A convex polyhedron has faces that consist of 30 squares, 20 triangles, and 12 pentagons. The polyhedron has 120 edges. How many vertices does it have?

Euler’s formula: V + F = E + 2

a:60
b:92
c:122
d:180
THE ANSWER IS A:60 ON EDGE 2021

Answer:

1.518 radians is the answer.

Step-by-step explanation:

Degree to radian conversion = 1° × [tex]\frac{\pi }{180}[/tex]

87° × [tex]\frac{\pi }{180}[/tex]

1.518 radians

Seems like there is a correction in the first question (RHS is tanx.tany)

(i) For convenience: let tanx = a ; tany = b

Thus, tanx + tany = a + b

Moreover, cotx = 1/tanx = 1/a ; coty = 1/b

Thus,

cotx + coty = 1/a + 1/b = (a + b)/ab

Hence,

=> (tanx + tany)/(cotx + coty)

=> (a + b) / { (a + b)/ab }

=> ab(a + b)/(a + b)

=> ab => tanx.tany , proved.

(ii) For convenience: let sinx = a ; cosx = b

As we know, sin²x + cos²x = 1 => a²+b²=1

=> (a³ + b³)/(a + b)

=> (a + b)(a² + b² - ab) / (a + b)

=> (a² + b² - ab)

=> 1 - ab => 1 - sinx.cosx , proved

(iii): let x/2 = A

=> tan(x/2) + cosx.tan(x/2)

=> tanA + cos2A.tanA

=> tanA [1 + cos2A]

=> tanA (2cos²A) {1+cos2A = 2cos²A}

=> (sinA/cosA) (2cos²A)

=> sinA (2cosA)

=> 2sinAcosA

=> sin2A

=> sin2(x/2)

=> sinx proved

Letting x/2 = A is not mandatory. I did it to decease words*(in a line).

Indentities used:

• sin²A + cos²A = 1

• (a³ + b³) = (a + b)(a² + b² - 1)

• 1 + cosA = 2 cos²(A/2)

• tanA = sinA/cosA.

• 2sinAcosA = sin2A

Answer:

1. C=35m?

2.C=700 or $700

Step-by-step explanation:

1. Total Cost= Rate x Number of Months

2. C=35m

Cost=rate x number of months

C=35(20)

C=700 or Total Cost=$700

Answer:

1. c = 35m

2. c = 35 · 20

20 · 35 = $700

Step-by-step explanation:

Answer:

(-21, -38)

Step-by-step explanation:

Given the simultaneous equation

10x-6y = 18 ... 1

9x+6y=39 ...2

Using the Elimination method

Subtract

10x - 9x = 18 - 39

x = -21

substitute x = -21 into 1;

From 1:

10x-6y = 18

10(-21)-6y = 18

-210 - 6y = 18

-6y = 18+210

-6y = 228

y = 228/-6

y =-38

Hence the solution to the system is (-21, -38)

Answer:

432 is the blank

Step-by-step explanation:

I just did this problem

Answer:

I believe it's C

Step-by-step explanation:

[tex]\\ \sf\longmapsto Area=30x^2-53x+12[/tex]

[tex]\\ \sf\longmapsto Area=30(3)^2-53(3)+12[/tex]

[tex]\\ \sf\longmapsto Area=30(9)-159+12[/tex]

[tex]\\ \sf\longmapsto Area=270-159+12[/tex]

[tex]\\ \sf\longmapsto Area=111+12[/tex]

[tex]\\ \sf\longmapsto Area=123[/tex]

And

[tex]\\ \sf\longmapsto Base=4x-6[/tex]

[tex]\\ \sf\longmapsto Base=4(3)-6[/tex]

[tex]\\ \sf\longmapsto Base=12-6=6[/tex]

Now

[tex]\\ \sf\longmapsto Area=\dfrac{1}{2}bh[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{2}6h=123[/tex]

[tex]\\ \sf\longmapsto 3h=123[/tex]

[tex]\\ \sf\longmapsto h=\dfrac{123}{3}[/tex]

[tex]\\ \sf\longmapsto h=41[/tex]

Answer:

the original volume is lesser than the new volume by 242.47 in³

Step-by-step explanation:

Volume of a cone is;

V = ⅓πr²h

Where;

r is radius

h is height

For the original chamber;

r = 5.7/2 = 2.85 inches

h = 12 inches

Volume of this original chamber is;

V_orig = ⅓ × π × 2.85² × 12

V_orig = 102.02 in³

In the new design, the chamber is scaled by a factor of 1.5.

