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

Help plz !!
What are the dimensions of AB?

Answers

Answer: c.2*1

Step-by-step explanation: in the picture

You need to remember two definitions.

First, the dimensions of a matrix are the number of rows by the number of columns. If a matrix has a row and b columns, it's an a*b matrix.

Second, before computing the product of two given matrices, you need to check an important condition.

If a matrix A has i row and j columns. And a matrix B has k row and l columns we can not apply the product AB only if j = k. In other words the numbers of columns of A (j) must be equal to the number of rows of B (k).

If this condition is checked, than the new matrix will be of dimensions : ixl

In our case i = 2, j = 3, k = 3, l = 1

So the dimensions will be 2x1 so the answer is C.

Good luck

m_ABC=M_ABD
what is the reason?

Answers

The reason in this case is :

Answer:

M=m and cis equivalent to d

0.02349 in standard form to 3 significant figure is?​

Answers

Answer:

I believe that would be 0.0235. I hope this helps you! :)

Answer:

0.0235

Step-by-step explanation:

dfrac{2349}{100000}

Round to the required significant figure: 0.0235

maths giving 10 point asap 1 question only​

Answers

N = -5 sorry I only answered the second one
▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄

Solve the following linear equations :

(i) x + 2 = 5x

2 = 5x - x

2 = 4x

x = 4/2

x = 2

(ii) 3(n - 1)/2 = n - 4

3 × (n - 1)/2 = n - 4

3n - 3/2 = n - 4

3n - 3 = 2(n - 4)

3n - 3 = 2 × (n - 4)

3n - 3 = 2n - 8

3n - 2n = -8 + 3

n = -5

▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄

pLsSsS hElP mE. iM dYiNg HeRe

Answers

Answer:

1. True

2. False

3. False

4. True

5. False

Step-by-step explanation:

Answer:

Step-by-step explanation:

1-  False

2- true

3- false

4- true

5-  true

What is the sum of the 15th square number and the 4th square number?

Answers

Answer:

241

Step-by-step explanation:

15th squared number = 225

4th squared number = 16

225 + 16 = 241

y = 6(x – 3)2 + 4
How do I rewrite the quadratic function in standard form

Answers

Answer:

6x^2 -36x + 58

Step-by-step explanation:

expand (x-3)^2 = x^2 -6x +9

6(x-3)^2 +4=6(x^2 -6x +9) +4 =6x^2 -36x + 54 +4 = 6x^2 -36x + 58

Given m||n, find the value of x.
т
Rt
>m
(2X-22)
(5x-8)°
>

Answers

Given angles are supplementary.

[tex]\\ \sf\longmapsto 2x-22+5x-8=180[/tex]

[tex]\\ \sf\longmapsto 7x-30=180[/tex]

[tex]\\ \sf\longmapsto 7x=180+30=210[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{210}{7}[/tex]

[tex]\\ \sf\longmapsto x=30[/tex]

Solve for the variables shown in the steps simplifying the expression below:
2^5·8^4/16=2^5·(2^a)^4/2^4=2^5·2^b/2^4=2^c.

Answers

Answer:

a=3, b=12, c=13

Step-by-step explanation:

Solve.
17. Kevin lives on a city block that has a perimeter of w- 2 miles. Each day he
runs around the block 3 times and then runs to the high school, which is an
additional 2 miles. How many miles does Kevin run in d days?

Answers

Answer: 8 miles a day

Step-by-step explanation:

(02.01)Which translation will change figure ABC to figure A'B'C'?

3 units right and 3 units up

4 units right and 3 units up

4 units right and 4 units up

4 units left and 3 units down

Answers

Answer:

4 units right and 3 units up.

Step-by-step explanation:

Can you translate the measurements to (cups, teaspoons, tablespoons etc.)

