there are 4, 6, and 7 points on three lines. How many triangles is it possible to create with given points as vertices?

Answers

Answer 1

4 triangles can be created with 3 points on a line.

20 triangles can be created with 6 points on a line.

30 triangles can be created with 7 points on a line.

Combination has to do with selection.

Note that a triangle has 3 vertices. If there are 4 points on a line, the number of triangles it is possible to create is derived using the combination formula shown as:

[tex]nC_r=\frac{n!}{(n-r)!r!}[/tex]

[tex]4C_3 = \frac{4!}{(4-3)!3!}\\4C_3 =\frac{4\times3!}{3!}\\4C_3=4triangles[/tex]

This means that 4 triangles can be created with 3 points on a line.

For a line with 6 points:

[tex]6C_3 = \frac{6\times 5\times 4\times 3!}{(6-3)!3!}\\6C_3 =\frac{6\times5\times 4\times3!}{3!3!}\\4C_3=20triangles[/tex]

This shows that 20 triangles can be created with 6 points on a line.

For a line with 7 points:

[tex]7C_3 = \frac{7\times 6\times 5\times 4!}{(7-3)!3!}\\4C_3 =\frac{7\times6\times 5\times4!}{4!3!}\\4C_3=30triangles[/tex]

This shows that 30 triangles can be created with 7 points on a line.

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Related Questions

Which of the following is equal to the expression below?
(8 x 320)^1/3
ОА.
835
OB.
30
Ос.
40
OD
1036
Reset

Answers

256/3.hope this helps

please help I domt understand ​

Answers

Answer:should be d

Step-by-step explanation:

Answer:

option 2

Step-by-step explanation:

[tex]D = \dfrac{3}{2}W\\\\w = 80 \ lbs\\\\D =\dfrac{3}{2}*80\\\\=3*40\\\\D = 120 mg[/tex]

Simplify the numerical expression:

(0.05)(-0.25)

A) -0.0125
B) 0.0125
C) -1.25
D) 1.25

Answers

Answer:

A) -0.0125

Step-by-step explanation:

-1/80 (fractional form)

You have 30 chocolate candy but Jayna has 10 more chocolate candy than you and Amy has A what does A equal to ?

Answers

Answer:

40

Step-by-step explanation:

so it is just like a regular equation like 30+10=40 but your just finding what A means so 40 yea

please answer i need help.

Given that AABC ADEF, find the length of side DF Show the equation and ALL algebra used to solve for the length of DE

Answers

Answer:

the length of side DF is 19

Step-by-step explanation:

you first need to find what x=

sides  AB=DF    AC=DE    BC=FE

so we can say that 3x+1=19

3x+1=19

-1        -1

3x=18

÷ by 3

x=6

then DF os 2x+7

so 2(6)+7

12+7=19

The length of a 10-minute video is decreased by 45% when the video is edited. What is the length of the edited video?

Answers

Answer:

The edited video would now be 5 Minutes 50 Seconds

Step-by-step explanation:

10-4.5=5.5

To subtract any percentage from a number, simply multiply that number by the percentage you want to remain. In other words, multiply by 100 percent minus the percentage you want to subtract, in decimal form. To subtract 20 percent, multiply by 80 percent (0.8).

Step-by-step explanation:

its 5.5 mins

here are the methods

1-0.45= 0.55  0.55*10= 5.5

or

its

45/100= 0.45  0.45*10min= 4.5  10mins-4.5mins= 5.5 mins

What is a unit rate $140 for 18 ft.²

Answers

Answer:

$7.78

Step-by-step explanation:

140/18 = 7.78

Find the GCF for the pair of numbers. ​9,4

Answers

The GCF of numbers is the greatest common factor of the numbers.

The numbers are given as: 4 and 9.

Factorize both:

[tex]\mathbf{4 = 1 \times 2 \times 2}[/tex]

[tex]\mathbf{9 = 1 \times 3 \times 3}[/tex]

The common factor between  both is 1.

So, we have:

[tex]\mathbf{GCF = 1 }[/tex]

Hence, the GCF of 4 and 9 is 1

Read more about GCFs at:

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PLEASE HELP

A. identify the vertex


B. Identify the intercept


C. Write the equation of the graph above


D. Fill in the end behavior:


As x , y ____


As x 3, y ____


E. Identify the domain and range:

Answers

We want to identify different things on the given graph.

The solutions are:

A) (3, -1)

B) x = 4

C) x = y^2 + 2y + 4

D) x ⇒ ∞, y ⇒ ∞

   x⇒3, y⇒ -1

A) The first thing we want to identify is the vertex, we could say that a vertex is a point of symmetry. (like the minimum/maximum of a parabola). Here we clearly do not have a point of symmetry, as we only have half of a parabola, but if it was a complete one, the vertex would be at the blue point, in (3, -1)

B) This is the point where the graph intercepts the x-axis, x = 4.

