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The radius of the red circle is $\frac{9 - 2 \sqrt{3}}{5}$, so the answer is 9 + 2 + 3 + 5 = 19.

Solutions are x = -1 and 1   means

(x+1)(x-1) = 0

x^2 +0x -1 = 0    multiply by -2 to get correct form

-2x^2 + 0x +2 = 0     a = -2      b= 0

Largest = 15.5      smallest = 1.5     middle = 9.5

look at this ---> https://web2.0calc.com/questions/linda-miah-and-noah-are-all-wearing-hats-with-numbers

Hi guest. 

I really like your solution, but I don't think AOD = 180 - BOC. 

Instead, I think we need to start with the fact that AOC = 90 and COA = 90 since lines are perpendicular. 

=^._.^=

A line goes through (2, 3) and (−8,2). The line has an x-intercept of P and a y-intercept of Q. Find the area of triangle OPQ

First I would find the equation of the line.

I think it is easiest to do this by introducing the  general point (x,y)  and then saying  gradient = gradient

\(\frac{y-3}{x-2}=\frac{2-3}{-8-2}\)

now simplify that.

Then find the x and y intercepts

Then use the area of a triangle formula

So how many numbers are there between 25 and 250 inclusive?

The prime numbers from 1-10: 2, 3, 5, and 7.

This means a 2/5 chance of rolling a prime number on 1 die. Thus, three dice have an 8/125 chance of rolling all prime numbers.

The chance that 1 die doesn't roll a prime number is 3/5, which comes from 1-2/5. This gives a 24/625 chance for one arrangement of dice rolls (i.e. PPPN). To find the total number of arrangements, we do 4 choose 3 = 4. Since there are 4 different ways to obtain this result, our answer is multiplied by 4 to get 96/625.

See https://web2.0calc.com/questions/quick-need-it-quick

Probability = favorable/possible

Possible = 13 choose 3 = 286

Favorable = 5 choose 1 * 6 choose 2 = 75

Answer: 75/286

see https://web2.0calc.com/questions/help_51882

The point-slope form of a line is y-y_1=m(x-x_1), where a point is (x_1, y_1). The slope of our line is (7-(-1))/(1-7) = -4/3. Thus, we may input (1,7) into y-y_1 = -4/3(x-x_1), getting y-7 = -4/3(x-1), so y=-4/3x + 4/3 + 7 = -4/3x + 25/3.

m+b = 7

I don't think there is a question here...?

56 = 8 * 7. This means that 8*11 mod 56 is equivalent to 8*4 mod 56, or 32.

Since 2*5 = 10, the answer is 32 + 10 = 42

Input x=1. a + b + 2 = 0.

Input x = -1. a - b + 2 = 0.

Add the equations: 2a+4=0 --> a=-2

-2 + b + 2 = 0, so b = 0. 

If giving 1/4 causes a 52  difference then  1/4 = 26 dollars and the each have 104  for a total of 208 dollars

6 + 3 + 3 + 1.5 + 1.5 + .75 + .75 =..........ft

How did you get 7/2?

This problem has a nice solution.

Notice that 1/x + 1/y = (x+y)/(xy). Thus, (xy)/(x+y) = 80. Mutliplying by x+y, we have xy = 80x+80y. This simplifies to xy - 80x - 80y = 0. 

Factoring out an x from xy-80x, we get x(y-80) - 80y = 0. A factoring tactic called SFFT will help here, to turn -80y into -80(y-80). This means we must add 80^2 = 6400 to both sides, getting x(y-80) -80y+6400 = 6400. This turns into x(y-80)-80(y-80)=6400, so (x-80)(y-80)=6400.

The sum x+y is minimized when x and y are the closest together, which you can estimate by taking √6400, or 80. The closest such x and y are 64 and 100, giving an answer of 164.

It seems you've worked out the steps to the answer; do you still need help?

A power of 4 is simply 2^(even integer). We must thus avoid even powers of 2. 

Since 2^10 = 1024, (2^10)^2 = 2^20 is a bit larger than 1,000,000. Thus, 2^19 will probably be the largest power of 2 less than 1,000,000. 

We then count all the odd numbers from 19 to 1, which accounts for 10 numbers.

See https://web2.0calc.com/questions/help-please_50938 for more information.

The greatest difference we may have is 18 (19-1), and the smallest is 2. Since all of these numbers are separated by 2, we can make all of the even numbers from 2 to 18, which accounts for 9 numbers. Notice that since all of the numbers are of the form 2a+1 (where a is an integer), their difference must be divisible by two, which means we can only have even numbers. Thus, the answer is 9.

[  5 / sqrt(80)  +  sqrt(845) / 9  ]   /   sqrt(5)

=  [  5 / sqrt(80)  +  sqrt(845) / 9  ]   x   [ 1 /  sqrt(5) ]

=  [  5 / sqrt(80) ]  x  [ 1 /  sqrt(5) ]    +    [ sqrt(845) / 9  ]  x  [ 1 /  sqrt(5) ]

=  [  5 / sqrt(400)  ]    +    [  sqrt(169) / 9  ]

=         5 / 20             +            13 / 9                     =     ...

At first, Tom's savings  =  x     and Sean's savings  =  x.

After Tom gave Sean  1/4  of his savings, Tom had  x - 1/4x  =  3/4x

                                                         and Sean had  x + 1/4x  =  5/4x

At this time, Sean had 52 more than Tom:  Tom + 52  =  Sean

                              --->                                 3/4x + 52  =  5/4x

                                                                                52  =  2/4x     --->     x  =  104  (to start with)

Now, Tom has  3/4(104)  =  78     and     Sean has  5/4(104)  =  130     for a total of  208.

Let  x  =  the number of diners:     604 + 5x  =  988 + 3x

Solve the above equation for x; this will be the number of diners.

How much?  Use the above answer in either the expression   604 + 5x   or   the expression   988 + 3x