Top flour 170g
Baking powder 5g
Sugar 10g
Butter 40g
Maple syrup 30ml
Milk 40ml

Answers

Answer:

Flour: 18.76 Tablespoons

56.28 Teaspoons

1.17 U.S. Cups

Baking Powder: 0.35 Tablespoons

1.04 Teaspoons

0.02 U.S. Cups  

Sugar: 0.80 Tablespoons

2.40 Teaspoons

0.05 U.S. Cups

Butter: 2.82 Tablespoons

8.46 Teaspoons

0.18 U.S. Cups

Maple Syrup:

0.127 Cups

2.029 Tablespoons

6.087 Teaspoons

Milk:

0.169 Cups

2.705 Tablespoons

8.115 Teaspoons

Hope this helps!!

Have A Blessed Day <333

please help with these question, giving brainliest :)

Answers

Answer:

Step-by-step explanation:

Lin rode her bike 1 mile in 4 minutes, 2 miles in 8 minutes. Every 1 minute she rode how many miles?

Answers

Answer: [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

4 minutes in 1 mile

so 1 minute in [tex]\frac{1}{4}[/tex] mile

please give me a brainliest answer

PLEASE HELP WE DON'T KNOW THE ANSWERS AND WE ARE ALL FAILING THIS CLASS PLS HELP//// I would like to thank you for helping us so much we greatly apricate this.

Answers

Answer:

leave unknown variables alone on one side. throw the numbers to the other side of the equation by changing sign

Simplify radicals please

Answers

Answer:

-24x^5 y^2 z^8 /3yz

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.
(Please show your work)

Answers

Answer:

12

Step-by-step explanation:

Since this is a right angle triangle, and we have two lengths already found, we can use pythagoras to find x.

We know that

a²+b²=c²

Where a, and b are the smaller lengths (the adjacent and opposite), and C is always the longest one (the hypotenuse).

We want to find x, which in this case is c. So,

to solve for c, we get

c=[tex]\sqrt{a^2+b^2 }[/tex]

So, after plugging in the values, we get

[tex]c=\sqrt{10.6^2+6.1^2}[/tex]

[tex]c=12.23\\\\=12 (rounded)[/tex]

>> Answer

___________

[tex] \: [/tex]

[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]

Step by step :

x² = (10,6)² + (6,1)²

x² = 112,36 + 37,21

x² = 149,57

x = 12,22mi

A rental car agency charges $220.00 per week, plus $0.15 per mile to rent a car How many miles can you travel in one for $319.00

Answers

Hey!

------------------------------------

We Know:

$220 per week.

$0.15 per mile you drive.

------------------------------------

Solution:

325 - 220 = 105

105 / 0.15 = 700

------------------------------------

Answer:

You can drive 700 miles in one week for $325!

------------------------------------

Hope this helped! Good Luck ;)

If there are four black kittens and two orange kittens how does the number of orange kittens compared to the total number of kittens in the litter write a comparison beginning with for every?

Answers

Answer:

For every two black kittens, there is one orange kitten.

Step-by-step explanation:

Simplify the ratio and put it in word form.

Answer:

For every three kittens there is one orange kitten

Step-by-step explanation:

The total number of kittens is equal to four black kittens + two orange kittens, which makes for six kittens.

So for every six kittens there are two orange kittens.

We can simplify this down further by dividing by the greatest common factor, 2.

So,

For every three kittens there is one orange kitten.

A line passes through the point (2, 4) and has a slope of -5/2

Answers

Answer:

y = -5/2 + 12

Step-by-step explanation:

A farmer wants to fence a small rectangular yard next to a barn. Fence for side parallel to the barn will cost 55 per foot and the fence for the other two sides will cost 45 per foot. The farmer has a total of 1650 dollars to spend on the project. Find the dimensions for the yard that will have the largest possible area.

Answers

Answer:

55 divided by 45= 1.222222222222    1650 divided by 1.222222= anserw

Step-by-step explanation:

Please please help me with this question please now and show your steps

Answers

y = x^2 - 8x + 7

a) y-intercept

The y-intercept is the point where it crosses the y axis so x would 0.
So putting in 0 for x:
y = x^2 - 8x + 7
y = 0^2 - 8(0) + 7
y = 0 - 0 + 7
y = 7
The y intercept is at the point (0,7).

b)
The zeroes are the points where it crosses the x axis so it’s when the y is set to 0.

