Answer: first: 1/6 second dice: 4/6
Step-by-step explanation:
So we know that a dice have the numbers 1,2,3,4,5, and 6 .
So the the probability that first die rolled 2 is 1/6 because there appears only on 2 .
and the probability that the second dice rolled a number greater than 2 is 4/6 or 2/3 because there are 4 numbers greater than 2 out of the 6 total .
Answer: There are no real roots.
Step-by-step explanation:
To find the roots of the function
f(x) = (2^x − 1) - (x2 + 2x − 3) with x ∈ R.
First open the bracket
2^x - 1 - x^2 - 2x + 3 = 0
Rearrange and collect the like terms
2x^2 - x^2 - 2x + 3 - 1= 0
X^2 - 2x + 2 = 0
Factorizing the above equation will be impossible, we can therefore find the root by using completing the square method or the quadratic formula.
X^2 - 2x = - 2
Half of coefficient of x is 1
X^2 - 2x + 1^2 = -2 + 1^2
( x - 1 )^2 = - 1
( x - 1 ) = +/- sqrt(-1)
X = -1 + sqrt (-1) or -1 - sqrt (-1)
The root of the function is therefore
X = -1 + sqrt (-1) or -1 - sqrt (-1)
Since b^2 - 4ac of the function is less than zero, we can therefore conclude that there is no real roots
I'm thinking this is what the problem looks like:

. The first thing to do is to move the

over to the other side because it has a common denominator with the other side. Doing that and at the same time combining them over their common denominator looks like this:

. The best way to solve for x now is to cross-multiply to get 3(4-x)=-4(x-4). Distributing through the parenthesis is 12 - 3x = -4x + 16. Solving for x gives us x = 4. Of course when we sub a 4 back in for x we get real problems, don't we? Dividing by zero breaks every rule in math that there ever was! So, yes, the solution is extraneous.
This is a form of the Pythagorean Theorem. We just need to know how far we went in the x direction and how far in the y direction then use
a^2 + b^2 = c^2 to find the value.
distance in the x direction (-4 to -4) that's easy it didn't move. so that is zero and thus would make the distance all in the y direction.
To move from 8 to -8 we take (8 - (-8)) = 8 + 8 = 16 which is your answer
6. What is one reason why the calculated area of the squash field would be useful to