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(2)

Angle ADB > Angle DAB

Therefore   BD < AB

Remember  that in a triangle

Longest side is opposite the  greatest ange

Next longest side  is opposite the next greatest angle

Shortest side is opposite the smallest angle

(1) Angle ADC  =  180 -120 =  60

Angle CAD  =180 - 60 - 65  =  55

So  AD > AC  > CD

Angle ABD = 180 - 120 - 35  = 25

So

AB > DB > AD

Therefore

AB > DB > AD  > AC > CD

And  BC >  CD

So  CD is the shortest  side

I'm guessing because $r^2+r+1=0$

   comparing:              $ax^2+bx+1=0$

therefore a=1, b=1, therefore resulting in $a+b=2$

14!     15!       16!       are all  integral multiples of 49

(they all contain 14 * 7 =  2 * 7^2  =  2 * 49  which is a multiple of 49)

Hi Cphill, u are completely corrrect, but they ask for multiple values, I suspect in $(x-1)(x^2+x+1)$, we also have to solve for $(x^2+x+1)=0$ to get the other 2 values since it always have two values.

Not totally sure about this one.....but.....here's what I found

Using the  second equation

ax^2   +  bx  +  1   =  0

ax^2  +  bx  =  -1

x ( ax + b)  =   -1

ax + b =    -1/x

Sub this into the first equation

x^2  -  1/x   =    0      multiply through  by  x

x^3   -  1   =    0     factor as a difference  of  cubes

( x - 1)  (x^2  + x + 1)  =  0

Only the first   produces a  single real solution     x   = 1

So....using the first equation 

(1)^2  + a(1)  +  b   = 0

1  +  a +  b  =   0

a  +  b   =  -1

The x intercepts  are symmetrical  about the  x coordinate of the  vertex

The other x intercept  is   ( 12  - (15-12) )  =   ( 12  - 3)   =   9

(-7/16)  (1/3)   =   -7/48  inch per year

deleted 

Here's  my attempt :

The only  possible prime products are  2, 3  or  5

This  means that  3  of the  dice  must  show 1   and the  other  shows a 2, 3, or 5

The probability  is

Choose   any one of the  four dice to show  one of the primes *  probability of showing three 1s on three of the  dice *  probability of showing  one of the primes on the remaining  die = 

 C (4,1)  ( 1/6)^3  ( 3/6)  =  

1/  108

Thank you. I got this as well but I wonder if I can solve without using trig

Angle DAC  = Angle DCE

sin DAC =  sin DCE 

DC/ 100 = 36/DC

DC^2 =3600

DC =   60

AD  =sqrt (AC^2 - DC^2)    =sqrt (100^2  - 60^2)  =  sqrt ( 6400) =  80

EC  =sqrt  (DC^2 - DE^2)  =  sqrt  (60^2  - 36^2)    = sqrt (2304)  =  48

Triangles  DEB  and ADC  are similar

DB/ DE  = AC/ AD

DB / 36  = 100 /80

DB /36 =  5/4

DB  =  (5/4) 36   =  45

BE/  DB = DC/ AC

BE/45 =  60 / 100

BE/45 =  3/5

BE  = 45 * 3/5 =   27

So....the perimeter =  AC +  EC + BE  + DB + AD  =

100  + 48  +  27  + 45  + 80 = 

300

Hi Guest!

Background

--x = + x

-+x = -x

+-x = -x

++x = x

Following these rules, let's simplify the answer options. 

Simplifying

A. 35 + 7 - 5

B. 35 - 7 + 5

C. 35 - 7 - 5

D. 35 + 7 + 5

What is the question asking for?

The question is asking for how much she has left. 

Spending means she's subtracting from the total. 

Thus, our equation should be 35 - 7 - 5. 

Answer

Looking at our answer choices, it's clear that C is the same as 35 - 7 - 5, meaning our final answer is C. 

I hope this helped. :)))))

=^._.^=

Hi Guest!

Formula

First, we need to know the formula. 

|found - exact| / exact * 100

Variables

Found = 495

Exact = 500

Solving

|495 - 500| / 500 * 100

5/500*100

1

Answer

So, ther percent error was 1%

I hope this helped. :))))))))

=^._.^=

What is the largest positive integer n for which n^3+100 is divisible by n+1?

n^3 + 100 mod (n +1) =

(98^3 + 100)  mod (98 + 1) =

941,292 mod 99 == 0

I assme that    a =  1/5   b  =1/2      c  = 3     d   = -1/4

Note  that      1/  [ a * 1/c) ]  =   1/ (a/c)   =  c/a

So we have

c/a   +  1/ (b*d)   =

(3)  / (1/5)   +    1  / ( 1/2 * -1/4 )  =

(3) * (5/1)  +   1   /( -1/8)   =

15    -   8    =

7

( x + 4)^3  +  (x + 5)^3  = (x + 7)^3  + ( x - 4)^3

In the expansion of this, the  x^3  terms on each side will "cancel"  and we  are left with

3x^2(4) + 3x(4)^2  + 4^3  + 3x^2(5) + 3x*(5)^2 + 5^3  =  3x^2(7) + 3x(7)^2 + 7^3 - 3x^2(4) + 3x(4)^2  - 4^3

Simplify

12x^2  + 48x + 64  + 15x^2  + 75x  +125  =  21x^2  + 147x  + 343 - 12x^2 + 48x  - 64

27x^2  + 123x + 189 =  9x^2 + 195x + 279 

18x^2  - 72x  - 90  =  0       divide through by  18

x^2  - 4x -  5   =   0       factor

(x - 5) ( x + 1)   =   0  

Set each factor to 0  and solve for x and we  get that

x =  5       or   x =   -1

I'm not entirely sure, but I think that the largest possible length of the shortest side occurs when it's a rhombus.

Therefore, every side will be sqrt(3^2+4^2)=5, so 5's our answer

Red areas  =    3 ( area of  circular arc in each circle of 240° )  =  2* area of  circle with radius   =1 =   2pi

The white area is 1/2 of this   =   pi

Area of  hexagon  =    3sqrt (3)  (side^2)  / 2 =   3sqrt (3)    3sqrt (3) * 2^2  / 2 =   6sqrt (3)

Total of  red, green areas =  

2pi +  6sqrt (3) - pi  = 

pi + 6sqrt (3)  ≈    13.53

Area = (3√3 / 2 * a²) + pi

j, k  must  both be larger than  3

Let  3  = z

Let j =  z + a

Let k =  z +  b

We have

1/ (z + a)   +  1/ (z + b) =  1/z

(z+ a  + z +b)  / [( z+ a) (z + b)=  =  1/z     cross-multiply

(2z  + a + b) z  =  (z + a) (z + b)   simplify

2z^2  + az + bz =   z^2  + az + bz  +  ab     

z^2   =   ab

3^2  =   9

Factors of  9    =  1, 3,  9

a  b          z +  a  =   j               z +  b  =     k  

1  9          3 +  1  =   4              3  + 9  =   12

3  3          3  + 3  =   6              3 + 3  =     6 

9  1          3  + 9  =  12             3 + 1  =     4

18/sin 50 = x / sin 80

x = 18 sin 50  * sin 80  = 23.14035         But I had to use trig ,,,,,,,

Thank You. I am not sure how to solve this without using trig

Here is pic