0 = x^2 - 8x + 7
Since it’s a quadratic equation we have to factor it. We fill in 2 numbers that add to -8 and multiplied to equal 7.
(x +____)(x+ ____)

The 2 numbers are 7 and -1 because -1*-7=7 and -7+(-1)=-8. So:
0 = (x-7)(x-1)

So now we have x-7 and x-1 equaling some quantity. If either of those happens to equal zero, it makes the whole equation 0, because (x-7)0=0 and 0(x-1)=0

So we can set each of it separately to 0 to solve for x.
x-7=0
x= 7

x-1=0
x= 1

The zeroes are at the points (1, 0) and (7, 0)

C.
The Vertex Form of a Quadratic is:
y = a(x-h)^2 + k. And the vertex is (h, k)

y = x^2 - 8x + 7
y - 7 = x^2 - 8x

We want to complete the square by adding some number to both sides of the equation so that when we factor it we are going to get (x-a)(x-a).

So take half of 8 to get two equal numbers that would be our “a”. 8/2=4 so we want (x - 4)(x- 4).

(x-4)(x-4) multiplies out to x^2 - 8 + 16.

continuing,
y - 7 = x^2 - 8x

Add 16 to both sides.
y - 7 + 16 = x^2 - 8x + 16

y + 9 = (x-4)(x-4)
y + 9 = (x-4)^2
y = (x-4)^2 - 9 is the vertex form.

The vertex is at the point (4, -9). So the axis of symmetry is at the line x = 4.

D. The vertex is solved in C as the point (-4, -9).

what is the mathematical sum for the equation “1+1” ?

Answers

Answer:

2... i think

step by set explanation:

I need the answer for this

Answers

Answer:

JK = 12.6

Step-by-step explanation:

Similarity says ratio of any cooresponding sides are equal to the ratio of any other cooresponding sides. SO

25.2/66 = JK/33

33(25.2/66) = JK

12.6 = JK

Pls help this is for a test ill give 20 points

Answers

Answer:

y = 2x+1

Step-by-step explanation:

Given, the slope of a line is 2 and y-intercept is 5.

Here, m=2 and c=1.

The equation of the line in slope-intercept form is given by

              y=mx+c

∴             y=2x+1 is a required equation.

Not sure if it correct or not.

Find the area use 3.14 for pi

Answers

Answer:

15.14 cm^2

Step-by-step explanation:

Area of rectangle = 4cm x 3 cm = 12cm^2

Radius of the circle = 2 cm

Area of 1/4 of a circle = (pi x r^2) / 4

= (3.14 x 4) / 4 = 3.14 cm^2

3.14 cm^2 + 12cm^2 = 15.14 cm^2

Factor the coefficient from 1.5a - 4.5

Answers

The answer is 1.5(a -3)

How old is Reena now,If 10 years ago she was 25 years old?​

Answers

Answer:

35

Step-by-step explanation:

If she was 25, 10 years ago she has aged 10 years since she was 25 making her 35.

Help like rn. Like rn please I will mark brainiest but pls help.

Answers

Answer:

90

and

20

i think so ye

Step-by-step explanation:

Answer:

Nvm

Step-by-step explanation:

U don’t need help anymore?

Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line 4x + 3y = 12? Drag and drop each choice into the boxes to correctly complete the table. Parallel Perpendicular Neither

Answers

Step-by-step explanation:

The line given:

4x + 3y = 12, its slope is m = - 4/3

Other lines to compare:

-3x + 4y = 8, the slope is m = 3/4, it is perpendicular line as the product of the slopes is  - 1;4x + 3y = 31, the slope is m = -4/3, same slope but different y- intercept, it is parallel line;3x + 4y = 12, the slope is m = -3/4, it is neither parallel nor perpendicular;-4x + 3y = - 1, the slope is m = 4/3, it is neither parallel nor perpendicular
4x+3y=123y=-4x+12y=-4/3x+12

Slope=m=+4/3

#1

-3x+4y=8

m=3/4

Perpendicular

#2

4x-3y=31

m=-4/3

Parallel

#3

3x+4y=12

m=-3/4

neither

#4

-4x+3y=-1

m=4/3

Neither
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