All Answers 356055 Answers

Why don't you become a member.

You seem like someone that answerers would like to know.

I am very aware that there have been a lot of registration problems lately but Admin hopes he has now fixed them.

If they are not fixed then the notigfications/complaints need to keep coming in. 

If you register then you could let us know if you had any problems ;)

Your right the first one is the best.

If you forget to do it then try the second one.  But you are right occasionally it refuses to cooperate.

If the second one fails then you can use the third one.

Alo:

Sometimes it is also impossible to get the Latex back up for editing which is the main reason why i usually add the Latex (not rendered) at the bottom of the post.  I figured someone would eventually ask me why I did this. But noone ever has :))

Mind you, I also leave the unrenedered LaTex there becasue someone might learn something from it. 

Thanks Melody.

Your first suggestion seems to work perfectly and that's what I'll be using from now.

I can't get the yellow box idea to work consistently though, probably something I'm doing wrong.

I actually used a different, although probably not easier method to Slimesewer

I said that if the ratio fo areas is 2 to 9 

then the ratio of the sides is   sqrt2  to  sqrt9

hence on my pic the first sides I could label were   sqrt(2) *x     and    3x

Then I took it from there.

I got the same as slimesewer, good work!

Sorry Chris, I believe you made a mistake somewhere.  

I draw the scale pic (just for fun)

I counted 

2(3+13+16+13+3) = 96

I will do the more difficult one and then you can almost copy and do the easier one.

'a' is a negative number so to stop my own confusion I let   a=-t    (so t is positive)

Now

cos(-t) = 0.8         (4th quad)

cos(t)=0.8

\(c=cos(-t+\frac{\pi}{6}) \\ c=cos(\frac{\pi}{6}-t )\\ c=cos(\frac{\pi}{6})cos(t)+sin(\frac{\pi}{6})sin(t)\\ c=\frac{\sqrt3}{2}*0.8+\frac{1}{2}*0.6\\ 10c=\frac{\sqrt3}{2}*8+\frac{1}{2}*6\\ 10c=4\sqrt3+3\)

If you do not understand then ask specific question, the mothod is almost identical.

LaTex:

c=cos(-t+\frac{\pi}{6}) \\
c=cos(\frac{\pi}{6}-t )\\
c=cos(\frac{\pi}{6})cos(t)+sin(\frac{\pi}{6})sin(t)\\
c=\frac{\sqrt3}{2}*0.8+\frac{1}{2}*0.6\\
10c=\frac{\sqrt3}{2}*8+\frac{1}{2}*6\\
10c=4\sqrt3+3

PV ==1,005,962 / 1.10^20 ==R 149,529.84

PV=149529.84;D=1700;R=0.10;N=20;PMT=0;PMT = -(R* (R + 1)^N *((D *(R + 1)^(-N)* ((R + 1)^N - N* R - 1))/R^2 - PV))/((R + 1)^N - 1)

PMT==R 6,500.00 - first annual payment.

Okay so if you have a graphing calculator (Ti-84 Plus maybe) there is a way to figure out i on your calculator. You press the blue button that says 2ND then press the decimal button and you get the i for imaginary numbers. But anywho,

i+2i^2+3 can be simplfied down to...

i+(-2)+3

=i+1

Sum == 1 / [1 - ( - 1/5)] ==1 / [1 + 1/5] ==1 / [6/5] ==5/6 [geno3141 made a small typo]

Let the area of small square he S

Shaded area be x.

Unshaded area be y.

as the largest square is made up of shaded and unshaded area So area of largest square = x + y.

Now given ratio of area of smallest square to largest square is 2:9.

i.e.                   S/(x + y) = 2/9 - 1

ratio of shaded area & unshaded area is 3:7.

(Shaded area)/(Unshaded area) = 3/7

x/y = 3/7

7x = 3y

y = 7/3x

put value of y in 1

S/(x + 7/3x) = 2/9

9s = 2(x + 7/3x)

9s = 20x/3

27/20 = x/s

27/20 = (Shaded area)/(Smallest Square)

Ratio of shaded area to the area of smallest square is 27:20

\(\left(h,\:k\right)=\left(\frac{77}{6},\:9\right),\:p=-\frac{3}{2}\)

Some Info I know so far is tan(a)=5/2, tan(b)=1/2 and tan(b+gamma)=3/2

First:  find the three values f(100), f(101), and f(102).

Then, go to https://www.calculatorsoup.com/calculators/math/factors.php 

This is a site that will find all the factors of these numbers.

Use this site to find your answer.

Placing the expression into graphing form:

                     y  =  3x² + 16x + 4  

                y - 4  =  3x² + 16x                            Place the  4 on the other side

                y - 4  =  3(x² + 16/3x       )                Factor out the 3

     y - 4 + 64/9  =  3(x² + 16/3x + 64/9)            Complete the square

           y + 28/9  =  3(x² + 16/3x + 64/9)            Simplify

          y  +  28/9  =  3(x + 8/3)²                             Factor

                       y  =  3(x + 8/3)² - 28/9                Rewrite

There is still a little left for you to do ...

This is a geometric series with first term = 1 and common ratio = -1/5.

Using the formula for an infinite geometric series with a common ration -1 < r < 1:

      Sum  =  1 / ( 1 - 1/5)  =  1 / (4/5)  =  5/4.  

If the average (mean) of 10 numbers is 85, then the sum of the numbers is 10 x 85  =  850.

Removing the numbers 70, 76, and 77, we get:  850 - 70 - 76 - 77  =  627.

There are now 7 numbers remaining, so the average of these 7 numbers is 627 / 7  =  89.57...

How long is each leg of the triangle?

\(\color{blue}c=14\\ {\color{blue}a=b=}\sqrt{2\cdot (\frac{c}{2})^2}=\frac{c}{2}\cdot \sqrt{2}=\color{blue}7\cdot \sqrt{2}\)

  !

thanks

8x² - 32x + 32  =  8(x² - 4x + 4)  =  8(x - 2)(x - 2)  has double root = 2.

235 ( 6 ) , 236 ( 6 ) , 237 ( 6 ) , 255 ( 3 ) , 256 ( 6 ) , 257 ( 6 ) , 266 ( 3 ) , 267 ( 6 ) , 355 ( 3 ) , 356 ( 6 ) , 357 ( 6 ) , 366 ( 3 ) , 367 ( 6 ) , 556 ( 3 ) , 557 ( 3 ) , 566 ( 3 ) , 567 ( 6 ) , 667 ( 3 ) , >>Total combinations = 18 [The numbers in brackets are the number of permutations of each combination]

>>Total number of permutations = 84

But is says that it is wrong

The point that must be on the graph is (7,9).

The answer is 3/5.  (This is the repeated root of 25x^2 - 30x - 9.)

A quadratic has a double root when the discriminant \(b^2-4ac\) is equal to \(0\).

~

Rearraging the equation grants \(x^2+bx+9=0 \Longrightarrow\) \(a = 1, b = b, c = 9\)

~

\(b^2 - 4(1)(9) = 0\)

\(b^2 = 36\\ b = \boxed{\pm 6}\)