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zzz [600]
3 years ago
9

Suppose I have 6 shirts, 4 ties, and 3 pairs of pants. If an outfit requires a shirt and pants, and can either have a tie or not

have a tie, how many outfits can I make?
Mathematics
1 answer:
Ulleksa [173]3 years ago
6 0
You only can make 3 pairs out of them
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Can someone help me
erik [133]

Answer:

   6 < x < 23.206

Step-by-step explanation:

To properly answer this question, we need to make the assumption that angle DAC is non-negative and that angle BCA is acute.

The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...

  (2x -12)/2 = arcsin(16/22×sin(24°))

  x ≈ 23.206°

Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...

  2x -12 = 0

  x -6 = 0 . . . . . divide by 2

  x = 6 . . . . . . . add 6

Then the range of values of x will be ...

  6 < x < 23.206

_____

* One way to do this is to make use of the law of cosines:

  22² = AB² + AC² -2·AB·AC·cos(48°)

  16² = AD² + AC² -2·AD·AC·cos(2x-12)

The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...

  22² = 2·AB²·(1-cos(48°))

  16² = 2·AB²·(1 -cos(2x-12))

The value of AB drops out of the ratio of these equations, and the result for x is as above.

4 0
3 years ago
Read 2 more answers
BESTIES PLEASE HELP ASAP WILL GIVE POINTS AND BRAINLIEST. Express as a trinomial (2x-6) (x-4)
zaharov [31]

Answer:

2x² - 14x + 24

Step-by-step explanation:

Use the FOIL method (First, Outside, Inside, Last).

First, multiply the first term of both parenthesis:

2x * x = 2x²

Next, multiply the outside terms of both parenthesis:

2x * -4 = -8x

Then, multiply the inside terms of both parenthesis:

-6 * x = -6x

Finally, multiply the last terms of both parenthesis:

-6 * -4 = 24

Combine like terms:

2x² - 8x - 6x + 24

2x² (-8x - 6x) + 24

2x² (-14x) + 24

2x² - 14x + 24 is your answer.

~

4 0
3 years ago
Read 2 more answers
Which of the following is in order from least to greatest
vovangra [49]
The third option is ordered least to greatest
4 0
3 years ago
I need to know what the variable is and please give me the equation.
Mumz [18]

Answer:

$9.50 = .25x

Step-by-step explanation:

38 quarters

6 0
2 years ago
Solve the following expression when<br> m = 5 and d = 4<br> m2 + 2d + 8 + d
Tatiana [17]
If you use substitution the should be answer 30
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