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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.

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What do the slope and y-intercept of a real-world linear function represent?
Alecsey [184]

Answer:

Word problems with linear equations (that is, with straight-line models) almost always work this way: the slope is the rate of change, and the y-intercept is the starting value.

Step-by-step explanation:

4 0
3 years ago
Patricia baked some cupcakes for sale. she put half of the cupcakes equally into 6 big boxes and the other half equally into sma
mojhsa [17]

Answer:

The answer is given below

Step-by-step explanation:

a)

Let us assume Patricia baked x number of cakes. She put half of the cupcakes (i.e x/2) equally into 6 big boxes.

6 big boxes contained \frac{x}{2} cakes, therefore 1 big box would contain \frac{x}{2}/6=\frac{x}{12} cakes.

Let us assume she put the other half into 14 small boxes, therefore each small box would contain \frac{x}{2}/14=\frac{x}{28} cakes.

There were 45 cupcakes in 3 big boxes and 8 small boxes altogether. That is:3(\frac{x}{12} )+8(\frac{x}{28})=45\\ 84x+96x=15120\\180x=15120\\x=84

Therefore Patricia baked 84 cup cakes

b)

She sold all the small boxes and collected $189, i.e she sold 14 small box for $189. Each small box = $189/14 = $13.5

6 0
3 years ago
An air conditioning manufacturer produces room air conditioners at plants in Houston, Phoenix, and Memphis. These are sent to re
blsea [12.9K]

Answer:

$16,000

Step-by-step explanation:

For easier understanding and calculation; we created a table for solving this question.

Destination →  Dallas     Atlanta     Denver      Availability

Source

<u>↓                                                                                           </u>

<u>Houston          $ 8         $ 12             $ 13          850          </u>

<u />

<u>Phoenix           $ 10       $ 14             $ 8           800            </u>

<u />

<u>Memphis         $ 11         $ 8             $ 14          350            </u>

<u>Requirement    800       700            250                             </u>

<u />

Minimum Shipping Cost to Dallas is from Houston and they have 850 air conditioners, Dallas need 800, so ship all required 800 air conditioners from Houston itself

Minimum shipping cost of Atlanta is from Memphis and they have 350 air conditioners, but Atlanta need 700, so ship all the 350 air conditioners that Memphis have to Atlanta

Minimum shipping cost to Denver is from Phoenix and they have 800 air conditioners, but Denver need 250, so ship all the required 250 air conditioners to Denver itself.

Destination →  Dallas     Atlanta     Denver      Availability

Source

<u>↓                                                                                           </u>

Houston          $ 8         $ 12             $ 13          850          

<u>                         (800)                                                           </u>

Phoenix           $ 10       $ 14             $ 8           800        

<u>                                                         (250)                             </u>

<u />

Memphis         $ 11         $ 8             $ 14          350            

<u>                                       (350)                                               </u>  

<u>Requirement    800       700            250                             </u>

Still Atlanta need 350 air conditioners more, the second minimum shopping cost to Atlanta is from Houston and they have 50 air conditioners left .

So, ship all the 50 air conditioners that Houston have to Atlanta

Also, sent the remaining 300 air conditioners that Atlanta need from Phoenix

Destination →  Dallas     Atlanta     Denver      Availability

Source

<u>↓                                                                                           </u>

Houston          $ 8         $ 12             $ 13          850          

<u>                         (800)      (50)                                                 </u>

Phoenix           $ 10       $ 14             $ 8           800        

<u>                                      (300)           (250)                             </u>

<u />

Memphis         $ 11         $ 8             $ 14          350            

<u>                                       (350)                                               </u>  

<u>Requirement    800       700            250                             </u>

The total cost of shipping = ($ 8 × 800) +( ( $ 12 × 50)+($ 14 × 300) +( $ 8 × 350) ) + ( $ 8 × 250)

= ( $ 6, 400) + $ ( 600 + 4, 200 + 2, 800 ) + $ 2, 000

= $ 16,000

Therefore, the total cost = $ 16,000

7 0
3 years ago
ALGEBRA 2:
xenn [34]

Step-by-step explanation:

it is 300,000 for a 3 day contract

7 0
2 years ago
PLEASE HELP ASAP!!
Vikentia [17]

Answer:

1) l=15 2) w=10

Step-by-step explanation:

l=w+5, 2l+2w=50

2(w+5)+2w=50

4w+10=50

w=10, l=15

7 0
3 years ago
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