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3 years ago

Given: ∠H and ∠X are supplementary. Prove: l || n

Mathematics

1 answer:

DiKsa [7]3 years ago

6 0

I won't write out a formal proof; here's an outline.

H+X=180. definition of supplementary
H+F=180 crossing lines
X=F supplements of the same angle are equal, or just algebra
l || n When the alternate angles of a transverse line between two lines are congruent, the lines are parallel

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Five cards are dealt from a standard 52-card deck. (a) What is the probability that we draw 1 ace, 1 two, 1 three, 1 four, and 1

Rudik [331]

Answer:

Step-by-step explanation:

As there are total 52 cards in a deck and we have to draw a set of 5 cards, we can use the formula of combination to find the total number of possible ways of drawing 5 cards.

Number of ways to draw 5 cards = $N_T$

$N_T\;=\;({}^NC_k)\\\\N_T\;=\;({}^{52}C_5)\\\\N_T\;=\;2,598,960$

(a) Assuming the cards are drawn in order (would not affect the probability). The of getting Ace, 2, 3, 4 and 5 can be obtained by multiplying the probability of getting cards below 6 (20/52) with the probability of getting 5 different cards (4 choices for each card).

$P(a)\;=\;\frac{20}{52}*\frac{4}{52}*\frac{4}{51}*\frac{4}{50}*\frac{4}{49}*\frac{4}{48}\\\\P(a)\;=\; 1.3133*10^{-6}$

(b) For a straight we require our set to be in a sequence. The choices for lowest value card to produce a sequence are ace, 2, 3, 4, 5, 6, 7, 8, 9, or 10. Hence, the number of ways are $({}^{10}C_1)$ .

For each card we can draw from any of the 4 sets. It can be described mathematically as: $({}^{4}C_1)*({}^{4}C_1)*({}^{4}C_1)*({}^{4}C_1)*({}^{4}C_1)\;=\;[({}^{4}C_1)^5]$

Therefore, the total outcomes for drawing straight are:

$N_S\;=\;({}^{4}C_1)*({}^{4}C_1)^5\;=\;10240$

Thus, the probability of getting a straight hand is:

$P(b)\;=\;\frac{N_S}{N_T}\\\\P(b)\;=\;\frac{10240}{2598960}\\\\P(b)\;=\; 0.0039$

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3 years ago

Carlos is making three cakes. One cake requires 3/4 of a cup sugar. How much sugar will he need to make all three cakes?

Natali [406]

Answer:B.9/12

Step-by-step explanation:

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3 years ago

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The distance between two points is 65‾√. One endpoint is (4,−3). It is known that the y-coordinate of the other endpoint is 7.

diamong [38]

Answer:

C & D

Step-by-step explanation:

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3 years ago

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Will give brainliest for answer

sleet_krkn [62]

Answer:

y > -x -3

Step-by-step explanation:

The graph is shaded <em>above</em> the <em>dashed</em> line, indicating y-values in the solution are greater than those on the line, so your inequality will start with ...

y >

The y-intercept of the line is (0, -3), so the "b" value in ...

y > mx +b

will be -3.

The line has a rise of -3 for a run of 3 (between the marked points), so the slope is ...

m = rise/run = -3/3 = -1

Then the inequality you want is ...

y > -x -3

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3 years ago

Find the distance between the points (8,10) and (4,7)

r-ruslan [8.4K]

Answer: 7 is the distance in between the points

Step-by-step explanation: How you find the distance between points is pretty simple once you know how to do it!

So first take your X coordinate take the first one (8) and subtract it from the second one (4) 8-4=4 so now we have 4 put that aside for a moment,

Now take your Y coordinate subtract the first one (10) from the second one (7), 10-7=3

Finally add the 3 and 4 together you get 7 that is why 7 is the distance in between the points

If you need further help or instruction please let me know!

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4 years ago