.

The first three terms of this arithmetic sequence are: 5, 9, 13

Your teacher wants to know what the general nth term is

We start with a = 5 and the common difference is d = 4

T(n) = nth term

T(n) = a + d(n-1)

T(n) = 5 + 4(n-1)

T(n) = 5 + 4n - 4

T(n) = 4n + 1

Let's try it out. Say we want to plug in n = 2

T(n) = 4n + 1

T(2) = 4(2) + 1

T(2) = 8 + 1

T(2) = 9

This works because the second figure indeed has 9 dots. I'll let you confirm the other figures.

============================================================

Part (ii)

Your teacher wants to know how many dots occur when n = 50

T(n) = 4n + 1

T(50) = 4(50)+1

T(50) = 200 + 1

T(50) = 201

Verifying this through drawing dots is going to be a very tedious task, and I don't recommend it unless you really want to. Hopefully the verification process of T(2) = 9, and similar (for small values of n) is enough to convince you that this equation works as intended.

Answer:

Step-by-step explanation:

-(--4,5)= -(4,5)= -4,5

Answer:

13

Step-by-step explanation:

Complementary angles add to 90 degrees

A+ B = 90

26+x  + 38+x = 90

Combine like terms

2x+64=90

2x+64-64 = 90-64

2x = 26

Divide by 2

2x/2 = 26/2

x = 13

Answer:

-60

Step-by-step explanation:

Answer:

68 degrees 90+22=112 180 subtract 112 = 68

Answer:

The correlation coefficient is approximately -0.9949

Step-by-step explanation:

The given data is presented as follows;

[tex]\begin{array}{lcl}x&&y\\-10&&2\\-8&&-3\\-1&&-15\\-4&&-10\\-6&&-6\\-7&&-5\\-5&&-8\\-3&&-13\\-2&&-14\\-9&&-1\end{array}[/tex]

The correlation coefficient, r is given as follows;

[tex]r = \dfrac{\sum(x_i - \overline x) \cdot (y_i - \overline y)}{\sqrt{\sum (x_i- \overline x)^2\times \sum (y_i- \overline y)^2 } }[/tex]

From MS Excel, we have;

∑([tex]x_i - \overline x[/tex])·([tex]y_i - \overline y[/tex]) = -155.5

∑([tex]x_i - \overline x[/tex])² = 82.5

∑([tex]y_i - \overline y[/tex])² = 296.1

Therefore, r = -155.5/(√(82.5 × 296.1)) ≈ -0.9949

The correlation coefficient, r ≈ -0.9949

Answer:

y(5y +2) -3a²

Step-by-step explanation:

that is the solution above

Answer:

abc is a triangle so ,

a is ( 9,6 )

b is ( 9,3 )

and c is ( 3,3 )

Answer:

F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

Step-by-step explanation:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have;

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5

The correct option is therefore, F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

Answer:

A. F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).

Step-by-step explanation:

Answer:

Step-by-step explanation:11/2x(8-4)=22

Answer:

Step-by-step explanation:

The angle bisector of a triangle divides the opposite side in 2 segments that are proportional to the other 2 sides of the triangle. Namely:

[tex]\frac{15}{18}=\frac{w}{30}[/tex] and cross multiply.

18w = 450 so

w = 25

Answer:

sorry I don't know

sorry I Don't know

Answer:

22/7, 23/7, 24/7, 25/7, 26/7, and 27/7.

Step-by-step explanation:

Answer:

A = 79°

Step-by-step explanation:

CosA = adjacent ÷ hypoteneous

A = Cos^-1(6÷32)

A. =. 79.19°

A= 79°

Answer:

-86

Step-by-step explanation:

-102-

98 so the answer is -86

Answer:

x=80

Step-by-step explanation:

The base angles have to be the same since the sides are both 14

The sum of the angles of triangle is 180

50+50+x = 180

100+x= 180

x = 180-100

x= 80

Step-by-step explanation:

3(6+b)+2b+1

18+3b+2b+1

5b+19

Answer:i would say 2 differentt teams where there is more then women than men in the team

Step-by-step explanation:

well how i came to this answer is that the team is limited to only 5 people giving the only team where there is more women over men is this first team would be 4 women and 1 men , second team would be 3 women and 2 men anything lower then 3 make its where the team has more men than women so the only options would be 2 team where either they go with 4 women or 3 women and you can't go with more then 4 because then there would be no men in the team which is what the question asks for please go with 2 teams

if this helps please make me brainlist ?!