(Type an ordered pair, using integers or decimals)

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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Answer:

we need more information to solve your problem.

Step-by-step explanation:

Answer:

y = -4/3x -9

Step-by-step explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

8x+6y = -54

Subtract 8x from each side

8x+6y-8x = -8x-54

6y = -8x-54

Divide each side by 6

6y/6 = -8x/6 -54/6

y = -4/3x -9

Answer:

y = -4/3x - 9

Step-by-step explanation:

Putting this into 'y=mx+c' form:

i) Firstly, make it only y on the LHS:

6y = -8x-54

ii) Secondly, making the 'y' have a co-efficient of 1. This can be done by dividing both sides by 6:

6y/6 = -8x/6 - 54/6

y = -4/3x - 9

Hence,

y = -4/3x - 9

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Multiply to get the answer:

Convert to scientific notation and find the ratio of the second number by the first:

Divide:

Answer:

g(

x

2

−

3

)

=

2

x

2

−

7

Step-by-step explanation:

brainliest

Step-by-step explanation:

4a)

the principle of similar triangles : they have the same angles.

and we do not forget : the sum of all angles in a triangle is always 180 degrees.

a = 180 - 65 - 45 = 70 degrees

b = 65 degrees

c = 70 degrees

b)

same principles.

x = 58 degrees

y = 52 degrees

z = 180 - 58 - 52 = 70 degrees

c)

same principles.

plus the fact that complementary angles around a point on one side of a line are also together 180 degrees.

x = 85 degrees

y = 180 - 40 - 85 = 55 degrees

z = 180 - 85 = 95 degrees

d)

again same principles.

y = 2x (as these 2 angles correspond to each other among the 2 similar triangles).

the angle POQ is again complementary with 87 degrees,

POQ = 180 - 87 = 93 degrees

x + y + 93 = x + 2x + 93 = 180

3x = 87

x = 29 degrees

y = 2x = 2×29 = 58 degrees

10- 9

11- 5

12- 1

13- 10

14- 3

15- 7

16- 3

17- 3

18- 6

Answer:

x= 3/7 i.d.k if this is correct I did it in my brain

Answer:

-18/29

Step-by-step explanation:

54 ÷ 3 = 18 - numerator

84 ÷ 3 = 29 - denominator

-54/84 = -18/29

Answer:

hsoabajakahaknanaKambaKla

Answer:

34 hours

Step-by-step explanation:

Lets call M the number of hours that Maddie volunteered. Ryan volunteered 1 + 3×M hours, and altogether they volunteered 45 hours, so:

1 + 3×M + M = 45

1 + 4M = 45 Subtract 1 in both sides

4M = 44 Divide both sides by 4

M = 11 hours

So Maddie volunteered 11 hours, and Ryan volunteered

1 + 3×11 = 34 hours

Angle 8 and angle 5 are vertical angles

Answer:

60%

Step-by-step explanation:

You could make a fraction to help solve for the answer. The denominator is 25 because you add 4 + 15 + 6. The numerator is 15, because it is the number of roses. 15/25 as a percent is 60% because you just times both the numerator and denominator by 4.

Answer:

1/5

Step-by-step explanation:

[tex]\lim_{x->4} \frac{x-4}{x^{2}-3x-4 } \\= \lim_{x->4} \frac{x-4}{(x+1)*(x-4) } \\\\= \lim_{x->4} \frac{1}{(x+1) } \\\\\\[/tex]

lim x->4   plug in x=4

1/(x+1) = 1/(4+1) = 1/5

Answer:b- 4,000

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

It is B because

4000-800=3200

then

3200+800=4000

so he answer is B.4000  

Answer:

1) = 90=acute angle   2)103=acute angle

Step-by-step explanation:

Answer:

1.) x = 90 (Right angle)

2.) x = 103 (Obtuse angle)

Step-by-step explanation:

[tex]1.)\\x+48+42=180\\x+90=180\\x=90\\\\2.)\\x+45+32=180\\x+77=180\\x=103[/tex]

→ You will pay $ 89.7.

The tip value is based on the bill value. Hence, to find the total payment you have to multiply 78 by 1.15 (this includes the tip, 1.15).