C) we want to write the equation, we start with the general parabola, this time as a function of y:

x = a*y^2 + b*y + c

Remember that the x-itercept is at x = 4. then c = 4.

x = a*y^2 + b*y + 4

The y-value of the vertex is -1, while the general y-value of the vertex is:

y = -b/2a = -1

And evaluating the equation in this value, gives us:

x = a*(-1)^2 + b*-1 + 4 = 3

Then we have two equations:

-b/2a = -1

a + -b + 4 = 3

We can rewrite the first one as:

-b = -2a

b = 2a

Now we can replace this on the other equation:

a - 2a + 4  =3

-a + 4 = 3

-a = 3 - 4 = -1

a = 1

And b = 2a = 2*1 = 2

Then the equation of the parabola is:

x = y^2 + 2y + 4

D) We can see that as x grows, y increases, so we can say that:

x ⇒ ∞, y ⇒ ∞

And for the other limit we can see that as x tends to 3, y tends to -1, then:

x⇒3, y⇒ -1

If you want to learn more, you can read:

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a researcher studied 30 people ages twenty to forty, 30 people ages forty-one to sixty, and 30 people ages sixty-one to eighty. the researcher set up two rooms—one with a faint rose smell, and one with a faint lemon smell. each participant was asked to enter each room and identify the smell in the room. what research method did the researcher use, and what outcome would be found?

Answers

If the researcher set up two rooms—one with a faint rose smell, and one with a faint lemon smell. each participant was asked to enter each room and identify the smell in the room. The research method that the researcher use , and what outcome would be found is: Cross-sectional. The outcome is: As people grow older their sense of smell decrease.

A cross-sectional is a research that is carried out by collecting data from different group of population or by drawing a random sample from a group of population  in which the researcher will then study or observe the data collected  at a particular period of time.

Based on the given information the researcher is making use of Cross-sectional research method as the researcher what to know how people perceive smell based on their age or how age determine people sense of smell.

The outcome that could be found based on the research is that as people age or grow older their sense of smell decrease or begins to decrease, which simply means that younger people have strongest sense of smell than older people.

Inconclusion If the researcher set up two rooms—one with a faint rose smell, and one with a faint lemon smell. each participant was asked to enter each room and identify the smell in the room. The research method that the researcher use , and what outcome would be found is: Cross-sectional. The outcome is: As people grow older their sense of smell decrease.

Learn more about Cross-sectional here:

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Buffalo Bart’s Endless Wings charges $5.60 for sides and a drink, and then $0.40 per chicken wing. The Spicy Chicken charges $10 for sides and a drink, and then $0.20 per chicken wing. About how many chicken wings must be purchased so that the total cost at Buffalo Bart’s Endless Wings and The Spicy Chicken is the same?

Answers

Answer:

22.

Step-by-step explanation:

About 22 chicken wings must be purchased for the total cost at Buffalo Bart’s Endless Wings and The Spicy Chicken to be the same.

Let's represent the number of chicken wings as "x".

The total cost at Buffalo Bart’s Endless Wings would be the sum of the initial cost for sides and a drink ($5.60) and the cost per chicken wing ($0.40 per wing times x):

Total cost at Buffalo Bart’s Endless Wings = $5.60 + $0.40x

The total cost at The Spicy Chicken would be the sum of the initial cost for sides and a drink ($10) and the cost per chicken wing ($0.20 per wing times x):

Total cost at The Spicy Chicken = $10 + $0.20x

To find the number of chicken wings where the total costs are the same, we'll set up an equation:

$5.60 + $0.40x = $10 + $0.20x

Now, solve for "x":

$0.40x - $0.20x = $10 - $5.60

$0.20x = $4.40

Divide both sides by $0.20:

x = $4.40 / $0.20

x = 22

So, about 22 chicken wings must be purchased for the total cost at Buffalo Bart’s Endless Wings and The Spicy Chicken to be the same.

To learn more on Equation click here:

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#SPJ3

find the next two terms of the sequence 1.1 , 2.2 , 3.3, 4.4, ….. A) 4.5, 5.5 B ) 5.6 C) 5.6, 6.7 D) 5.5, 6.6

Answers

Answer:

D)

Step-by-step explanation:

the cost is 15,000.00 and a markup of 90%

help plez :)

Answers

Very good question, well the answer you might be looking for is
Revenue: 28,500 $
Profit: 13,500
From what I calculated

Have a blessed day and God bless.
16,666.66666666667 !

PLEASE HELP ME
the linear functions f(x) and g(x) are represented on the graph where g(x) is a transformation

Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)

Part B: Solve for k in each type of transformation. (4 points)

Part C:
an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Answers

Answer/Step-by-step explanation:

Given :  

The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):

To Find: two types of transformations that can be used to transform f(x) to g(x).

