hectictar

HMMMMM I see what you did there......   👀    

Haha thank you! We'll see about that college stuff...I have a feeling that I'm gonna be asking a bunch of questions on here when that time comes... 

From looking at this, we can see that

CD  =  14 - (2 + 5)

CD  =  7

And...

AC  =  2 + 5  =  7

BD  =  5 + 7  =  12

So, the ratio of AC to BD   =   \(\frac{AC}{BD}\)   =   \(\frac{7}{12}\)

Let's find the two points on the parabola that touch the line y = 5 .

y  =  x² + 3x + 2             We want to find the  x  values when  y  is equal to  5  .

5  =  x² + 3x + 2             Subtract  5  from both sides of this equation.

0  =  x² + 3x - 3              Use the quadratic formula to find  x  .

x  =  \({-3 \pm \sqrt{21} \over 2}\)

Four children have small toys. The first child has 1/10 of the toys, the second child has 12 more toys than the first, the third child has one more toy of what the first child has and the fourth child has double the third child. How many toys are there? 

Let's call the total number of toys  " t " .

first child's toys  =  t/10

second child's toys  =  12 + first child's toys  =  12 + t/10

third child's toys  =  1 + first child's toys  =  1 + t/10

fourth child's toys  =  2 * third child's toys  =  2 * (1 + t/10)  =  2 + 2t/10

So.....

t  =  first child's toys + second child's toys + third child's toys + fourth child's toys

t  =  ( t/10 ) + ( 12 + t/10 ) + ( 1 + t/10 ) + ( 2 + 2t/10 )

t  =  t/10 + 12 + t/10 + 1 + t/10 + 2 + 2t/10                     Combine like terms

t  =  5t/10 + 15

t  =  t/2 + 15                Subtract  t/2  from both sides.

t - t/2  =  15

t/2  =  15                     Multiply both sides by  2  .

t =  30

1.

The question is...

$8,880  is  6%  of what number?               Let's call the number  " p " for selling price.

$8,880  =  0.06 * p                                      Divide both sides by 0.06

$8,880 / 0.06  =  p

$148,000  =  p

The question is...

1300  out of  3000  is  what  out of  100

\(\frac{1300}{3000}\,=\,\frac{\text{what}}{100} \\~\\ 0.4\overline3\,=\,\frac{\text{what}}{100} \\~\\ 0.4\overline3\,*100=\,\text{what} \\~\\ 43.\overline3\,=\,\text{what}\)

So...

1300  out of  3000  is  43\(\frac13\)  out of  100  .

1300  out of  3000  is  43\(\frac13\)  %

73,  89,  81,  95,  87

The highest value in the list is  95  .

The lowest value in the list is  73  .

range  =  highest value - lowest value

range  =  95 - 73

range  =  22

3x² + 7x - 6

Multiply the  3  and  -6  together to get  -18 .

What two numbers add to  7  and multiply to  -18  ? →  +9  and  -2

So...we can split the middle term like this...

=  3x² + 9x - 2x - 6            Now factor a  3x  out of the first two terms.

=  3x(x + 3) - 2x - 6            Now factor a  -2  out of the last two terms.

=  3x(x + 3) - 2(x + 3)         Now factor a  (x + 3)  out of both remaining terms.

=  (x + 3)(3x - 2)