Factor the expression completely. xy^4 - x^2y

Mathematics

1 answer:

VladimirAG [237]3 years ago

7 0

Answer:

Step-by-step explanation:

xy(y^3 - x)

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The coordinates A(2, 1), B(7, 1), C(2, 4) form what type of polygon?

Digiron [165]

Step-by-step explanation:

$Slope \: of \: AB = \frac{1 - 1}{7 - 2} = \frac{0}{5} = 0 \\ \\ Slope \: of \: BC = \frac{4 - 1}{2 - 7} = \frac{3}{ - 5} = - \frac{3}{ 5} \\ \\ \because \: Slope \: of \: AB \neq \: Slope \: of \: BC \\ \\ \therefore \: given \: points \: are \: non - collinear. \\$

Hence, coordinates A(2, 1), B(7, 1), C(2, 4) form a triangle.

6 0

3 years ago

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A standard deck of cards contains 52 cards. One card is selected from the deck.(a)Compute the probability of randomly selecting

Aneli [31]

a. There are four 5s that can be drawn, and $\binom43=4$ ways of drawing any three of them. There are $\binom{52}3=22,100$ ways of drawing any three cards from the deck. So the probability of drawing three 5s is

$\dfrac{\binom43}{\binom{52}3}=\dfrac4{22,100}=\dfrac1{5525}\approx0.00018$

In case you're asked about the probability of drawing a 3 or a 5 (and NOT three 5s), then there are 8 possible cards (four each of 3 and 5) that interest you, with a probability of $\frac8{52}=\frac2{13}\approx0.15$ of getting drawn.

b. Similar to the second case considered in part (a), there are now 12 cards of interest with a probability $\frac{12}{52}=\frac3{13}\approx0.23$ of being drawn.

c. There are four 6s in the deck, and thirteen diamonds, one of which is a 6. That makes 4 + 13 - 1 = 16 cards of interest (subtract 1 because the 6 of diamonds is being double counted by the 4 and 13), hence a probability of $\frac{16}{52}=\frac4{13}\approx0.31$ .