All Answers 358405 Answers

1.  factorize 9(2a-b)^2 - 4(2a-b)^2 -13 

$$\small{\text{$
\begin{array}{rcl}
9x^2 - 4x^2 -13 &=& 5x^2 - 13 \qquad | \qquad x= 2a-b \\\\
5x^2 - 13 &=& 0\\
5x^2 &=& 13 \\\\
x^2 &=& \dfrac{13}{5}\\\\
x^2 &=& 2.6 \\
\mathbf{x_{1,2} } & \mathbf{=} & \mathbf{\pm\sqrt{2.6}}\\\\
5x^2 - 13 &=& 5\cdot(x-\sqrt{2.6})(x+\sqrt{2.6})\qquad | \qquad x= 2a-b \\\\
9(2a-b)^2 - 4(2a-b)^2 -13 = 5(2a-b)^2 - 13 &=&
5\cdot\left[(2a-b)-\sqrt{2.6}\right] \left[(2a-b)+\sqrt{2.6} \right] \\\\
\end{array}
$}}$$

Percentage change = 100*(57 - 28)/57 ≈ 50.9%

In general the percentage change is the difference between the final amount and the initial amount divided by the initial amount and multiplied by 100.

.

 x = $${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$      und      x = $${\frac{{\mathtt{1}}}{{\mathtt{m}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$

Gruß radix !

I think anonymous you gave me a good laugh..... This is what I can imagine tins expression to be right now -__-

Genius , all paradises are the same.....it's not like Christian heaven has a black sky and a Muslim heaven has a white sky or a Hindu heaven has a red sky.its all the same!

whatever is it.,.....I don't like coke..... I didn't say I can't drink it I just said I don't like it......doesn't matter if I drink it or not........which I really do....lol •.•

$$\small{\text{$
\begin{array}{rcl}
\boxed{~~ax^2+bx+c=0 \qquad
x_{1,2} = \dfrac{ -b\pm \sqrt{b^2-4ac} }{2a} ~~}
\end{array}
$}}$$

$$\small{\text{$
\begin{array}{rcl}
a=m ~~b=-1~~c=-\dfrac{m-2}{4}\\\\
x_{1,2} &=& \dfrac{ -b\pm \sqrt{b^2-4ac} }{2a} \\\\
x_{1,2} &=& \dfrac{ 1\pm \sqrt{1^2-4m\left(-\dfrac{m-2}{4}\right) } }{2m} \\\\
x_{1,2} &=& \dfrac{ 1\pm \sqrt{1+m\left(m-2\right) } }{2m} \\\\
x_{1,2} &=& \dfrac{ 1\pm \sqrt{1+m^2-2m} }{2m} \\\\
x_{1,2} &=& \dfrac{ 1\pm \sqrt{1-2m+m^2} }{2m} \\\\
x_{1,2} &=& \dfrac{ 1\pm \sqrt{(1-m)^2} }{2m} \\\\
x_{1,2} &=& \dfrac{ 1\pm (1-m) }{2m} \\\\
x_1 &=& \dfrac{ 1 + (1-m) }{2m} \\\\
x_1 &=& \dfrac{ 2-m }{2m} \\\\
x_1 &=& \dfrac{ 2 }{2m} - \dfrac{ m }{2m} \\\\
\mathbf{x_1} & \mathbf{=} & \mathbf{ \dfrac{ 1 }{m} - \dfrac{ 1 }{2} } \\\\\\
x_2 &=& \dfrac{ 1 - (1-m) }{2m} \\\\
x_2 &=& \dfrac{ 1 - 1 + m)}{2m} \\\\
x_2 &=& \dfrac{ m }{2m} \\\\
\mathbf{x_2} & \mathbf{=} & \mathbf{\dfrac{ 1 }{2}}
\end{array}
$}}$$

Sabi92, if you do not understand Geno's answer, you need to post questions about it on the original thread. :)

$${{\mathtt{mx}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\frac{\left({\mathtt{m}}{\mathtt{\,-\,}}{\mathtt{2}}\right)}{{\mathtt{4}}}} = {\mathtt{0}}$$

integer solutions :   m = -2       x = 1

                               m = 2        x = 0

Perimeter of a quadrant  =  $${\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{r}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{r}} = {\frac{{\mathtt{r}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{r}} = {\mathtt{r}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{\pi}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)$$

24/100 is equal to 24%

Well TR, I’m impressed. All this time, I thought you were just a half-wit.

This is a very strangely worded question - that is probably why no one has answered it already. :/

The point (1,-2) is on the graph of f(x). Describe the following transformations on f(x), and determine the resulting point.

g(x)=2f(x)+3          We know that f(1)=-2

so g(1)=2*-2+3 = -4+3 = -1

so every output value from the f function is doubled and then 3 is added to get the output for the g function.

g(x)=f(x+1)−3

g(0)=f(0+1)-3 =f(1)-3 = -2-3=-5

I don't know what the question wants - it is weird ://      Sorry

g(x)=−f(2x)

g(x)=−f(−x−1)+3

 if a jelly bean machine has 16 pink jelly beans, 34 blue jelly beans, 24 black jelly beans, and 26 purple jelly beans, what is the probability that a jelly bean chosen at random will be black?