Thus;

r_new = 2.85 × 1.5 = 4.275 inches

h_new = 12 × 1.5 = 18 inches

V_new = ⅓ × π × 4.275² × 18

V_new = 344.49 inch³

V_new - V_orig = 344.49 - 102.02 =

Thus, the original volume is lesser than the new volume by 242.47 in³

Answer:

C.

Step-by-step explanation:

The median is the middle line of the box. 30 is for Town A and 40 is for Town B. 30 is less than 40

Answer:

15 cm

Step-by-step explanation:

You need to remember 2 theorems about a rhombus.

1.  The diagonals of a rhombus bisect each other

2.  The diagonals of a rhombus are perpendicular to each other

In other words, the diagonals of a rhombus are perpendicular bisectors.

BE = 9 and AE = 12

ΔAEB is a right triangle.  So, the Pythagorean theorem says

[tex]9^{2} + 12^{2} = AB^{2}[/tex]

[tex]AB^{2}[/tex] = 81 + 144

       = 225

AB = [tex]\sqrt{225} = 15[/tex] cm

Answer:

dot plot a visual display in which each piece of data is represented by a dot above a number line.

Step-by-step explanation:

Answer:

5.063 seconds

Step-by-step explanation:

Use a graphing calculator to graph, then use the table functions to solve for 1304

or say

1304= rest of equations and solve for X

Answer:

30 thousands, or 30,000 units.

Step-by-step explanation:

Since the question refers to 10 x 3 thousands, to determine how many thousands are in the answer, the following calculation must be performed:

10 x 3 = 30

So there are 30 thousand in the answer, which is equal to 30,000.

Answer:

thousandths

Step-by-step explanation:

Answer:

Answer:jeans = x = 16.85

shirts = y = 8.95

Step-by-step explanation:

That’s the answer bud

Answer:

ok

Step-by-step explanation:

Answer:

Dont say its a test youll get reported and banned by brainly

Step-by-step explanation: also the answer is:  3/5 x 3/5 = 925 = 0.36

Answer: 1/1

Step-by-step explanation:

1/1 because it = 1 so that means 3/5 x 1/1 is 3/5

Answer:

I.d.k I think 1 :)

Step-by-step explanation:

have a great day

Answer:

1/12

Step-by-step explanation:

0.2252

(Please mark me brainliest! thank you in advance!!)

Answer:

y=-3/4x+3

Step-by-step explanation:

The formula is y=mx+b

m is the slope

b is the y-intercept

If you plug it in, you get y=-3/4x+3

Hope this helps!

Answer:

B. $700

Step-by-step explanation:

The answer is A because.....

Step 1: Find the 7% of 2000.

a.) 7% of 2000 is 140.

b.) Check- So: 140/2000= 0.07 (7%)

Step 2: Multiply 140x5 which equals $700.

Although, I can’t really see the second question‘s options, as the calculations made for the previous question, she paid $140 each year.

I rlly hope this is helpful! If so, please, please, please mark brainliest! Thanks! :)

Answer:

c

Step-by-step explanation:

Answer:

u 2

and stay positive :)

Step-by-step explanation:

Hello! I do not know if you meant to put up a question, but I also hope that you have an amazing day! :)

Answer:

B

Step-by-step explanation:

when simplifying base stays the same we only deal with exponent I think I need help too

Answer:

Cos(π/2 - θ) = A

Step-by-step explanation:

We know that:

Sin(θ) = A

And we want to find the value of Cos(π/2 - θ)

Here we can use the cosine relationship:

Cos(a - b) = Cos(a)*Cos(b) + Sin(A)*Sin(B)

Then:

Cos(π/2 - θ) = Cos(π/2)*Cos(θ ) + Sin(π/2)*Sin(θ)

We know that:

Cos(π/2) = 0

Sin(π/2) = 1

Then:

Cos(π/2 - θ) = Cos(π/2)*Cos(θ ) + Sin(π/2)*Sin(θ) = 0*Cos(θ ) + 1*Sin(θ)

                    = 1*Sin(θ) = A

Cos(π/2 - θ) = A

Answer:

72.37%

Step-by-step explanation:

Calculation for what The sensitivity of the physical examination was

Using this formula

Sensitivity=Positive physical examination cases/Physical examination screening for breast cancer

Let plug in the formula

Sensitivity=5,500 cases / 7600 women

Sensitivity=0.7237*100

Sensitivity=72.37%

Therefore The sensitivity of the physical examination was 72.37%

Answer:

72.37% is the answer for this

Answer:

.4

Step-by-step explanation:

y=2x

y=2(.2)

y=.4

there is your answer