[tex]\Large \text {$Total = 78 \times 1.15 = 89.7 $}[/tex]

Or you can first find how many 15% is from $78:

[tex]\Large \text {$0.15 \times 78 = 11.7$}[/tex]

And then add this to $78:

[tex]\Large \text {$78 +11.7 = 89.7$}[/tex]

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Answer:

$89.70

Step-by-step explanation:

15/100=0.15

78 * 0.15 =89.70

Answer:

y = 150º

Step-by-step explanation:

The sum of internal angles of a triangle must be 180º and the sum of y + (x-20) forms a straight line which is also 180º, so:

2x + x + (x - 20) = 180

4x - 20 = 180

4x = 200

x = 50

x - 20 = 50 - 20

x - 20 = 30

y = 180 - 30

y = 150º

Answer:

423

Step-by-step explanation:

123423

The constant speed for the given distance and time is 123/2 miles/hour.

Given that, Andrea drove [tex]20\frac{1}{2}[/tex] miles in 1/3 of an hour at constant speed.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Here, [tex]20\frac{1}{2} = \frac{41}{2}[/tex]

Now, speed = Distance ÷ Time

= 41/2 ÷ 1/3

Change division to multiplication and reciprocal the fraction

That is, 41/2 × 3/1

= 123/2 miles/hour

Therefore, the constant speed for the given distance and time is 123/2 miles/hour.

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Answer: The answer is 18x + 26

Step-by-step explanation:

What I did was simplify the Expression of (3x+8)+6(2.5x-3) then combine the terms and last evaluate the Expression.

Answer:

Your answer should be C

Step-by-step explanation:

Answer:

3x - 2y = -18

Step-by-step explanation:

3x - 2y = -18 and (-2, 6)

(3)(-2) - (2)(6) = -6 - 12 = -18

Step-by-step explanation:

9) y= -2x - (5/2)

10) y = -5 + (5/2)

Answer:

5 houses

Step-by-step explanation:

She needs to visit 5 houses as 20 divided by 4 is 5

Answer:

[tex]12x^{2} -11x-5[/tex]

Step-by-step explanation:

1) Distribute

[tex]4x(3x-1)-2(3x+1)-(x+3)\\12x^{2} -4x-2(3x+1)-(x+3)[/tex]

2) Distribute

[tex]12x^{2} -4x-2(3x+1)-(x+3)\\12x^{2} -4x-6x-2-(x+3)[/tex]

3) Distribute

[tex]12x^{2} -4x-6x-2(x+3)\\12x^{2} -4x-6x-2-x-3[/tex]

4) Subtract the numbers

[tex]12x^{2} -4x-6x-2-x-3\\12x^{2} -4x-6x-5-x[/tex]

5) Combine like terms

[tex]12x^{2} -4x-6x-5-x\\12x^{2} -11x-5[/tex]

Answer:

[tex]{ \rm{ \sqrt{32} = \sqrt{2 \times 16} }} \\ \\ = { \rm{ \sqrt{2 \times 4 \times 4} }} \\ \\ = { \rm{ \sqrt{2} \times( \sqrt{4}) {}^{2} }} \\ \\ = { \rm{ \sqrt{2} \times 4 }} \\ \\ = { \rm{4 \sqrt{2} }} \\ \\ { \rm{ \sqrt{32} = 5.656854....}} \\ \\ { \boxed{ \rm{ \sqrt{32} = 5.66 \: }}}[/tex]

9514 1404 393

Answer:

  5.66

Step-by-step explanation:

For an integer x = s² +r, where s and r are also integers, a first approximation of the square root of x will be ...

  y = √x ≈ s +r/(2s+1)

An iterative improvement on the estimate can be had by ...

  y' = s + r/(s +y)

Here, this means a first estimate can be obtained as ...

  32 = 5² +7   ⇒   s = 5, r = 7

  √32 ≈ y1 = s +r/(2s +1) = 5 7/11

Then an iterative improvement will be ...

  y2 = s +r/(s +y1) = 5 +7/(10 7/11) = 5 77/117 ≈ 5.658 ≈ 5.66

_____

Additional comment

The above iterator will add about 1 decimal place for each iteration. The Babylonian method will roughly double the number of good decimal places with each iteration. For an approximate root of p/q, the next iteration using that method would be ...

  p'/q' = (x·q² +p²)/(2pq)

Then our above estimate of 5 7/11 for the root of 32 would be refined to ...

  p'/q' = (32·11² +62²)/(2·11·62) = 7716/1364 = 5 224/341 ≈ 5.65689.... This compares favorably to the first digits of the actual root: 5.65685....

The value of the function if the independent variable is equal to -1 is -2

Given the function p(x) = x^3 - 1

The input variable "x" is the independent variable. If the independent variable is equal to -1, the value of the function will be expressed as:

P(-1) = (-1)^3 - 1

P(-2) = -1 -1

P(-2) = -2

Hence the value of the function if the independent variable is equal to -1 is -2

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