$$\small{\text{probability ~}} =
\dfrac{ 24 \text{ black} }
{
16 \small{\text{ pink } }
+ 34 \small{\text{ blue }}
+ 24 \small{\text{ black }}
+ 26 \small{\text{ purple }}
} = \small{\dfrac{24}{100}
= 0.24 = 24 \% }$$

$$\\ a) \text{
Compute x+y and} \sqrt{x^2+y^2} \text{ when } x=5 \text{ and } y=12\\\\
b) \text{ When is } \left[x+y=\sqrt{x^2+y^2}~?\right]\\
\text{ When is } \left[x+y\neq\sqrt{x^2+y^2}~?\right]$$

a)

$$\small{\text{$
\begin{array}{rcl}
x+y &=& 5 + 12\\
x+y &=& 17 \\\\
\sqrt{x^2+y^2}&=& \sqrt{5^2+12^2}\\
\sqrt{x^2+y^2}&=& \sqrt{25+144}\\
\sqrt{x^2+y^2}&=& \sqrt{169}\\
\sqrt{x^2+y^2}&=& \sqrt{13^2}\\
\sqrt{x^2+y^2}&=& 13\\
\end{array}
$}}$$

b)

$$x+y \stackrel{\textcolor[rgb]{1,0,0}{?}} = \sqrt{x^2+y^2} \qquad \text{ squaring } \\\\
(x+y)^2 \stackrel{\textcolor[rgb]{1,0,0}{?}} = x^2+y^2\\\\
x^2+2xy+y^2 \stackrel{\textcolor[rgb]{1,0,0}{?}}= x^2+y^2 \\\\
\boxed{~~
x^2+\underbrace{\textcolor[rgb]{1,0,0}{2xy}}_{=0}+y^2 = x^2+y^2
~~}\\\\
\boxed{~~
x^2+\underbrace{\textcolor[rgb]{1,0,0}{2xy}}_{ \neq0}+y^2 \neq x^2+y^2
~~}$$

Thanks Alan,

OR

You could solve it by completing the square method

$$\\x^2-4xm+(2m-\frac{1}{4})=0\\\\
x^2-4xm\;=\;-(2m-\frac{1}{4})\\\\
x^2-4xm+(2m)^2\;=\;-2m+\frac{1}{4}+(2m)^2\\\\
(x-2m)^2\;=\;-2m+\frac{1}{4}+4m^2\\\\
(x-2m)^2\;=\;4m^2-2m+\frac{1}{4}\\\\
(x-2m)^2\;=\;4(m^2-\frac{m}{2}+\frac{1}{16})\\\\
(x-2m)^2\;=\;4(m-\frac{1}{4})^2\\\\
x-2m\;=\;\pm 2(m-\frac{1}{4})\\\\
x\;=\;2m\pm 2(m-\frac{1}{4})\\\\
x\;=\;2m+ 2m-\frac{1}{2}\qquad or \qquad x\;=\;2m- 2m+\frac{1}{2}\\\\
x\;=\;4m-\frac{1}{2}\qquad or \qquad x\;=\;\frac{1}{2}\\\\$$

You would have to give a specific example.    

Place it on a graph in quadrant IV.

The reference angle (the angle formed with the x-axis) is 60°.

The side opposite the 60° angle has value -√(3)/2.

The side adjacent the 60° angle has value 1/2.

The hypotenuse has value 1.

sin(300°)  =  opposite side / hypotenuse  =  (-√(3)/2) / 1  =  -√(3)/2.

cos(300°)  =  adjacent side / hypotenuse  =  (1/2) / 1  =  1/2.

tan(300°)  =  opposite side / adjacent side  =  (-√(3)/2) / (1/2)  =  -√(3)/2.

sin(x) · sin(x) = sin²(x)

So, the answer is  -sin²(x)

Because 7 ate nine.  :)

$109.3125 is between $109.30 and $109.35; it is closer to $109.30 than it is to $109.35.

(When x is measured in degrees) these two functions:  y = sin(x)  and  y = cos(x - 90°) have exactly the same values.

A calculator will tell you that 2³⁰  =  1 073 741 824

5 + 2P  =  10 - 2P

Add 2P to both sides:

5 + 4P  =  10

Subtract 5 from both sides:

     4P  =  5

Divide both sides by 4:

       P  =  5/4  or 1.25

Assuming that m is a constant and you are solving for x:

     mx² - x - (m - 2)/4  =  0

     mx² - x - m/4 + 2/4  =  0

Multiplying by 4:

    4mx² - 4x - m + 2  =  0

Solving, using the quadratic formula with  a = 4m,  b = -4,  and  c = -m + 2   --->   c = 2 - m

   x  =  [ 4 ± √( 4² - 4(4m)(2 - m) ) ] /  [ 2(4m) ]

   x  =  [ 4 ± √( 16 - 32m + 16m²) ) ] /  (8m)

   x  =  [ 4 ± √( 16( 1 -2m + m²) ) ] /  (8m)

   x  =  [ 4 ± 4√( 1 - 2m + m² ) ] /  (8m)

   x  =  [ 4 ± 4√( 1 - 2m + m² ) ] /  (8m)

  x  =  [ 4 ± 4√( m² - 2m + 1 ) ] /  (8m)

  x  =  [ 4 ± 4√( m - 1)²) ] /  (8m)

  x  =  [ 4 ± 4|m - 1|) ] /  (8m)

  x  =  [ 1 ± |m - 1|) ] /  (2m)

When  m - 1 > 0:  x  =  [ 1 + m - 1 ] / (2m)   --->   x  =  m / (2m)   --->   x = 1/2

When  m - 1 < 0:  x  =  [ 1 - (m - 1) ] / (2m)   --->   x  =  (2 - m) / (2m)