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Prove that the points of ABCD below form a parallelogram by
showing that opposite sides are parallel and opposite sides are congruent.

3. A(-6, -4), B(4, 2), C(6, 8), D(-4, 2)

Slope  of  AB  =   (2 - - 4)  / (4 - - 6)  =  6 / 12  =  1/2

Slope of  CD  = ( 2 - 8)  /( -4 - 6)  =  -6 / -12  = 1/2

AB  =   sqrt   [ ( -6 - 4)^2  +  ( -4 - 2)^2  ]   =  sqrt  [ (-10)^2  +(- 6)^2 ]  = sqrt 136

CD  =sqrt  [ ( -4 - 6)^2  + ( 2 - 8)^2 ]    =sqrt [ 10^2  + (-6)^2  ] = sqrt 136

Now...using the same procedure....

Find  the slope of AD    and  BC

Then....using the distance formula   find   AD  and BC

Let me know  if  you get  stuck

1)  a) Slope  of  AB    =  (4 - 0)  / ( 4 - - 2)  =  4/ ( 4 + 2)  =  4 / 6  =  2 / 3 

     b)  Any parallel line to AB  will have  the same slope

     c)  A perpendicular line has a  negative reciprocal slope =  -3 /  2

Use slopes to show that △RST is a right triangle.

2. R(-3, -4), S(2, 2), T(14, -8)

Slope of RS  = ( 2 - - 4)  / ( 2 - - 3)  =  6 / 5

Slope of  ST    = ( -8-2) /( 14 - 2)  =  -10 / 12  =  - 5 / 6

RS  and  ST  have  negative reciprocal slopes......thus......they meet at right  angles

ah sorry i mean yes!!!

So what is it?

nooo....

Is it 960?

wha no

In decimal form it is 0

Triangle :
A,B,C 
A,D,B
D,E,B
E,D,C
 

Let's just plug this inn. 

3A + 2(4) + 5 = 58

3A + 13 = 58

3A = 45

A = 15

=^._.^=

If your are still stuck, I will post the answer :)))

Here's a start: Let 'a' be the number of apples, and 'o' be the number of oranges. Since 3/8 of all the fruits are apples, 3/8(a + o) = a. Since the difference between the number of oranges and apples is 240, o - a = 240 (it's because there is more oranges). Now start working :).

\(\frac{14x + 22}{x + 2} = -3x + 1\)

\(14x + 22 = (-3x + 1)(x + 2)\)

\(14x + 22 = -3x^2 -6x + x + 2\)

\(3x^2 + 6x + 14x - x + 22 - 2 = 0\)

\(3x^2 + 19x + 20 = 0\)

\(x = {-(19) \pm \sqrt{(19)^2-4(3)(20)} \over 2(3)}\)

\(x = {-19 \pm \sqrt{361-240} \over 6}\)

\(x = {-19 \pm \sqrt{121} \over 6}\)

\(x = {-19 \pm 11 \over 6}\)

\(x = -5\)

\(x = -\frac{4}{3}\)

\(-5 + -\frac{4}{3} = \frac{-15 - 4}{3} = -\frac{19}{3}\)

show your work?

dang

Tom baked some cupcakes. If he gave each of his friends 5 cupcakes, he would have 25 cupcakes left. If he gave each of his friends 9 cupcakes, he would need to bake another 35 more cupcakes. How many cupcakes did Tom bake?

no. of friends = f, guess the no. of cupcakes 

                 

What do you know?

Fixed no. of cupcakes (at first) and friends

15 friends 

9 - 5 = 4 

25 + 35 = 60

60 / 4 = 15 (no. of freinds).

5 * 15 + 25 = 100

9 * 15 - 35 =100

100 cupcakes

Other way to think about it is

X^5 = 32, what's the 5th root of 32? 2.

2^5 = 32

X=2

a+b+c=0

a^3+b^3+c^3=-1

a+b=-c

a^3+b^3 - (a+b)^3  = -1

(a+b)^3 = a^3 +b^3 +3abb +3aab

Cancel cubes

3aab + 3abb = -1

3ab(a+b)=-1

3ab(-c) =-1

3abc = 1

abc = 1/3

The area of triangle ABD works out to 272/5.

X -200 = 50 + 1/3(x-50)

3X -600 = x + 100

2x = 700

X = 350

(350, infinity)

no it works you dumb xd