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I just started doing this when the pic disappeared.  Maybe it was copyrighted??

What are the end points for the linear segments.  

What is a^2 + b^2?

Hello Guest!

\(x^2 + 5x + 18 = 0 \\ x=-\frac{5}{2}\pm \frac{\sqrt{47}}{2}\cdot i\)

          a          b

\(a^2+b^2=\frac{25}{4}+\frac{47}{4}\)

\(a^2+b^2=6.25+11.75\)

  !

CPhill, your answer is incorrect.

The probability that exactly 3 dice show the same is \({5 \choose 3} \times {1 \over 6^3} \times{5 \over6^2} \times 6\). \(5 \choose 3\) ways to pick the rolls that are the same, \({1 \over 6}^3\) chance of 3 successes,  \({5 \over 6}^2\) chance of 2 failures, and 6 different trios of numbers that are the same. 

The probability that exactly 4 dice show the same is \({5 \choose 4} \times {1 \over6}^4\times {5 \over6} \times 6\). With the same logic as above.

The probability that all 5 dice show the same is \({1 \over 6}^5\times6\). 

Add everything up, and you get \(\color{brown}\boxed{23\over108}\)

1/x + 1/y  =  1/8     --->     1/y  =  1/8 - 1/x

                                         1/y  =  (x - 8) / 8x

                                            y  =  8x / (x - 8)

x + y  =  x + 8x / (x - 8)     --->     x + y  =  [ x(x - 8) ] / (x - 8) + 8x / (x - 8)

                                                              =  (x² - 8x + 8x) / (x - 8)

                                                              =  x² / (x - 8)

For values between 0 and 8, the value of x + y is negative.

For values above 8, the value is positive and increasing.

Thus, the smallest value of x + y occurs at the integer value x = 9.

You can find this value ...

Draw a vertical line from B. Label the point where it intersects AC point D.

 \(\triangle{ABD}\) is a 30-60-90 triangle. This means that BD is 10.

Using the Pythagorean Theorem, you find that AD is equal to \(\sqrt{300} = 10\sqrt3\).

To find DC, we need to use trig.

We use sin \(({\text{opposite}\over\text{hypotenuse}})\), and have: \({\sin(40)}={10\over{BC}}\)

This means that \(\color{brown}\boxed{BC \approx 15.55723}\)

Draw CX from point C perpendicular to line AD, with X on AD.

The length of CX is the distance from C to line AD.

Triangle(CXA) will be a right triangle with CA the hypotenuse.

Since triangle(DAB) is an isosceles right triangle with the right angle at B, 

angle(DAB) = 45^o.

This makes angle(CAD) = 45^o.

For triangle(CAX), sin( angle(CAX) ) = CX / CA.

--->                                      sin(45^o)  =  CX / 10

Finish this equation to find the length of CX, the distance from C to line AD.

y = 5/4 x + b     is the gneral form.....plug in the point given to solve for 'b'

1 = 5/4 (4) + b    shows  b = -4

y = 5/4 x -4    

unfortunately its not correct... thanks for trying, though!!

The smallest integer value of c is 12.

The equation of the line is y = 5/4*x - 2.

By the triangle inequality, the minimum distance is 12*sqrt(2) - 6.

can hey u help me with my homework please

I got the same answer as CPhill. 

Since the radii are equal length, thus the other angle is 50 degrees, and the central angle is 80 degrees. We can use law of cosines, so cos 80 is approximately 0.17, and the radii are 18 units each.

That means the length of the chord^2 = 18^2 + 18^2 - 2*18*18*cos80 degrees.

Length of chord^2 = 648 - 648*0.17.

We get:

Length of chord^2 = 535.476.

Length of chord is 23.14.

Thus, in terms of pi it would be approximately 7.3658pi.

:)

nope, but thanks for trying! 

Let the sides of the triangle be  a  and  b  and the hypotenuse  c.

c = 12

Area  =  ½·a·b   --->   4  =  ½·a·b   --->    a·b   =  8   --->   b  =  8 / a

a² + b²  =  c²   --->   a² + (8/a)²  =  12²   --->   a² + 64/a²  =  144

                                                                --->   a⁴ + 64  =  144a²

                                                                --->   a⁴ - 14a² + 64  =  0

Using the quadratic formula:  a²  =  [ 144 + sqrt(20480) ] / 2

                                   or         a²  =  [ 144 - sqrt(20480) ] / 2

Finding the square roots of the answers, either  a = 0.6677011      (approximately)

                                                                       or  a = 11.98140957  (approximately)

When a has either of these two values, b will have the other value.

From here, find the value of sinA =  0.6677011 / 12

                                       and sinB  =  11.98140957 / 12

(or vice versa, it makes no difference).

From here, use the formula for 2sin(x) = 2sin(x)cos(x)

to find your answer.

The only place where this occurs is at 45 degrees  

sin = cos =  sqrt(2)/2

thanks

Rewrite  -4  <  1/x  < 3  into its two parts:  -4  <  1/x   and   1/x  <  3

Divide the problem into two parts:

Part 1:  x < 0:

            (Remember that when you multiply both sides of an inequality by a negative number,

              you must change the sense of the inequality.

              Also remember that, for this part, x is negative.)

            -4 < 1/x   --->   -4x > 1   --->   x < -1/4

            1/x < 3   --->   1 > 3x   --->   3x < 1   --->   x < 1/3

            Since these two inequalities are combined by the word and, the solution to this

            part is the more restrictive of the two answers:  x < -1/4    

Part 2:  x > 0

             -4 < 1/x   --->   -4x < 1   --->   x > -1/4

             1/x < 3   --->   1 < 3x   --->   3x > 1   --->   x > 1/3

             The more restrictive of these two is:  x > 1/3

Since the answer consists of two parts, either Part 1 or Part 2, the final answer is the 

     region:  x < -1/4  or  x > 1/3

     which is:  (-inf, -1/4)  union  (1/3, inf)

0   and -3 and    -1  

Notice that all the numbers will be a factor of 9; no matter what x is, under certain conditions it will be a difference of multiples of 9.

Have you tried using the formula- \(d=st\) (or d=rt, whatever you want to call it); distance=speed*time.

X = 0

1+1/x=0

x+1=0

x=-1

1+1/(1+1/x) = 0

1 + 1/x + 1 = 0

2+ 1/x = 0

2x +1 = 0

2x = -1

x = -1/2

0+(-1)+(-1/2)=-3/2

10 and 2 o'clock.

9    and  3   o'clock

all the angles of a triangle add up to 180 degrees. 1+2+5=8 and 180/8=22.5 so angle a is 22.5, p is 45, and

i'll let you take it from here 

   hope this helps,

      XxmathguyxX