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uysha [10]
2 years ago
8

Given right triangle A w/a hypotenuse length of 3y + x and a leg of y-x, and right triangle B, w/ a hypotense length of y+5 and

a leg length of x+5, for what values of x and y are the triangles congruent by HL?
Mathematics
1 answer:
SpyIntel [72]2 years ago
4 0
Triangle A

hypotenuse: 3y + x
leg: y - x

Triangle B

hypotenuse: y + 5
leg: x + 5

Congruency => 3y + x = y + 5 and y - x = x + 5

Solve the system

3y + x = y + 5 -> 2y + x = 5
y - x = x + 5 -> y - 2x = 5

  2y + x = 5
-2y + 4x = -10

5x = -5
x = -1
y = (5 -(-1)) / 2 = 6/2 = 3

Verify:

 hypotenuses
3y + x = 9 - 1 = 8
y + 5 = 3 + 5 = 8

Legs:

y - x = 3 -(-1) = 3 + 1 = 4
x + 5 = -1 + 5 = 4.

Then both hypotenuses and both legs are congruent.

Answer: x = -1 and y = 3


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Suppose that $1,000 is deposited into an account that yields 0.85% interest, compounded annually.
andrey2020 [161]
<h3>Answer:  1034.44 dollars</h3>

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

Work Shown:

A = P*(1+r/n)^(n*t)

A = 1000*(1+0.0085/1)^(1*4)

A = 1034.43596172007

A = 1034.44

---------------------

Notes:

  • P = 1000 is the deposit or principal
  • r = 0.0085 is the decimal form of the annual interest rate of 0.85%; we can say 0.85% = 0.85/100 = 0.0085
  • n = 1 represents how many times per year we're compounding the money (ie annually)
  • t = 4 = number of years
  • The result of 1034.44 dollars is only possible if you do not withdraw any of the money in the four year time period.
4 0
2 years ago
Suppose you have two urns with poker chips in them. Urn I contains two red chips and four white chips. Urn II contains three red
Neporo4naja [7]

Answer:

Multiple answers

Step-by-step explanation:

The original urns have:

  1. Urn 1 = 2 red + 4 white = 6 chips
  2. Urn 2 = 3 red + 1 white = 4 chips

We take one chip from the first urn, so we have:

The probability of take a red one is : \frac{1}{3} (2 red from 6 chips(2/6=1/2))

For a white one is: \frac{2}{3}(4 white from 6 chips(4/6=(2/3))

Then we put this chip into the second urn:

We have two possible cases:

  • First if the chip we got from the first urn was white. The urn 2 now has 3 red + 2 whites = 5 chips
  • Second if the chip we got from the first urn was red. The urn two now has 4 red + 1 white = 5 chips

If we select a chip from the urn two:

  • In the first case the probability of taking a white one is of:  \frac{2}{5} = 40%  ( 2 whites of 5 chips)
  • In the second case the probability of taking a white one is of:  \frac{1}{5} = 20%  ( 1 whites of 5 chips)

This problem is a dependent event because the final result depends of the first chip we got from the urn 1.

For the fist case we multiply :

\frac{4}{6} x \frac{2}{5} = \frac{4}{15} = 26.66%   ( \frac{4}{6} the probability of taking a white chip from the urn 1, \frac{2}{5}  the probability of taking a white chip from urn two)

For the second case we multiply:

\frac{1}{3} x \frac{1}{5} = \frac{1}{30} = .06%   ( \frac{1}{3} the probability of taking a red chip from the urn 1, \frac{1}{5}   the probability of taking a white chip from the urn two)

8 0
3 years ago
A theme park charges $52 for a day pass and $110 for a week pass. Last month, 4,432-day passes were sold and 979-week passes wer
Naddika [18.5K]

Answer:    $52 x 4 =230,464    $110 x 979 = 107,690.         ESTIMATED ANSWER: 300,000

230,464

+107,690= 338,154                

Step-by-step explanation: Hope this helped you!

3 0
2 years ago
when the intreast earned is $27, the intreast rate is 1.5%, and the time is 2 years, what is the principal
Nikolay [14]

Answer:

27

Step-by-step explanation:

3 0
3 years ago
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Is 5 a factor of 24r + 45?<br> yes<br> no<br><br><br> HELP PLSSS
____ [38]

Answer:no

Step-by-step explanation:

4 0
3 years ago
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