A. vertical angles are congruent
b. alternate interior angles are congruent
c. if alternate interior angles are congruent, lines are parallel <span />
Answer:
x=4
Step-by-step explanation:
x^3-4x^2-16x+64
(x^2-16)(x-4)
x-4=0
+4 +4
x=4
x^2-16=0
+16 +16
x^2=16
√ x^2=√ 16
x=4
For three fair six-sided dice, the possible sum of the faces rolled can be any digit from 3 to 18.
For instance the minimum sum occurs when all three dices shows 1 (i.e. 1 + 1 + 1 = 3) and the maximum sum occurs when all three dces shows 6 (i.e. 6 + 6 + 6 = 18).
Thus, there are 16 possible sums when three six-sided dice are rolled.
Therefore, from the pigeonhole principle, <span>the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice is 16 + 1 = 17 times.
The pigeonhole principle states that </span><span>if n items are put into m containers, with n > m > 0, then at least one container must contain more than one item.
That is for our case, given that there are 16 possible sums when three six-sided dice is rolled, for there to be two same sums, the number of sums will be greater than 16 and the minimum number greater than 16 is 17.
</span>
Answer:
w is the variable
Step-by-step explanation:
the letters you see next to the numbers the variable.
Answer:
24 birds
Step-by-step explanation:
Let b represent the number of birds at the shelter on Wednesday. Then the cost of care for the 41 animals is ...
5b +7.5(41 -b) = 247.50
-2.5b +307.50 = 247.50 . . . . . simplify
-2.5b = -60 . . . . . . . . . . . . . . . . subtract 307.50
b = 24 . . . . . . . . . divide by -2.5
The number of birds at the shelter on Wednesday was 24.
