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photoshop1234 [79]
3 years ago
9

Triangles FIM and LAK below are similar, with mZF =

Mathematics
1 answer:
Assoli18 [71]3 years ago
8 0

Answer:

LA = 8

Step-by-step explanation:

Since ∆FIM ~ ∆LAK, therefore, the ratio of their corresponding sides are equal.

Thus:

FI/LA = FM/LK

FI = 4

LA = ?

FM = 6

LK = 12

Plug in the values

4/LA = 6/12

4/LA = 1/2

Cross multiply

LA*1 = 2*4

LA = 8

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They won 15 games

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Montano1993 [528]

Answer:

x = 9

Step-by-step explanation:

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2 years ago
I really need help please answer
belka [17]

Answer: Choice B) between 6:48 AM and 5:12 PM

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

Explanation:

I've seen this problem before, and the first part states that if the temperature is above 25 degrees C, then the air conditioner turns on to start cooling the castle.

We want to find values of t that satisfy f(t) > 25

This is the same as trying to solve f(t) - 25 > 0

So we have,

f(t) = 24 - 5\cos\left(\frac{\pi}{12}t\right)\\\\   f(t)-25 = 24 - 5\cos\left(\frac{\pi}{12}t\right)-25\\\\   f(t)-25 = -1 - 5\cos\left(\frac{\pi}{12}t\right)\\\\   f(t)-25 > 0\\\\ -1 - 5\cos\left(\frac{\pi}{12}t\right) > 0\\\\

To solve this inequality, we can graph using Desmos as I've done so below. See the attached image.

Note how I used x in place of t. This is because the graphing calculator graphs (x,y) coordinates.

Furthermore, note how I marked the two points (6.769, 0) and (17.231, 0)

Between these two points is when the curve is above the x axis, when f(t) > 25 is true. This is when the temperature is above 25 degrees C, and when the air conditioner is working.

When t = 6.769, this means that roughly 6.769 hours have passed since midnight which means we're somewhere between 6 am and 7 am. The only value that works from the answer choices is 6:48 AM.

Note how 0.769*60 = 46.14 is fairly close to 48. This error is likely due to how things are rounded.

Then focusing on the point  (17.231, 0) means that t = 17.231. So 17.231 hours have elapsed since midnight and we're now at roughly 1700 hours

1700 hours in military time = 17-12 = 5 pm

The time value t = 17.231 is between 5 pm and 6 pm. The only thing that works is 5:12 pm.

We can then note how 0.231*60 = 13.86 which is also probably due to rounding error (it's fairly close to 12 though).

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

In short, we found the function for f(t)-25 and graphed it as shown below. The two points (6.769, 0) and (17.231, 0) help us see when the AC is turned on, which is roughly between 6:48 AM and 5:12 PM. This seems like a reasonable time for the AC to be operational. Something like between 5:12 PM and 6:48 AM seems like a bad idea because the AC would be working mostly at night, instead of during the day.

Anything beyond t = 24 represents the next day, which is when the cycle starts all over again. So we only need to focus on the window from t = 0 to t = 24. Specifically, the portion of the f(t)-25 curve that is above the x axis.

8 0
3 years ago
7(3w-3)=-12<br> HURRY PLEASE
Lady_Fox [76]

Answer:

3/7

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Tickets for a concert were \$5$5dollar sign, 5 for each child and \$8$8dollar sign, 8 for each adult. At one of the concerts, ea
OlgaM077 [116]

Answer:

Step-by-step explanation:

Let c represent the number of children that attended the concert.

Let a represent the number of adults that attended the concert.

At one of the concerts, each adult brought 4 children with them, and 10 children attended without an adult. This means that the number of children that attended is

c = 4a + 10

Tickets for a concert were $5 for each child and $8 for each adult. The total ticket sales were $1730. It means that

5c + 8a = 1730

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c = 4a + 10

5c + 8a = 1730

4 0
3 years ago
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