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2+2x>.6(13+x)

20+20x>78+6x

14x>58

x>58/14

x=5

:D

\(\displaystyle f(x)=2-\cos(x)+\sin^{2}(x) \\=2-\cos(x)+1-\cos^{2}(x) \\ = 3-\{\cos^{2}(x)+\cos(x)+1/4-1/4\} \\ = 3-\{(\cos(x)+1/2)^{12}-1/4\} \\ =13/4-(\cos(x)+1/2)^{2}.\)

So, max will be 13/4 when cos(x) = -1/2, and min will be 13/4 - 9/4 = 1, when cos(x) = 1.

A company makes triangular plates for individual slices of pizza. For each plate, the base is 9 inches and the height is 14 inches. The area of the top of the plate is ____ inches squared.     

The formula for the area of any triangle is one-half x base x height.  

  1 

–––  x  9 in  x  14 in  =  63 in²  

  2  

_.

I need that In an algebra way...

but thank you 

There are 8 vans and 52 non-vans.  Given that a non-van leaves, there are 8 vans and 51 non-vans, or 59 vehicles in total.

Hence, the probability that a van leaves next is 8/59.

Circles with radii 1 and 2 are inscribed in triangle ABC, as shown.  Find the area of triangle ABC.

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XY = 3       ZY = 1        WY = 2

∠BAW = sin^-1(1/3)

∠ABW = 90 - ∠BAW              ∠YBW = 1/2 (∠ABW)

BW = YW / tan(∠YBW)            AW = BW * tan(ABW)

[ABC] = AW * BW

That is really nice of you to say Pangolin.  Your solution is impressive as well.

Both of our solutions require a lot of geometry knowledge.  Especially if you were doing it under test conditions and could not look things

up.

For mine, and I think yours as well, the answerer would have to know that the point I is the centre of an incircle.  

For mine, an answerer needs to know the perpendicular distance formula. 

This was an interesting question and I am glad I was pushed to answer it without using trigonometry.

It would of course be nice to get proper feedback from the asker.  

Thanks, parpar  !!!

We can all use  more joy......and more peaches, too 

arc BD  = 4x 

And angle  DEA will intercept  an   arc of 90 +  BD =   90 + 4x

So...its measure  = (90 +  4x)   / 2

And angle CDE  = 3x

Let BC  and DC  intersect  AE  at   F and G respectively

Angle   FGC   = 180 - [ angle  DEA  + angle CDE ] = 180 -  [(90 + 4x)  /2  +  3x]

Angle  GFC  = 90 - BCA  = 90 - x

Angle BCD  =2x

So  ....in triangle  GFC  we  that

Angle FGC  + Angle  BCD  + Angle  GFC   =180

180 - [ (90 + 4x)  / 2  +  3x ]   + 2x + [   90 - x ]  = 180

180 - 45  - 2x   -  3x  +  2x  +  90  - x  = 180

 -4x  + 45   = 0

4x  = 45

x  = 45/4 =     11.25° = ABC

Let ∠ABC = x, ∠BCD = 2x , and ∠CDE = 3x. If ∠BAE is 90º, what is the measure of ∠ABC in degrees?

https://web2.0calc.com/questions/please-help_54385

(Answered brilliantly by thelizzybeth, Jun 25, 2020)

Let f(x) = 2 - cos(x) + sin(x)^2. Find the minimum and maximum values of f(x).

Hello Guest!

\(f(x) = 2 - cos(x) + sin^2(x)\\ \frac{df(x)}{dx}= sin(x)+2sin(x)cos(x) =0\)

\(sin(x)(1+2cos(x))=0\)

\(sin(x)=0\\ x=arcsin(0)\\ \color{blue}x_1=0\\ \color{blue}x_3=\pi =180^\circ\\ \color{blue}x_5=2\pi=360^\circ \)

\(1+2cos(x)=0\\ cos(x)=-\frac{1}{2}\\ x=arccos(-\frac{1}{2})\)

\(x_2=\frac{2}{3}\pi=120^\circ\\ x_4=\frac{4}{3}\pi=240^\circ\)

  !

