All Answers 356462 Answers

this was incorrect

If (x - 3)(4x + 9) = ax^2 + bx + c, then find a + b + c.

When you see a factored form going into a quadratic, what do you do? Of course, you multiply!

(x - 3)(4x + 9)

How do you multiply, you ask? Remember 5th grade, when the teacher taught all about the distributive property? This is just like that: you take one variable from one group, and multiply it with the other two from the other group.

x * 4x = 4x^2

x * 9 = 9x

-3 * 4x = -12x

-3 * 9 = -27

So, now that we multiplied, what do we do? Did you just say, Combine Like Terms? If you did.....you are correct! So...combine we go:

Degree 2: 4x^2

Degree 1: 9x - 12x = -3x

Constant: -27

Together, this is 4x^2 - 3x - 27.

But, that is not what we are looking for, right? We want to find a + b + c. Is that hard? No:

4 - 3 - 27 = -26

There you go, you have the answer. 

The takeaway:

Whenever you see that something should be expanded, EXPAND IT! (unless you could use the binomial theorem or specified)

:)

l = lost

w = win = 3l + 20         summed = 136

l     +   3l+20 = 136     

              solve for 'l'  

                        then  w = 3l+20

I think what guest is doing is trying to show the picture. But...he/she did not realize that the picture needs to be a .jpg or download, NOT any regular link. Guest could have checked, because if there was a red x in the preview instead of the picture, it would have come out white

:)

Do you know what "sine" means?

It is the opposite over hypotenuse.

You can think of it like:

Sine Opposite Hypotenuse Cosine Adjacent Hypotenuse Tangent Opposite Hypotenuse 

Which comes out to be:

soh cah toa

Know that, we now know that the hypotenuse of the triangle is 41, and the shorter leg of the triangle is 9. 
 

Using Pythagorean triples, we see that the is a 41, 40, 9 triangle.

this means that the tangent is 9/40, or D

:)

Does it cost that much to multiply? Maybe a few seconds...

As you see, variables can be replaced, anytime, anywhere. So...we replace the x and y in the xy with the values defined. Maybe I'm being a little too "professional" for your tastes, but here is what I am trying to say:

xy = -8 * 9

What did we do, you may ask? We replaced the variables with the defined values!

Assuming you know how to multiply:

-8 * 9 = -72

And there we go! 
 

:)

ok thanks, I didn't see that.

11 with 1,4,7

22 with 2,5,8

33 with 0,3,6,9

10 possibilities

----------

44 with 1,4,7

55

66

--------

77

88

99

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

3*10 = 30 possibilities

Just like you already said.       

A binomial in the form a3 + b3 can be factored as (a + b)(a2 – ab + b2). 

\(x^3+y^3=(x+y)(x^2+y^2-xy)\\ 2(x^3+y^3)=(x+y)(2x^2+2y^2-2xy)\\ \frac{2(x^3+y^3)}{(x+y) }=2x^2+2y^2-2xy\quad(1)\\~\\ (x+y)^2=x^2+y^2+2xy \qquad(2)\\ (1)+(2)\\ \frac{2(x^3+y^3)}{(x+y) }+(x+y)^2=3x^2+3y^2\\ 2(x^3+y^3)+(x+y)^3=3(x+y)(x^2+y^2)\\ Let \;\;A=x+y\\ 2(x^3+y^3)+A^3=3A(x^2+y^2)\\ 2*52451+A^3=3A*1753\\ 104902+A^3=5259A\\ A^3-5259A+104902=0\\\)

Wolfram|Alpha factored this as  

\((A-59)(a^2+59A-1778)=0\)

So A can be 59, this will be the only integer value of A

so

\(\fbox{x+y=59} \)

LaTex:

x^3+y^3=(x+y)(x^2+y^2-xy)\\
2(x^3+y^3)=(x+y)(2x^2+2y^2-2xy)\\
\frac{2(x^3+y^3)}{(x+y)  }=2x^2+2y^2-2xy\quad(1)\\~\\

