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
Licemer1 [7]
3 years ago
10

Given two points A and B, there is only one segment that you can name: AB. With three collinear points A, B, and C, there are th

ree different segemnts that you can name: AB, AC, and BC. With five colinear points A, B, C. D, and E, how many different segments can you name?
Mathematics
1 answer:
aksik [14]3 years ago
4 0

Answer: 10

Imagine you have 2 slots or boxes that are empty. They represent the possible choices for the letter you pick. For example, you can place B in slot 1 and D in slot 2. There are 5 choices for slot 1 (A,B,C,D,E) and four choices for slot 2. Why 4? Because after we pick the letter for slot 1, we have one less letter to pick from. We can't reuse that letter.

Now multiply those values 5 and 4 to get 20. There are 20 different ways to pick a pair of letters from a pool of 5 total. However, order does NOT matter because the segment AB is the same as BA. Since order doesn't matter, we are doubly counting when we shouldn't. In other words, our count is two times higher than it should be. Instead of 20 pairs, it's actually 20/2 = 10 pairs. That's why the answer is 10.

The list of 10 segments are: {AB,AC,AD,AE,BC,BD,BE,CD,CE,DE}

Side note: you can use the nCr combination formula with n = 5 and r = 2 to get the same answer.

You might be interested in
A punter kicks a football into the air. The pathway of the football can be represented by the equation h=-16t^2+82t (where t= ti
Phantasy [73]

Answer:64

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
find the values for c and d that make the function differentiable:f(x) = 5x^2 + c if x = or < than 3dx^2 - 3 if x > 3
daser333 [38]

9514 1404 393

Answer:

  c = -3; d = 5

Step-by-step explanation:

The function is differentiable if it is continuous and the derivative is continuous.

This function will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...

  5(3^2) +c = 45 +c

From the right, the limit is ...

  d(3^2) -3 = 9d -3

__

The derivative will be continuous if the limit as x approaches 3 from either side is the same. From the left, the limit is ...

  f'(x) = 10x

  = 10(3) = 30

From the right, the limit is ...

  f'(x) = 2dx

  = 2d(3) = 6d

__

This gives us a pair of simultaneous equations in 'c' and 'd':

  45 +c = 9d -3

  6d = 30

The latter tells us d = 5. Then the former tells us ...

  45 +c = 9(5) -3   ⇒   c = -3

The function is differentiable if c = -3 and d = 5.

_____

<em>Additional comment</em>

With these values, the function becomes ...

  f(x)=\begin{cases}5x^2-3&\text{if }x\le 3\\5x^2-3&\text{if }x>3\end{cases}

4 0
2 years ago
9. What is the volume of the given prism? Round the answer to the nearest tenth of a centimeter.
LiRa [457]

Answer:

The answer is 541.8 cm³

Step-by-step explanation:

you just have to multiply the measures of each side:

(8.8)(4.7)(13.1) = 541.8

8 0
3 years ago
All numbers that can be expressed as
aev [14]
Fractions? i dont really know
7 0
3 years ago
A=20<br> B=10<br> C=23<br> D=29.2
11111nata11111 [884]
It’s 20 inches I think
3 0
2 years ago
Other questions:
  • Question 9 (3 points)
    8·2 answers
  • Find m2ABC.<br>(2x)=(5x+5)<br><br>OPTIONS<br><br>25<br>60<br>50<br>130<br>​
    10·1 answer
  • Alex lives 3 miles from school. Ricardo lives 18 miles from school. Ricardo lives how many times further from school than Alex?
    7·1 answer
  • -4-(3+6²)÷13-1²•(-12)=
    8·1 answer
  • Find the area of the following shape. Show all work
    12·1 answer
  • Who to tell if the question is rational or irrational
    6·1 answer
  • Plz help me with this <br> 1/3×3
    7·1 answer
  • I need help finding <br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B3%7D%5E%7B9%7D%20%7D%7B%20%7B3%7D%5E%7B%20-%205%7D%
    12·1 answer
  • Help <br> what are the intersepts?
    11·1 answer
  • 6 x 2 1/5 estimated please hurry
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!