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
Lynna [10]
3 years ago
13

Number 7. Please asap.

Mathematics
2 answers:
love history [14]3 years ago
6 0

7a)

\frac{n(n - 3)}{2} = 665\\n(n - 3) = 665 \cdot 2\\n(n - 3) = 1330\\n^2 - 3n = 1330\\n^2 - 3n - 1330 = 0\\n = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \cdot 1 \cdot (-1330)}}{2 \cdot 1} = \frac{3 \pm \sqrt{9 + 5320}}{2} = \frac{3 \pm \sqrt{5329}}{2} = \frac{3 \pm 73}{2}\\n_1 = \frac{3 + 73}{2} = \frac{76}{2} = 38\\n_2 = \frac{3 - 73}{2} = \frac{-70}{2} = -35

If n is the amount of sides then there's 38 sides in a polygon with 665 diagonals

7b)

We do the same as 7a) but with 406. We get that n_1 = 30.04 and n_2 = -27.04. A polygon cant have 30.04 sides

lidiya [134]3 years ago
4 0

Answer: A. 38 sides

B. When solved, you get -27.04 sides or 30.04 sides. Neither of these are possible because the number of sides cannot be negative or a decimal.

Step-by-step explanation: Part A:

If the polygon has 665 diagonals, set your original n-sided polygon equal to it.

n(n - 3)/2 = 665

Multiply both sides by 2 so it’s not in the denominator.

n(n - 3) = 1330

Distribute n and subtract 1330 from both sides so it is equal to zero.

n² - 3n - 1330 = 0

Factor it:

(n - 38)(n * 35) = 0

Solve for n by setting it equal to zero:

n = 38 & n = -35

The number of sides cannot be negative, therefore, the answer to Part A is 38 sides.

Part B:

Set your original n-sided polygon equal to 406 and solve to prove that a polygon cannot have 406 diagonals.

n(n - 3)/2 = 406

Multiply both sides by 2 so it’s not in the denominator.

n(n - 3) = 812

Distribute n and subtract 812 from both sides so that it is equal to zero.

n² - 3n - 812 = 0

This cannot be factored, so plug it into the Quadratic Formula. Here are the values you need for the Quadratic Formula based on the polynomial above:

a = 1

b = -3

c = -812

When you solve this, you will get:

n = -27.04 and n = 30.04

A polygon cannot have negative sides and it cannot have decimal sides. It has to be a positive integer (positive whole number).

You might be interested in
If the base is 8 in. and the height is 7 in. What is the area?
kap26 [50]

Answer:

The formula of area is Pi×R×R

and then you add all sides and answer of your question is 30cm

8 0
2 years ago
Read 2 more answers
What is the answer ?
eduard

Answer:

926

Step-by-step explanation:

920 - 444 = x - 450

476 = x - 450

x= 476 + 450 = 926

x = 926

7 0
2 years ago
Read 2 more answers
Write an expression that represents the quotient of r and 3
elena-s [515]
Quotient means divide, so the expression would be r/3, I believe

hope it helps
5 0
3 years ago
Which of these is an example of a literal equation?
Marina86 [1]

Answer: ax - by=k

Step-by-step explanation:

8 0
3 years ago
the ratio of dogs to cats is 5:3 ,the ratio of fish to dogs is 6:1 .what is the ratio of cats to fish
e-lub [12.9K]

Answer:

10: 1

Step-by-step explanation:

We have to make the dogs art of the ratio equal first.

5:3>30:18

6:1> 180: 30

After this we have to simplify the ratio.

Cats to fish is 180:18 (divide by 2) 90:9 (then by 3) 30 : 3 (and finally by 3 again) 10 : 1

4 0
2 years ago
Other questions:
  • Triple the sum of 45 and 55
    7·2 answers
  • PLZ ANSWER PLZ PLZ PLZ HELP 1 QUESTION!!!
    8·1 answer
  • Problem Solving
    9·1 answer
  • Expand and simplify (x+5)(x-2)
    7·1 answer
  • HELP ME POR FAVOR PLEASE PLEASEE
    7·1 answer
  • Which of the following is not a function<br>B is not right​
    7·2 answers
  • Joe asked the children in his class which flavours of ice-cream they like.
    14·1 answer
  • In right triangle ABC, mZC=90 , and sin A = 3/5, what is the value of cos B?
    15·1 answer
  • two dice are rolled, given that the total showing on the two dice is 7, find the probability that one of the dice shows the numb
    5·2 answers
  • PLEASE HELP! WILL GIVE BRAINLIEST!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!