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Here's one way (messy though!):

I have forgotten how to do this.  

I would like to be reminded of the method though.  Any takers?

I think so too.   

hm...

height 1 is not always less than height2+height3...

if an iscoceles triangle is really tall, then.... yeah...

wait a sec......

ABCAABBCC is not one rep,

look closely,

ABCAABBCCABCAABCC

one b and 2 b's

correct me if i am wrong but aren't there infinite places to put a dot, like at the 5.66666666666666 point mark or 4.508971893719038470 mark?

x^2 + 2y^2 + 6x + 8y - 121 = 0

(x + 3)^2 + 2(y+2)^2 - 121 - 17 = 0

(x + 3)^2 + 2(y+2)^2 = 138

(x + 3)^2/138  + (y+2)^2/69 = 0

This is the formula of an eclipse. :))

=^._.^=

Try graphing the inequality 2x + y > -8. 

Start by graphing the line 2x + y > -8, and shade the area above the line.

Anything in that shaded area will fit the equation.

=^._.^=

-2(s + 7) > 4s + 8

(when dividing by a negative, we flip the sign)

s + 7 < 2s + 4

3 < s

In interval notation, you write that as (3, infinity). 

We use parenthesis since s can not be 3. 

=^._.^=

A

think about how many letters there are in a rep. i presume you can understand without an explanation. 50/9, then count the remainder.

There will be as many zeros at the end of the answer as there are factors of 10

in the answer.

To find the number of factors of 10, find the number of factors that are 5

and the number of factors that are 2.

25  =  5x5

20  =  5x4

15  =  5x3

So, there are 4 factors of 5.

There are more than 4 factors of 2, so there are a total of 4 factors of 10.

Therefore, there will be four zeros at the end of the answer.

Which angle is the right angle?

Angle Bisector Theorem:  AE / AB  =  DE / CB

--->     9 / 15  =  12 / BC

Solve for BC ...

The easiest way to solve this is to use Vietas. The sum and products of the roots are -8 and 7, respectively. 

We know the sum is \(-b\over a\). We also know a = 1, so b must be 8. 

We also know the product is \(c \over a\). Because we know a = 1, c must be 7. 

This means that the quadratic is \(\color{brown}\boxed{ x^2 + 8x+ 7}\)

Only \(\color{brown}\boxed{4}\) do, I, A, E, and D. 

Write as system:

a = apples

b = bananas

1.5a + 0.3b = 6

a+b = 8

1.5a + 1.5b = 12

1.5a + 1.5b = 12

1.5a + 0.3b =  6

           1.2b =  6

                b = 5

Now plug 5 into the second equation and solve for a 

The sum is equal to 8/5.

The probability is 1/3.

p(8) = 1/8.

(b) There are 108/3 = 36 unique sets.

(c) For the first card, there are 3 ways to choose the number.  For the second, there 2 choices, and then there is only 1 choice.  So there are 3*2*1 = 6 ways that the numbers can be chosen.  Doing this for the other attributes, we get 6*6*24*6 ways.  But the order of cards doesn't matter in a set, so we divide by 3!: 6*6*24*6/3! = 864.  So there are 864 sets for part (c).

(d) The cards can have the same number, color, shape, or shading.  If all the colors are the same, then there are 6*24*6/3! = 144 sets.  If all the numbers are the same, then there are 144 sets.  We get the same number for shape and shading, so there are 4*144 = 576 sets for part (d).

(e) We need to choose two of the attributes.  There are C(4,2) = 6 ways of choosing two attributes.  For each of these two attributes, there are 3 options.  For the other two attributes, there are 3 ways of assigning the choices, so there are 6*3*3*3*3 = 486 sets for part (e)

(f) First we choose which attributes are the same.  There are C(4,3) = 4 ways of choosing which attributes are the same.  There are then 3*3*4 = 36 ways to assign which is which for each of these three attributes, and there are 4 ways to assign the choices for the fourth attribute, so there are 4*36*4 = 576 sets for part (f).

Write it as an equation: \(20m= {m(m+1) \over 2}\)

The first term is the height of the first plant, and the second term is the sum of an arithmatic series that represents the height of the second plant. 

Solving, we find it took \(\color{brown}\boxed{39}\) months

8t^2 <= -10t+3

8t^2  + 10 t   -3   <= 0            This is a bowl shaped parabola......the area in question will be between and include the zeroes

quadratic formula shows the zeroes (roots)         t = 1/4   and - 1.5  

-1.5 <= t <= .25  

2,16