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bija089 [108]
3 years ago
12

Angle CAB=90 AB=AC=DE BD=9 CE=8 Find DE

Mathematics
1 answer:
zalisa [80]3 years ago
3 0

Answer:

  29

Step-by-step explanation:

Let x represent the length of DE. Then ...

  AB = x

  AD = AB -BD = x - 9

__

  AC = x

  AE = AC -CE = x - 8

And the Pythagorean theorem applied to triangle ADE tells us ...

  x^2 = (x -9)^2 +(x -8)^2

  0 = x^2 -34x +145 = (x -5)(x -29)

Solutions are the values of x that make a factor zero: 5 or 29.

The length of DE must be greater than 9, so the appropriate solution from the above equation is x = 29.

The length of DE is 29.

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How many passwords of 4 digits are there(a)if none of the digits can be repeated?(b)start with 5 and end in an even digit?
liraira [26]

Answer:

5040,56

Step-by-step explanation:

We have to construct pass words of 4 digits

a) None of the digits can be repeated

We have total digits as 0 to 9.

4 digits can be selected form these 10 in 10P4 ways (since order matters in numbers)

No of passwords = 10P4

= 10(9)(8)(7)\\=5040

b) start with 5 and end in even digit

Here we restrain the choices by putting conditions

I digit is compulsorily 5 and hence only one way

Last digit can be any one of 0,2,4,6,8 hence 5 ways

Once first and last selected remaining 2 digits can be selected from remaining 8 digits in 8P2 ways (order counts here)

=56

3 0
3 years ago
Solve for x: 3(x + 1) = −2(x − 1) + 6. (1 point)<br><br> 1<br> 4<br> 5<br> 25
Nikolay [14]

Answer: 1

Step-by-step explanation:

You are welcome :)

3 0
3 years ago
288,500 house with a 30 yr mortgage and 3.25% interest rate is
Murljashka [212]

A good deal on the mortgage I suppose. A bit expensive, but if you have the money go for it.

5 0
3 years ago
Need some help with this
kramer

Answer:

Step-by-step explanation:

The total number of outcomes the two fair number cubes are thrown is 36. This can be seen by counting the outcomes shown on the table.

a) for a sum of 4, there are only 3 possible outcomes. They are 3,2 2,2 and 1,3

Therefore, the probability of getting a sum of 4 will be

3/36 = 1/12

b) for a sum of 5, there are only 4 possible outcomes. They are 4,1 3,2 2,3 and 1,4

Therefore, the probability of getting a sum of 4 will be

4/36 = 1/9

c)for a sum of 6, there are only 5 possible outcomes. They are 5,1 4,2 3,3 2,4 and 1,5

Therefore, the probability of getting a sum of 6 will be

5/36 = 5/36

The probability that the sum of the results of the throw is 4,5 or 6 would be

1/12 + 1/9 + 5/36 = (3 + 4 + 5)/36 = 12/36 = 1/3

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3 years ago
Find the distance between two points: (1,4) and (11,9)
Marina CMI [18]

Answer:

√125=5√5

here you go

5 0
3 years ago
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