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The largest possible value of b is 5.

f(2) = 1/4.

You get equality when a = b = c = 0.

First of all   x cannot = 2  or  -2   because the denominator would be zero....not allowed

  the denomintor factors to  (x-2)(x+2)

(x+1) /  (x-2)(x+2)   >0            so look at the intervals from   - inf to -2     then   -2  to -1    then   -1 to 2   then  2 to +inf

                                                                                                    <0                        >0                      <0                >0

so   x can be        (-2,-1) U (2, + inf)          (remember x cannot = 2 or -2    and at x = -1 the fxn = 0            

Factor the denominator to get

(x+1)/[(x+2)(x-2)]

and then check what happens around all the critical points (-2, -1, 2) to see that the solution is (in interval notation):

(-2, -1) U (2, ∞)

Hope this solution helps!

it seems like you are missing some numbers in the question. If you reply to this with the complete form of the question I will answer it for you in a bit. Your question seems similar to this one though:

to solve the question, you need to find all the multiples of 16 and 25, and then subtract the overlap.

4000/16 = 250, so there are 250 multiples of 16 that work.

4000/25 = 160, so there are 160 multiples of 25 that work.

The overlap in this question occurs when a number is divisble by both 16 and 25. We counted those overlapping numbers twice so we need to go back and subract them off once.

4000/(16*25) = 4000/400 = 10, so there are 10 overlapping numbers.

The final answer to this problem, therefore, is 250 + 160 - 10 = 400

Hope this solutions helps!

It is not 12... but thank you for your time

An x between 0 and 360 which satisfies the given sine and cosine is 

x = 150˚

Now we need to find 2520/360, which is 7. 

All that is left to do is add 2520 to 150, which is 2670˚.

I hope this solution helps!

You can just brute force this one:

6 cases:

• all 6 blue
  • this case is pretty easy to see, (6,0). 1 solution for this case.
• 5 blue 1 green
  • two people sit next to the person with green eyes and everyone is sitting next to someone with blue eyes (6, 2). 1 solution for this case as well.
• 4 blue 2 green 
  • if the greens are next to each other, there is one solution (6, 2)
  • if the greens are one apart, there is another solution (6, 3)
  • if the greens are two apart, there is one more (6, 4), for 3 solutions in this case. 
• 3 blue 3 green
  • all 3 greens next to eachother (5, 5)
  • 1 green separate from the other 2 (5,5)
  • blue and greens alternate (3,3). In this case we have a repeating solution so only 2 more posibilities. 
• 2 blue 4 green
  • same as the 4 blue 2 green, just flipped for 3 more solutions.
• 1 blue 5 green
  • same as the 5 blue 1 green, just flipped for 1 additional ordered pair.
• all 6 green
  • same as all 6 blue, just flipped for 1 additional ordered pair.

Adding up the bolded numbers, we get a final answer of 12 ordered pairs.

Hope this solutions helps!

Parallel lines cut off equal arcs of a circle.

Since EF || GH, arc(EH) = arc(FG).

This means that  x² - 2x  =  56 - 3x.

Solve this equation for x.

Use that value of x to find the size of arc(EH) and arc(FG).

The size of arc(GH) is given.

Use these arcs to find the size of arc(EPF).

Amount of ammonia to start    .8 ( 5 gal)

drain some amount x to replace with water

amount of ammonia  removed  = .8x

add water then have 5 gallons of 50%      =    .5 (5)

.8(5)  - .8x = .5 (5)         x is the amount removed and replaced with water (in GALLONS....You will need to convert to quarts)

.8 x   +   .4(10)    =  .64 (10+x)     solve for x

Angle U =40                 (which is 1/2 of 80)

Angle V = 17.5             (1/2 of 35)

angle Y = 180-40-17.5 = 122.5^o

the equation of the circle you described is

(x-5)²+(y-15)²=130

we are also told that

x = 2y

now all we do is substitute in 2y for x and solve:

(2y-5)²+(y-15)²=130

4y²-20y+25+y²-30y+225=130

y²-10y+50=26

y²-10y+24=0

(y-4)(y-6)=0

so y=4 or y=6

but since we are looking for the maximum value of x, and 2y=x, we want the larger y, 6.

Plugging this into 2y=x, we get

2(6)=x

x=12

Hope this solution is helpful!

The slope of -3/2 means that for every 3 you go down in the plane, you go to the right 2. To get from -2 to 4 for x, you need to move right 6, so you need to move down 9 to stay on the line described, which will bring you to the point (4, -2). So,

y = -2

Hope this helps!

$10,000  x  10%  x   5 years =$5,000  Simple interest earned over 5 years.

$10,000 + $5,000 = $15,000 Total principal + interest over 5 years.

We can start off by simplifying this expression:

3(x - 4) + 4(7 - 2x^2 + 5x) - 8(2x - 1)

3x - 12 + 28 - 8x^2 + 20x - 16x - 8

3x + 16 - 8x^2 + 4x - 8

7x + 8 - 8x^2

Coefficient of x is the number in front of x.

Which means the coefficient of x in 7x is 7.

The Solar System as a whole orbits the center of the Milky Way Galaxy at ~2 million Km/hour.

Starting with  3x² - 24x + 55

write it in the form  a(x + d)² + e

We will need to complete the square and factor out a number ...

The number that we can factor out of the x² term and the x term is 3:

    3x² - 24x + 55

=  3(x² - 8x) + 55

Now, we need to complete the square:

=  3(x² - 8x + 16) + 55 - 48

Factor:

=  3(x - 4)² + 7

Your turn ...

Thank you!!!

thank you!

Circumference of circle A:  C  =  2·pi·r   --->   C  =  2·pi·12  =  24pi

The portion of the circumference of 4pi is  4pi / 24pi    1/6

1/6^th of the circle would be 60^o.

Circumference of circle :  C  =  2·pi·r   --->   C  =  2·pi·3  =  6pi

The portion of the circumfBerence of pi is  pi / 6pi    1/6

1/6^th of the circle would be 60^o.

These central angles are congruent.

                   2x² =  -2y² + 12x - 4y + 20

Divide by 2:  x² =  -y² + 6x - 2y + 10

Rearrange:                           x² - 6x      + y² + 2y        =  10

Complete the square on x:  x² - 6x + 9 + y² + 2y        =  10 + 9

Complete the square on y:  x² - 6x + 9 + y² + 2y + 1  =  10 + 9 + 1

Simplify:                                           (x - 3)² + (y + 1)² =  20

This means the the center is at (3, -1) and the radius:  r  =  sqrt(20)

So the width of the square is twice the radius:  width  =  2·sqrt(20)

And th area is:  [ 2·sqrt(20) ]²  =  4·20  =  80