=================================================================

Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)

Solution Part A:

f(x) = x/5  + y/(-10) = 1  

=> 2x  - y  =  10

=================================================================

Part B: Solve for k in each type of transformation. (4 points)

Solution Part B:

g(x) = x/(-3) + y/6  = 1

=> 2x  -  y  = - 6  

=================================================================

an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)

Solution Part C:  

Transformations :

g(x)  = f(x)  +  16

g(x) = f(x + 8)

Which number is different from the others? 100, 300, 400, 900, 81, 25, 3600
15 POINTSSSSSS

Answers

Answer:

81 is the answer

Step-by-step explanation:

:>>>>>>>>

HELP ME PLEASE!! I"M TRYING :(

Answers

Answer:

3/8×4/5

= 3/10

...........

option a

Answer:

3/10

Step-by-step explanation:

HOPE IT HELPS U!!!!

HELP PLEASE
-8b= 2d-2/h
solve for d

Answers

Answer:

[tex]{ \rm{ - 8b = 2d - \frac{2}{h} }} \\ \\ { \rm{ - 8b + \frac{2}{h} = 2d}} \\ \\ { \boxed{ \rm{d = - 4b + \frac{1}{h} }}}[/tex]

M is the midpoint of segment AB.


AM=13x


BM=8x+10


AB=

Answers

13x = 8x + 10
5x = 10
x = 2

AM = 13(2) = 26

Since AM is half of AB,
AB = 26+26 = 52

AB = 52

Given the function f(x)= e^3x, write an expression that represents the derivative of f using the limit shown below.

Answers

Answer:

f'(x)=6x+8

Step-by-step explanation:

please solve the equation and describe what mistake asif did

Answers

Hey
Here it is!!

8x+1=5
8x=4
x= 4/8
x=1/2

Answer:

1/2

Step-by-step explanation:

8×+1=5

8×=5-1

8×=4

×=4/8=1/2

Write -7 / 9 as a rational number 3 different ways.

Answers

I)-7/9=-7×2/9×2=-14/18
(2)-7/9=-21/27
(3)-7/9=-28/36

The quantities x and y are proportional. Find the constant of proportionality (r) in the equation y=rx

Answers

Answer:

y=rx 1/4/5/5/5

Step-by-step explanation:

Answer:

r = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The proportional equation is

y = rx ( divide both sides by x )

[tex]\frac{y}{x}[/tex] = r

Substitute any ordered pair from the table

Using (14, 7 ) , then

r = [tex]\frac{7}{14}[/tex] = [tex]\frac{1}{2}[/tex]

Consider the function F(x)=5x-1. Find the value of x for which the value of the function is equal to 89

Answers

Answer:

Sorry if im late

Step-by-step explanation:

The correct statements are:

The value of f(-10) = 82

The graph of the function is a parabola

The graph contains the point (20,-8)

Answer:

x=18

Step-by-step explanation:

89=5x-1

89+1=5x

90=5x

18=x

What is 10/13 in a decimal rounded to the nearest 100

Answers

Answer:

0.77

Step-by-step explanation:

10/13 as a decimal is 0.769230

0.769230 to the nearest 100 is 0.77

Hope this helps :D

Joie buys lunch at a local café for $8.60. If she leaves a 15% tip, how much does she spend at the café?

Answers

Answer:

$9.89

Step-by-step explanation:

1. Divide 15 from 100, which leaves you with 0.15%.

2. Multiply 8.60 and .15; that will get you 1.29.

3. Finally, add 1.29 to 8.60 to get your answer!  

please help! & please explain your answer!!

Answers

Answer:

9

Step-by-step explanation:

Plan A remains with $450 stable charge and Plan B is:

200 + 30x, with x being the number of physical training sessions

In order Plan B to be cheaper we set an inequality:

200 + 30x < 45030x < 250x < 250/30x = 8.33 < 9

15 examples of real life situations where we apply approximation​

Answers

Answer:

Have a splendiferous day!

Hope this helps!

Step-by-step explanation:

Shopping at the grocery store

Rough calculations of math

Figuring out time it would take to reach a location

Making nearly accurate measurements

Trying to stay within a budget

Solving extremely complicated numbers

Dealing with decimals

For quick calculations in a business

To prepare ahead, e.g an overestimate

and so on.

I already answered this, but I ain't sure ‘bout the answer that I got. So, I need clarifications, can you solve this for me please? ​

Answers

Step-by-step explanation:

35x׳/7 = (35x×⅕)+(35x×1/x)

15x=7x+35

8x=35

x=4.375.

hope this helps you.

Solution:

[tex]35x( \frac{3}{7} = \frac{1}{5} + \frac{1}{x} ) \\ = > 35x \times \frac{3}{7} = > 35x \times \frac{1}{5} + 35x \times \frac{1}{x} \\ = > 5x \times 3 = 7x + 35 \\ = > 15x = 7x + 35 \\ = > 15x - 7x = 35 \\ = > 8x = 35 \\ = > x = \frac{35}{8} \\ = > x = 4.375[/tex]

Answer:

x = 4.375



In comparing two distributions, which attribute would you not compare?

A. Joint frequency

B. Shape

C. Spread

D. Center

Answers

A. Joint frequency, it’s right I checked it myself

Answer:

If joint frequency isn't an option it is Marginal frequency

7,218 round off thousand​

Answers

correct answer: 7,0007,218 rounded to the nearest 1,000 would be 7,000!
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