Will someone be nice and help me with math?

Question

name 6 points A,B,C,D,E, and F, no three of which are colinear. Name the line defined by thees points. How many lines are there.

number og diagonal of a Heptagon, Octagon, and a 12 sided figure.

and what do you call a 12 sided figure.

How many diffrent (non congruent) convex quadrilaterals can you make on a 3-by-3 dot grid, using dot vertices's?

what are perpendicular segments?

finish the pattern.../

-5,3,-2,1,-1,0 _ _

1,5,14,30,55_ _

y=mx+b

6 1

1 2

-4 3

_ 50

6.5 1

7 2

7.5 3

_ 50

Answer 1

Name 6 points A,B,C,D,E, and F, no three of which are colinear. Name the line defined by these points. How many lines are there.

Since no three points are colinear, then each of AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF are different lines. Therefore, the number (n) of lines is 15

n = (6 choose 2) = (6 x 5) / 2 = 15

Why does this formula work?

Each of the six points can be paired with the other 5 points.

Therefore, there are 6x5 = 30 ordered pairs of points.

But using this method, each pair is counted twice, ie AB and BA; CD and DC; BF and FB. Therefore we must divide 30 by 2 = 15

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Number of diagonals of a heptagon(7-sided), octagon(8-sided), and a dodecagon (12-sided).

Start with heptagon (7-sided):

Calculate number of lines defined by vertices (7 points)

Using same reasoning as with 6 points,

NumLines = (7x6)/2 = 21

But 7 of those lines make up the perimeter of heptagon

NumDiagonals = NumLines - 7 = 21 - 7 = 14

Use same reasoning for octagon and dodecagon.

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Finish the pattern...

-5, 3, -2, 1, -1, 0, _, _

after first two, the next number is sum of previous two numbers:

1ˢᵗ: -5

2ⁿᵈ: 3

3ʳᵈ: -5+3 = -2

4ᵗʰ: 3-2 = 1

5ᵗʰ: -2+1 = -1

6ᵗʰ: 1-1 = 0

7ᵗʰ: -1+0 = -1

8ᵗʰ: 0-1 = -1

Solution: -1, -1

1, 5, 14, 30, 55, _, _

increase by successive squares:

1ˢᵗ: 1² = 1

2ⁿᵈ: 1+2² = 5

3ʳᵈ: 5+3² = 14

4ᵗʰ: 14+4² = 30

5ᵗʰ: 30+5² = 55

6ᵗʰ: 55+6² = 91

7ᵗʰ: 91+7² = 140

Solution: 91, 140

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y=mx+b

(6, 1)

(1, 2)

(-4, 3)

(_, 50)

Since these are all solutions to y=mx+b, they all lie on the same line, i.e. any two of these points will have the same slope

Using (6,1) and (1,2): m = (1-2)/(6-1) = -1/5

Using (1,2) and (-4,3): m = (2-3)/(1+4) = -1/5

Using (-4,3) and (a,50): m = (3-50)/(-4-a) = -1/5

Solving for a:

-47/(-4-a) = -1/5

(-4-a)(-1) = (5)(-47)

4+a = -235

a = -239

(6.5, 1)

(7, 2)

(7.5, 3)

(_, 50)

Use same logic as above

Using (6.5, 1) and (7, 2): m = (1-2)/(6.5-7) = -1/-0.5 = 2

Using (7, 2) and (7.5, 3): m = (2-3)/(7-7.5) = -1/-0.2 = 2

Using (7.5,3) and (a,50): m = (3-50)/(7.5-a) = 2

Solving for a:

-47/(7.5-a) = 2

(7.5-a)(2) = -47

15 - 2a = -47

-2a = -62

a = 31