(x+y)^2=x^2+y^2+2xy \qquad(2)\\
(1)+(2)\\
\frac{2(x^3+y^3)}{(x+y)  }+(x+y)^2=3x^2+3y^2\\
2(x^3+y^3)+(x+y)^3=3(x+y)(x^2+y^2)\\
Let \;\;A=x+y\\
2(x^3+y^3)+A^3=3A(x^2+y^2)\\
2*52451+A^3=3A*1753\\
104902+A^3=5259A\\
A^3-5259A+104902=0\\

(A-59)(a^2+59A-1778)=0

Hi Melody: They have to be "Multiples of 3".

9 with all three digits the same

9*9*1=81 ways to choose a two different digit ones.

[The first and last number can be 1,2,3,4,5,6,7,8,9        9 choices

the middle number can be any number, including 0 but not including the number already chosen  9 choices]

So I get 90 ways.

Ok how about this.

\(x*f(x)>0 \qquad \\ \text{both factors are positive AND when both factors are negative}\\ \text{x is positive right of the y axis and f(x) is positive above the x axis, so both are positive only in the 1st quadrant.}\\ \text{x is negative left of the y axis and f(x) is negative below the x axis, so both are negative only in the 3rd quadrant.}\\ \)

So the statement will be true whenever the graph is in the 1st or the 3rd quadrant.     

Let the number of dimes =D

The number of nickels    =3D

The number of quarters  =D + 7

0.1*D + 0.05*3D + 0.25*[D + 7] =4.25, solve for D

D = 5 dimes

5 x 3 = 15 nickels

5 + 7 = 12 quarters.

Check: [0.1 x 5] + [ 0.05 x 15] + [0.25 x 12] =0.50 + 0.75 + 3.00 =$4.25 

∠A = x

∠B = 2x + 4

∠C = 3x - 30

x + (2x + 4) + (3x - 30) = 180

I'll give you a good hint juriemagic   

Can you take it from there ?

\(x^2+2xy+2y^2\\ =(x^2+2xy+y^2)+y^2\\ =?\)

To be honest, before I even thought about it, I graphed it.  

Given the points J(4,-7) and L(-2,13), find the coordinates of point K on JL such that the ratio of JK to JL is 1:4

Coordinates of K ( 2.8, -3 )

Hi Melody,

Thank you for answering. The question is about a parabola and straight line intercepting on a plane, and all the normal questions one can expect to find, is asked. Then the one I asked about. I was thinking that, to make a drawing of this whole thing just for a 4 point question I do not understand, is way not worth the effort. So, I think I'm going to sit this one out. Anyways, as usual, thank you very much for being out there!!!!..I do appreciate!

Given the points C(-1,-5) and D(-7,-11), find the coordinates of point E on CD such that the ratio of CE to ED is 5:3

Because the triangle is isosceles, the two labelled angles are the same. Thus:

5x + 6 = 8x - 15   so  3x = 21 hence x = 7

These two angles are therefore 41°

We must have 41 + 41 + Y = 180, so Y = 180 - 82 = 98°

(111, 141, 171, 222, 252, 282, 303, 333, 363, 393, 414, 444, 474, 525, 555, 585, 606, 636, 666, 696, 717, 747, 777, 828, 858, 888, 909, 939, 969, 999) >>Total = 30 such numbers

Given the points C(-1,-5) and D(-7,-11), find the coordinates of point E on CD such that the ratio of CE to ED is 5:3

Hello Guest!

\(x_E=x_C-\frac{5}{8}(x_C-x_D)=-1-\frac{5}{8}(-1-(-7))\\ x_E=-4.75\)

\(y_E=y_C-\frac{5}{8}(y_C-y_D)=-5-\frac{5}{8}(-5-(-11))\\ y_E=-8.75\)

The coordinates of point E are

\(E(-4.75,-8.75)\)

  !

Angle Y is 102 degrees.

The coordinates of E are (2,1).

The coordinates are K are (7,17).