All categories

3 years ago

If a polyhedron has 5 faces and 7 vertices, then it must have how many edges? Please show step-by-step work

Mathematics

1 answer:

Juli2301 [7.4K]3 years ago

8 0

Answer:

10 edges

Step-by-step explanation:

we know that

The Euler's formula state that: In a polyhedron, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

$V - E + F = 2$

in this problem we have

$V=7\\E=?\\F=5$

substitute the given values

$7 - E + 5 = 2$

solve for E

Combine like terms in the left side

$12 - E = 2$

subtract 12 both sides

$- E = -10$

Multiply by -1 both sides

$E =10$

You might be interested in

Find the 19th term of the arithmetic sequence whose common difference is =d5 and whose first term is =a12.

emmasim [6.3K]

An=a1+d(n-1)
a1=first term
d=common difference
n=which term

common difference is 5 first term is 2
an=5+2(n-1)
19th term is n=19
a19=5+2(19-1)
a19=5+2(18)
a19=5+36
a19=41

19th term is 41

4 0

3 years ago

Simplify the expression:<br> 2+(a +5) =

nekit [7.7K]

Answer:

a+7

Step-by-step explanation:

2 + 5 = 7
7+a or a+7

6 0

3 years ago

Read 2 more answers

CCA has stated in 2017 that 36.5 % of its students are first generation college students.Suppose you sample 15 CCA students and

nignag [31]

Answer:

Step-by-step explanation:

The formula for binomial distribution is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - p) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 36.5% = 36.5/100 = 0.365

q = 1 - p = 1 - 0.365

q = 0.635

n = 15

a) P(x = 0) = 15C0 × 0.365^0 × 0.635^(15 - 0) = 0.0011

P(x = 1) = 15C1 × 0.365^1 × 0.635^(15 - 1) = 0.0095

P(x = 2) = 15C2 × 0.365^2 × 0.635^(15 - 2) = 0.038

P(x = 3) = 15C3 × 0.365^3 × 0.635^(15 - 3) = 0.095

P(x = 4) = 15C4 × 0.365^4 × 0.635^(15 - 4) = 0.16

P(x = 5) = 15C5 × 0.365^5 × 0.635^(15 - 5) = 0.21

k P(X = k)

0 0.0011

1 0.0095

2 0.038

3 0.095

4 0.16

5 0.21

b) mean = np = 15 × 0.365 = 5.475

c) standard deviation = √npq

= √15 × 0.365 × 0.635

= 1.86

d) z = (x - mean)/standard deviation

x = 2

z = (2 - 5.475)/1.86 = - 1.87

6 0

3 years ago

Solve the inequality <br> 10<3x+19

Kamila [148]

Answer:

The answer is ->

x>-3

8 0

3 years ago

choose the equation of the horizontal line that passes through the point (−5, 1). y = −5 x = 1 y = 1 x = −5

crimeas [40]

Horizontal line passing through (-5, 1) is y = 1

8 0

3 years ago