1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
klio [65]
3 years ago
12

A gem cutter cuts a polyhedral crystal from a garnet gemstone. The crystal has 10 fewer vertices than edges and twice as many ed

ges as faces. How many faces, vertices, and edges does the crystal have?
Mathematics
1 answer:
Vikki [24]3 years ago
3 0

Answer:

vertices (V) = 6, faces (F) = 12 and edges (E) = 16

Step-by-step explanation:

A polyhedron is a three-dimensional shape with straight edges and flat faces and sharp corners.The point where the faces of a polyhedron meet each other is known as the edge while the corners of the polyhedron is known as the vertices.

Euler formula gives the relationship between the number of vertices (V), faces (F) and edges (E) of a polyhedron. This formula is given as:

F + V - E = 2.

Given that:

E - V = 10, Therefore E = V + 10

F = 2 × V = 2V

Substituting into the Euler formula:

2V + V - (V + 10) = 2

2V + V - 10 - V = 2

2V = 12

V = 12/2 = 6

Therefore, E = V + 10 = 6 + 10 = 16

F = 2V = 2 × 6 = 12

You might be interested in
Jason leaves Detroit at 2:00 PM and drives at a constant speed west along I-96. He passes Ann Arbor, 40 mi from Detroit, at 2:50
Vladimir [108]

Answer:

d = 48t will represent the distance 'd' traveled in 't' hours.

Step-by-step explanation:

Jason leaves Detroit at 2:00 PM and passes through Ann Arbor at 2:50 PM which is 40 mi distant from Detroit.

Speed during this journey was constant.

Jason traveled 40 mi in 50 minutes or \frac{5}{6} hours from Detroit to Ann Arbor.

By the formula,

Speed = \frac{\text{Distance traveled }}{\text{Time taken to travel this distance}}

Speed = \frac{40}{\frac{5}{6}}

           = 48 mi per hour

If he travels 'd' miles in 't' hours then by the formula of speed,

48 = \frac{d}{t}

d = 48t

7 0
3 years ago
Find the original price of a pair of shoes if the sale price is $20 after a 50% discount.
MrMuchimi
The Original Price is $40

Explanation:
50 1 20
—- = — Which means ——
100 2 40

7 0
3 years ago
A(x+1)(x-1)+b(x-2)(x+1)+(x+1)^2=9x-x-10 What is a+b?
igor_vitrenko [27]

a(x+1)(x-1)+b(x-2)(x+1)+(x+1)^2=9x^2-x-10

(x+1)(a(x-1)+b(x-2)+(x+1))=(x+1)(9x-10)

a(x-1)+b(x-2)+x+1=9x-10

Now this equation is much simpler!

(a+b)x-a-2b+x+1=9x-10

(a+b)x-a-2b=8x-11

(a+b-8)x-a-2b-11=0

a+b-8=(a+2b-11)/x

I can't solve it 3 variables and 1 equations means infinite answers so yea.

4 0
3 years ago
At the rate of $2.00 per square foot the cost of painting the rectangular board with a semicircular top shown in the figure is $
Elenna [48]
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.
<span> 
it consists of a rectangle, dimensions  L = 4ft and W = 3ft = Ar = 4ft x 3ft = 12 ft^2

</span>then, you have one half of the area of the circle that has diameter  R = 3ft - radius will be r = 1.5ft the area of that half will be:

Ac = r^2 \pi/ 2
= (1.5 ft)^2 x 3.14 / 2
= 2.25 ft^2 x 3.4/2 
= 7.065 ft^2/ 2 
= 3.5325ft^2

A = Ar + Ac
A = 12ft^2 + 3.5325ft^2
A = 15.5325ft^2

<span>At the rate of $2 per square foot, the cost will be: 
$ 15.5325*2 = 31.07 </span>
5 0
3 years ago
Read 2 more answers
In 2014, the population of Arizona was approximately 5.23 x 10. if it’s land area
mash [69]
I don’t understand what you’re trying to find! I think it cut off. If you were talking abt the multiplication it makes 52.3
7 0
2 years ago
Other questions:
  • Heeeeeelllllllllllpppppp
    6·1 answer
  • Find all points having an x-coordinate of 4 whose distance from the point (-2,-1) is 10
    7·1 answer
  • 3x+5=19 how do I solve this problem ???
    7·2 answers
  • The midpoint of segment AB is (6, 5). The coordinates of point A are (7, 10). Find the coordinates of point
    5·1 answer
  • The temperature of a city at sunset was -1 overnight,the temperature decreased by 11 what was the lowest temperature overnight i
    12·1 answer
  • Please help its math
    7·2 answers
  • How do you solve equations by substitution​
    15·1 answer
  • PLZ HELP THIS IS MY LAST QUESTION SO PLZ HELP :(
    13·2 answers
  • PLEASE HELP THIS IS DUE TODAY
    14·1 answer
  • You want to buy 4 pens, each costing 27 cents. How many dollar bills should you take to the store? im not in college btw lol
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!