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Welcome! :D

thank you for it! :)

Let's factor these out!

x^2-4x-32=0

=(x-8)(x+4)

So, the solutions are x=8 and x=-4.

The difference between these solutions is 12.

So, our answer is 12.

26 letters - 2 = 24 letters

choice of 24 letters for first letter
since letters can be repeated we have 24*24 = 576 letter combinations

now we have ten numbers, 0 through 9
again they can be repeated
(AA0000 is allowed)
10^4 = 10,000
so
576 * 10,000 = 5.76 * 1,000,000
= 5,760,000 

now answerd!

How many prime numbers p exist such that p 2 + 2 is also a prime number? 

Before I go to the trouble of trying to find an answer, I need to know does p 2 + 2 mean p² + 2 ? 

The first thing you can do is eliminate all even numbers because no even number is prime, except 2. 

That is hard!!! I will try to attempt it, but I'm not sure I'll get it!

1. a \star b= 2a+3b

We plug in 4 and 3 for a and b. We have:

4 \star 3=2(4)+3(3)

4\star3=8+9

4\star3=17.

2. We plug in 50 for N in the given equation. Our answer is 8.

3. We can add all  equations together to get 2a+2b+2c=0. Then a+b+c=0. c must be -8, a must be 3, and b is 5. The product of abc is -8(3)(5)=-8*15=-120.

4. We prime factorize 756 to get 2^2 • 3^3 • 7. Mode is the number that appears most in the set. Since 3 appears 3 times in the prime factorization, which is the most, 3 is the mode of his list.

Volume of a pyramid is lwh/3. We plug in the length, width, and height into the equation.

lwh/3

=4(6)(6)/3

=144/3

=48 ft^3

To center something that is 2 1/2 inches wide in an area that is 3 3/4 inches wide:

1)  subtract  2 1/2 from 3 3/4   --->   3 3/4 -  2 1/2  =  1 1/4

2)  divide this answer by 2 so that there is an equal amount on each side:

               1 1/4  /  2  =   5/4  /  2  =  5/4 x 1/2  =  5/8

60 out of 100  =  60/100  =  0.60  =  60%

36%

0.589  =  58.9%

Which percentage is greatest?

Circle A has radius 5, and Circle B has radius 2. If CD = 12 and is a common tangent, what is AB?

Hello Guest!

\(\overline {AB}^2=12^2+(5-2)^2\\ =144+9\\ =153\\ \overline{AB}= \sqrt{153}\)

\(\overline{AB}=12.369\)

  !

Originally, there is a right triangle:  call the length of the pole "p"

At first, the distance from the bottom of the pole to the wall is "g"

and the distance from the top of the pole to the ground is 8.

--->   p²  =  g² + 8²

If the pole is moved another 2 feet from the wall, it will lie on the ground; now the distance from the bottom of the 

pole to the wall is  g + 2; so  p  =  g + 2.

Substituting  "g + 2" for "p" in the above equation:  (g + 2)²  =  g² + 8² 

                                                                           g² + 4g + 4  =  g² + 64

                                                                                   4g + 4  =  64

                                                                                         4g  =  60

                                                                                           g  =  15

The pole is  g + 2  =  17

No matter what n is, a = 7

7 mod 9 = 7

log(x + 4) + log(3x + 2)  =  log( (x + 4)(3x + 2) )  =  log( 3x² + 14x + 8 )

log(100) - 2log(2)  =  log(100) - log(2²)  =  log(100) - log(4)  =  log(100/4)  =  log(25)

Combining:  log( 3x² + 14x + 8 )  =  log( 25 )

--->                        3x² + 14x + 8  =  25

--->                        3x² + 14x -17  =  0

--->                      (3x + 17)(x - 1)  =  0

--->     either  3x + 17  =  0            or     x - 1  =  0

                                x  =  -17/3     or           x  =  1

The answer  -17/3  doesn't check; the answer  1  does.

Since  f(-4)  =  -60/13 

and     f(-4)  =  (a/b)x,

then a possibility is:   f(-4)  = (15/13)(-4)   --->   a = 15  and  b = 13

[other possibilities are multiples of  (15/13)]

Let's see what happens with f(4)   --->   f(4)  =  a·b·(4)²  =  (15)·(13)·4²  =  3120.

Since this checks out,  a = 15  and  b = 13.

My computer says there are 292 such numbers. if you want a list of them, then let me know.

Note: I did not include "perfect squares", such as 4, 9, 16.....etc.

Step 1:  Mark point "X" on AC at the end of the blue line segment.

Step 2:  BX = DC   --->   BX = ...

Step 3:  XC = BD   --->   XC = ...

Step 4:  AX = AC - XC   --->   AX = ...

Step 5: Use the Pythagorean Theorem on triangle(AXB) to find AB ...

A/B  = a/8

B/C= 12/c

A/B * B/C    =   a/8 * 12/c

A/C = 12a/8c    =   2/1

      soooo   12a = 16c

                     a/c  = 16/12  =   4/3

yeah forumofweb2.0cal do your own homework