#1**+2 **

One thing that you should know is that any quadrilateral's angles sum to 360. Thus, we can make the equation

(q) + (5q + 15) + (3q - 55) + (4q - 20) = 360

This is just simple algebra that you should be able to do. You can simplify this, and then once you find out what q is, figure out what the largest angle is.

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ShockFish

BTW this question was also answered here: https://web2.0calc.com/questions/geometry_51921

ShockFishMay 15, 2022

#1**+4 **

We can use complementary counting, which is, subtracting the possibilities that don't satisfy the condition from the total amount of possibilities.

For the first die, the probability that two dice don't show the same number is 1.

For the second die, the probability is 5/6, because one possibility was taken from the first die.

For the third die, the probability is 4/6 or 2/3 because two possibilities have been taken from the two dice already rolled.

Therefore, we see that the fourth and fifth have 3/6 (1/2) and 2/6 (1/3) as their probability.

We multiply these all together and we get

1 * 5/6 * 2/3 * 1/2 * 1/3 = **5/54**.

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ShockFish

(This question was also answered here: https://web2.0calc.com/questions/help-one-more-problem)

ShockFishFeb 4, 2022

#1**+3 **

According to Wikipedia, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

The first one is just a mess.

The second one fits all conditions.

The third one has a variable exponent.

The fourth one has a negative exponent.

Thus the only one that is a polynomial is the second one, or **x^4 - 2**.

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ShockFish

ShockFishFeb 3, 2022