SOLUTION: You roll a red die and a green die. What is the size of the sample space of all possible outcomes or rolling these two dice, given that the red die show an odd prime number and the

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Question 352149: You roll a red die and a green die. What is the size of the sample space of all possible outcomes or rolling these two dice, given that the red die show an odd prime number and the green die shows an even number? .23
Answer by ulidelri94@yahoo.com(1) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-3=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%28-2%29-sqrt%28+16+%29%29%2F2%5C1+=+-1

Quadratic expression 1x%5E2%2B-2x%2B-3 can be factored:
1x%5E2%2B-2x%2B-3+=+1%28x-3%29%2A%28x--1%29
Again, the answer is: 3, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-3+%29
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+2%2C%0D%0A++++1%5Cx+%2B+-1%5Cy+=+0+%29%0D%0A++We'll use substitution. After moving 1*y to the right, we get:
1%2Ax+=+2+-+1%2Ay, or x+=+2%2F1+-+1%2Ay%2F1. Substitute that
into another equation:
1%2A%282%2F1+-+1%2Ay%2F1%29+%2B+-1%5Cy+=+0 and simplify: So, we know that y=1. Since x+=+2%2F1+-+1%2Ay%2F1, x=1.

Answer: system%28+x=1%2C+y=1+%29.
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • Graphical form: x%5E2-2x simplifies to 3
  • Text form: x^2-2x simplifies to 3
  • Cartoon (animation) form: simplify_cartoon%28+x%5E2-2x+%29
    For tutors: simplify_cartoon( x^2-2x )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+x+%29%5E2-2%2Ax.
Replaced x with 3
It becomes highlight_green%28+3+%29%5E2-2%2Ax.
Look at highlight_red%28+3+%29%5Ehighlight_red%28+2+%29-2%2Ax.
Replace constants in factor: highlight_red%28+3+%29,highlight_red%28+2+%29 with highlight_green%28+9+%29
It becomes highlight_green%28+9+%29-2%2Ax.
Look at 9-2%2Ahighlight_red%28+x+%29.
Replaced x with 3
It becomes 9-2%2Ahighlight_green%28+3+%29.
Look at highlight_red%28+9+%29-highlight_red%28+2%2A3+%29.
Replace constants in expression: highlight_red%28+9+%29,highlight_red%28+-2%2A3+%29 with highlight_green%28+3+%29
It becomes highlight_green%28+3+%29.
Result: 3

Universal Simplifier and Solver


Done!
Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation 4+x+%2B+2+y+=+8 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+-4%2F2.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 8/4 = 2.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 8/2 = 4.
  • Slope is -4/2 = -2.
  • Equation in slope-intercept form: y=-2*x+4.
graph%28+500%2C+500%2C+2-8%2C+2%2B8%2C+4-8%2C+4%2B8%2C+-2%2Ax%2B4+%29+
Solved by pluggable solver: Linear System solver (using determinant)
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+2%2C%0D%0A++++1%5Cx+%2B+-1%5Cy+=+0+%29%0D%0A++

Any system of equations:


has solution

or



(x=1, y=1}