NEED HELP WITH THIS ASAP!!

Pentagon PQRST and its reflection, pentagon P'Q'R'S'T', are shown in the coordinate plane below:

Ad libitum [116K]

<span>I have graphed the given coordinates of both pentagons. The reflection was across the y-axis where coordinates of Pentagon PQRST (-x,y) resulted to Pentagon P'Q'R'S'T' (x,y). The line of reflection between the pentagons was x = 0. Line of reflection is the midway between the pre-image and its reflection.</span>

4 0

2 years ago

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What is the length of the hypotenuse of the triangle when x=14

astra-53 [7]

The length of the hypotenuse will be equal to H=122.25 when value of x=14.

<h3>What is pythagorean theorem?</h3>

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal the square of the sum of the other two sides.

It is given that:

Value of x=14

The perpendicular is =6x+5=6x14+5=89

The base is =6x=84

So by using the Pythagorean theorem:-

$H^2=P^2+B^2\\\\\\H^2=89^2+84^2\\\\\\H=\sqrt{89^2+84^2}\\\\\$

Hence the value of hypotenuse will be H=122.25

To know more about the Pythagorean theorem follow

brainly.com/question/343682

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8 0

1 year ago

Need help not sure what to do

Rama09 [41]

5a)

2x + 94 = 7x + 49 (vertical angles are equal)

2x - 7x = -94 + 49

-5x = -45

x = 9

Answer

9

5b)

4y + 7x + 49 = 180 (supplementary angles, sum = 180)

4y + 7(9) + 49 = 180

4y + 112 = 180

4y = 68

y = 17

Answer

17

6)

x = 6x - 290 (vertical angles are equal)

-5x = -290

x = 58

Answer

58

7 0

2 years ago

7) PG & E have 12 linemen working Tuesdays in Placer County. They work in groups of 8. How many

BabaBlast [244]

Part A

Since order matters, we use the nPr permutation formula

We use n = 12 and r = 8

$_{n}P_{r} = \frac{n!}{(n-r)!}\\\\_{12}P_{8} = \frac{12!}{(12-8)!}\\\\_{12}P_{8} = \frac{12!}{4!}\\\\_{12}P_{8} = \frac{12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\\\_{12}P_{8} = \frac{479,001,600}{24}\\\\_{12}P_{8} = 19,958,400\\\\$

There are a little under 20 million different permutations.

<h3>Answer: 19,958,400</h3>

Side note: your teacher may not want you to type in the commas

============================================================

Part B

In this case, order doesn't matter. We could use the nCr combination formula like so.

$_{n}C_{r} = \frac{n!}{r!(n-r)!}\\\\_{12}C_{8} = \frac{12!}{8!(12-8)!}\\\\_{12}C_{8} = \frac{12!}{4!}\\\\_{12}C_{8} = \frac{12*11*10*9*8!}{8!*4!}\\\\_{12}C_{8} = \frac{12*11*10*9}{4!} \ \text{ ... pair of 8! terms cancel}\\\\_{12}C_{8} = \frac{12*11*10*9}{4*3*2*1}\\\\_{12}C_{8} = \frac{11880}{24}\\\\_{12}C_{8} = 495\\\\$

We have a much smaller number compared to last time because order isn't important. Consider a group of 3 people {A,B,C} and this group is identical to {C,B,A}. This idea applies to groups of any number.

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Another way we can compute the answer is to use the result from part A.

Recall that:

nCr = (nPr)/(r!)

If we know the permutation value, we simply divide by r! to get the combination value. In this case, we divide by r! = 8! = 8*7*6*5*4*3*2*1 = 40,320

So,

$_{n}C_{r} = \frac{_{n}P_{r}}{r!}\\\\_{12}C_{8} = \frac{_{12}P_{8}}{8!}\\\\_{12}C_{8} = \frac{19,958,400}{40,320}\\\\_{12}C_{8} = 495\\\\$

Not only is this shortcut fairly handy, but it's also interesting to see how the concepts of combinations and permutations connect to one another.

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<h3>Answer: 495</h3>

5 0

1 year ago

Which step comes first? 12÷3•(15-6)+3

bagirrra123 [75]

Pemdas

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3 0

2 years ago

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