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Let's consider the two colors Sam has as color A and color B. We can list out the possible ways he can color the equilateral triangle:

1. All three sides have color A (AAA).
2. All three sides have color B (BBB).
3. Two sides have color A and one side has color B (AAB).

Note that when the triangle has two sides of color A and one side of color B, there is only one distinct coloring, as rotating or reflecting the triangle would still result in the same AAB configuration.

Therefore, Sam can color the equilateral triangle in 3 different ways.

Correct! Thanks!

3) 4 points of intersection.

Sorry, that's wrong.

2) f and g have two intersections, and f and g^{-1} have two intersections, so the sum is 4.

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1)  (-1,0)U(0,1)

thanks man

a. f(x) + g(x) = 5x^3 + 20x^2 + 2.

b. The constant c is -2.

c. f(x)*g(x) = 4x^6 + 29x^5 + 48x^4 - 8x^3 + 86x^2 + 30x - 63.

The correct answer is 381, but thanks for trying!

Thanks!

To solve the problem of Let a and b be real numbers such that a - b = 4 and a^3 - b^3 = 52 1, we can use the following approach:

(a) We can use the formula for the difference of cubes to factor a^3 - b^3 = (a - b)(a^2 + ab + b^2) and substitute a - b = 4 to get:

52 = 4(a^2 + ab + b^2) 13 = a^2 + ab + b^2

We can then use the formula for the sum and product of roots to find the possible values of ab, given that a + b = (a - b) + 2b = 4 + 2b:

a + b = 4 + 2b a^2 + ab + b^2 = 13

Substituting a = 4 + 2b - b and simplifying, we get:

b^2 - 6b + 9 = 0 (b - 3)^2 = 0

Thus, b = 3 and a = 7, so ab = 21 is the only possible value.

(b) We can use a - b = 4 to express a as a function of b, and substitute into the equation a + b = 2a - 4 to get:

a + b = 2(a - 2) + b = 2b

Therefore, a + b can be any even number.

(c) From part (a), we know that a = b + 4, so substituting into the equation a^3 - b^3 = 52 and simplifying, we get:

3b^2 + 12b + 16 = 0 b^2 + 4b + 16/3 = 0 (b + 2)^2 + 8/3 = 0

This equation has no real solutions, so there are no possible values of a and b other than a = 7 and b = 3 that satisfy the given conditions.

Therefore, the answer is: (a) ab = 21. (b) a + b can be any even number. (c) a = 7 and b = 3 are the only possible values.

In Mathematics, fractions are defined as the parts of a whole. The whole can be an object or a group of objects. In real life, when we cut a piece of cake from the whole of it, then the portion is the fraction of the cake. A fraction is a word that is originated from Latin. In Latin, “Fractus” means “broken”.

Fail to be rejected, because the proportion of drivers speeding goes down as the number of police cars per mile on a roadway increases

No, he is incorrect, because the researcher used an observational study, and therefore no causation can be drawn.

r ==(2 - a) /a ==2/a - 1

They are exactly the same. 2/a - 1 is easier for calculating things because you only have one "a".

Your (2 - a) / a ==2/a - a/a ==2/a  -  1 which is what I did. OK?

QR = 84.

15566==5!/2!2!  ==30 permutations 

23556==5!/2!     ==60 permutations

33455==5!/2!2!  ==30 permutations

Total ==30 + 60 + 30 ==120 - number of possible sequences of rolls.

https://web2.0calc.com/questions/let-b-a-and-d-be-three-consecutive-vertices-of-a

https://brainly.com/question/30569514

However I think you are talking about this: https://web2.0calc.com/questions/please-help-asap_12707#:~:text=2%20Answers&text=The%20rolls%20must%20be%201,5!%2F2%20%3D%2060%20ways.