hectictar

Happy Birthday heureka!!!!

1.  a trapezoid

1.

midpoint of  (a, b)  and  (5a, -7b)   =   ( [a + 5a]/2 ,  [b + -7b]/2 )   =   ( 6a/2 ,  -6b/2 )   =   ( 3a, -3b )

Let's call the length of the class period  " p ".

From the problem statement, we can make this equation:

p  -  10%  of  p   =   45 minutes

p  -  0.1p   =   45 minutes

0.9p   =   45 minutes      (In other words, 90% of the class period is 45 minutes.)

                                       Divide both sides of the equation by  0.9 .

p   =   45 / 0.9 minutes

p   =   50 minutes          

Thanks!!

DB and DP trisect angle ADC,   so   m∠ADP  =  m∠PDB  =  m∠BDC  =  90° / 3  =  30°

∠ABD  and  ∠BDC  are alternate interior angles, so they have the same measure.

If we draw a line from  P to  BD  that is perpendicular to side BD, we will have congruent triangles.

The angle measures of these triangles are  30°, 60°, and 90° .

The side opposite the  60°  angle  =  1 , so

the side opposite the 90° angle  =  2 / √3

perimeter of triangle BDP   =  2  +  2/√3  +  2/√3   =   2  +  4/√3   =   2  +  4√3 / 3

2 + 4 + 3 + 3   =   12

343 /   125   =   (scale factor)³

scale factor   =   [343 / 125]^1/3

height of larger cylinder   =   5 * scale factor

height of larger cylinder   =   5 * [343 / 125]^1/3

height of larger cylinder   =   5 * 7 / 5

height of larger cylinder   =   7      feet

4.

\(\quad\,(7-\sqrt7)(-6+\sqrt7) \\~\\ =\,(7)(-6)+(7)(\sqrt7)+(-\sqrt7)(-6)+(-\sqrt7)(\sqrt7) \\~\\ =\,-42+7\sqrt7+6\sqrt7-7 \\~\\ =\,-49+13\sqrt7\)

35%  of what number is  21

35%  *  what number  =  21

35/100  *  what number  =  21       Multiply both sides of this equation by  100/35 .

what number   =   21 * 100/35

what number   =  60

35%  of  60  is  21

17 is what percent of  68 ?   In other words...

17 out of 68 is what out of 100  ?

17 / 68   =   what / 100

17 / 68 * 100   =   what

25   =   what

17  is  25  percent of  68 ,  as you found! 

what number is  16%  of  80

what number   =   16%  *  80

what number   =   16/100 * 80

what number   =   12.8

12.8  is  16%  of  80 ....You got it!!

\(\quad\,\frac{\sqrt3-\sqrt6}{\sqrt3+\sqrt6} \\~\\ =\,\frac{\sqrt3-\sqrt6}{\sqrt3+\sqrt6} \,\cdot\,\frac{\sqrt3-\sqrt6}{\sqrt3-\sqrt6}\\~\\ =\,\frac{3\,-\,2\sqrt{18}\,+\,6}{3\,-\,6} \\~\\ =\,\frac{9-2\sqrt{18}}{-3} \\~\\ =\,\frac{9-6\sqrt{2}}{-3} \\~\\ =\,-3+2\sqrt2\)