Let's see if we can discover some pattern

20 , 10,  5, 16, 8, 4, 2, 1, 4, 2, 1

The pattern  begins a cycle of 4,2,1   after the 5th term

The  nth term  in the 3 number pattern  is  (n) mod 3  +  1

100 mod 3 + 1 =

1  + 1 = 

2nd term   =

2

We have  8 possibilities

-    -     -  =   -8

 -   -     +  =   0

-   +     +  =   6

+   +    + =   10

+   -     -  =    -4

+   +   -  =    2    

+   -    +   =  4

-   +    -    =  -2

We want all the  unique  sets of     3  people  chosen  from 5   and then all the arrangements of the elements in  those  sets

A permutation will do this 

P(5,3)   =   60   ways

Thx for helping :)

Hi Guest!

1 hour and 25 minutes = 85 minutes. 

So if it takes 10 minutes putting everything away, then it means she spent 75 minutes washing cars (85 - 10).

75 minutes for 3 cars means that each car takes 25 minutes to wash (75/3).

I hope this helped. :))))

=^._.^=

I think the answer is....

Let the number of $1    = x

Number of $2    =  11 + x

Number  of $3    =  x - 10

So

x +   (11 + x)  +  ( x -10)    = 100

Let the number of $1    = x

Number of $2    =  11 + x

Number  of $3    =  x - 10

So

x +   (11 + x)  +  ( x -10)    = 100

Can you take it from  here   ????

If it's divisible  by     x + 2  and x - 1    then  -2   and 1   are roots

Using synthetic division

-2  [  1        -1        1        -   p             q                  4                 ]

                  -2        6        -14          2p + 28       -4p -2q -56

       _______________________________________________

        1       -3         7      -p - 14       2p +q + 28      -4p - 2q  - 52    =  0  

Rearranging the last equation  we  have that

-4p - 2q =  52

-2p - q =   26     (2)

1   [   1       -  1           1        -   p              q                   4    ] 

                    1            0           1              -p + 1            -p + q  + 1

      _________________________________________________

          1        0           1       -p  + 1          - p + q +1       -p + q   + 5    =  0

Rearranging the last equation

p  - q  =  5

q =  p  - 5       (1)

Sub (1)  into (2)

-2p - (p - 5) =  26

-3p  = 21

p= -7

q =  p-5  =  -12

Hi Guest!

The biggest square length is 3*brown - green. 

3*(2) - (1) = 5. 

The second biggest square length is 5-1 = 4. 

The first side of the large rectangle is the largest square length + brown = 7

The second side is  large rectangle is largest square + second biggest square = 9.

Thus, the area is 7*9 = 63

I hope this helped. :)))

=^._.^=

1+2=3 so the side length of the square on the bottom right is 3.

1+3=4 so the side length of the square on the bottom left is 4.

4+3=7 so the width of the rectangle is 7.

2+2+2-1=5 so the length of the big square is 5.

5+4=9 so the length of the rectangle is 9.

7*9=63 so the area is 63

:D

A) The number of boxes were multiplied by 10 and the time by 2 so the number of machines must be multiplied by 10/2=5 meaning there are 16 additional machines.

B) We have two equations.5B=2M and 8(B+2)=3(M+7). Solving these gets us 12 bears and 32 monkeys so there are 44 total figurines.

C) 7W=10V and 8(W-3)=9(V+3). This gets us Winnie had 30 and Vincy 21. There are 51 total batches.

D) Lets set the uncle's age as U and the grandpa's as G. We are given 3U=G and 4(U-8)=G-8. Therefore U=24 and G=72. Grandpa is 72 years old.

E) Set gold ribbons as G and silver ones as S. We know that 2G=S and 4(G-10)=3(S-32) that gives us G=28 and S=56. Ms. Elizabeth started with 84 ribbons.

F) There are 6 drips every 20 seconds meaning there are 18 a minute. There are 121 minutes (including 10:00 and midnight) and 121*18=2178 so there are 2178 total drips.

:D

Hi websiteNOPE199,

The answer is 96390, you can just plug it into a calculator. 

Generally, I like to use the standard algorithm for multiplying large numbers. 

Here's a link to a video: https://www.khanacademy.org/math/cc-fifth-grade-math/multi-digit-multiplication-and-division/imp-multi-digit-multiplication/v/multiplication-6-multiple-digit-numbers

I hope this helped. :)))

=^._.^=