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3 years ago

What is the length of the line segment with endpoints (7,-1) and (-3,5)?

Mathematics

1 answer:

Galina-37 [17]3 years ago

8 0

Formula to find the length of two endpoints: $\sqrt{(x^2-x^1)^2+(y^2-y^1)^2}$

Now, solve with the given endpoints.

$\sqrt{(x^2-x^1)^2+(y^2-y^1)^2} \\\sqrt{(-3-7)^2+(5-(-1))^2} \\\sqrt{(-10)^2 + (6)^2} \\ \sqrt{100+36}\\\sqrt{136}$

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Now, simplify using what we know about radicals.

Solution in picture.

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The length between the endpoints is 2√34 (Option B)

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Best Regards,

Wolfyy :)

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Choose 5 cards from a full deck of 52 cards with 13values (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A) and 4 kinds(spade, diamond, h

Delvig [45]

Answer:

a) 182 possible ways.

b) 5148 possible ways.

c) 1378 possible ways.

d) 2899 possible ways.

Step-by-step explanation:

The order in which the cards are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question, we have that:

There are 52 total cards, of which:

13 are spades.

13 are diamonds.

13 are hearts.

13 are clubs.

(a)Two-pairs: Two pairs plus another card of a different value, for example:

2 pairs of 2 from sets os 13.

1 other card, from a set of 26(whichever two cards were not chosen above). So

$T = 2C_{13,2} + C_{26,1} = 2*\frac{13!}{2!11!} + \frac{26!}{1!25!} = 182$

So 182 possible ways.

(b)Flush: five cards of the same suit but different values, for example:

4 combinations of 5 from a set of 13(can be all spades, all diamonds, and hearts or all clubs). So

$T = 4*C_{13,5} = 4*\frac{13!}{5!8!} = 5148$

So 5148 possible ways.

(c)Full house: A three of a kind and a pair, for example:

4 combinations of 3 from a set of 13(three of a kind ,c an be all possible kinds).

3 combinations of 2 from a set of 13(the pair, cant be the kind chosen for the trio, so 3 combinations). So

$T = 4*C_{13,3} + 3*C_{13.2} = 4*\frac{13!}{3!10!} + 3*\frac{13!}{2!11!} = 1378$

So 1378 possible ways.

(d)Four of a kind: Four cards of the same value, for example:

4 combinations of 4 from a set of 13(four of a kind, can be all spades, all diamonds, and hearts or all clubs).

1 from the remaining 39(do not involve the kind chosen above). So

$T = 4*C_{13,4} + C_{39,1} = 4*\frac{13!}{4!9!} + \frac{39!}{1!38!} = 2899$

So 2899 possible ways.

4 0

3 years ago

If c=2m+d then m is equal to?

arlik [135]

To solve this, you start off by moving the d over to the other side

then you can divide everything by 2 , this will get the m by itself

Therefore, your answer is

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3 years ago

The circumference of the Astrodome in Houston, Texas is 2,230 ft. Find the area of the astrodome and explain how you did this us

Degger [83]

Answer:

The radius of Astrodome is 355.09 foot,

The Area of Astrodome is 395919.146 square foot .

Step-by-step explanation:

Given as :

The circumference of Astrodome = 2230 foot

∵ The circumference of circular shape = 2 × $\pi$ × radius

where $\pi$ = 3.14

So, The circumference of Astrodome = 2 × $\pi$ × radius

Or, 2230 foot = 2 × 3.14 × radius

Or, 2230 foot = 6.28 × radius

∴ radius = $\dfrac{2230}{6.28}$

I.e radius = 355.09 foot

Now,

∵The area of circular shape = $\pi$ × radius²

So, The area of Astrodome = $\pi$ × radius²

Or, The area of Astrodome = 3.14 × radius²

Put the value of radius = 355.09 foot

So , The area of Astrodome = 3.14 × (355.09)²

or, The area of Astrodome = 3.14 × 126088.9

∴ The area of Astrodome = 395919.146 square foot

Hence , The radius of Astrodome is 355.09 foot, and The Area of Astrodome is 395919.146 square foot . Answer

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3 years ago

Mr. Browne works for $6.00 per hour. His wife works for $8.00 per hour. One week they each earned the same pay. If they get paid

Tcecarenko [31]

Answer:

In explanation

Step-by-step explanation:

If Mr.brown worked 20 hours and his wife wold of worked 15 hours they would both earn 120$.

Another one is if Mr.brown works 40 hours and his wife works 30 hours they each could make 240$

Hope this helps have a great day:)

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elena55 [62]

Answer:

Step-by-step explanation:

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$\dfrac{2}{4}=\dfrac{4}{8}=0.5$

B. Second two rectangles are dilations because

$\dfrac{2}{4}=\dfrac{3}{6}=0.5$

C. Third two rectangles are not dilations because

$\dfrac{3}{4}\neq \dfrac{2}{3}$

D. Fourth two rectangles are dilations because

$\dfrac{3}{4}=\dfrac{1.5}{2}=0.75$

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3 years ago

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