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True [87]
3 years ago
7

Which of the following equations is equivalent to

Mathematics
1 answer:
Cerrena [4.2K]3 years ago
5 0

Answer:

4a - 40 = 1

Step-by-step explanation:

4/5 a - 8 = 1/5

Multiply each side by 5 to clear the fractions

5(4/5 a - 8) = 1/5 *5

distribute

4a - 40 = 1

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Help plzzzzzzzzzzzzzzzzzzzzz
Klio2033 [76]
The human ran 0.45 miles per minute.

27 divided by 60 = 0.45

The 60 is the number of seconds in a minute.

Hope this helped! :)
6 0
3 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
ABC is translated left 3 units to form the image ∆A′B′C′.
Varvara68 [4.7K]

Answer:

A = (-2 , -1)                 A’ = (-5 , -1)

B = (2 , -1)                  B’ = (-1 , -1)

C = (2, 2)                   C’ = (-1 , 2)

Step-by-step explanation:

Move each coordinate to the left 3 times! You will result in the prime coordinates of the letters!

4 0
2 years ago
50 people plan to attend the dance and each person will eat 2 slices of cake. If each cake contains 20 slices, how many cakes sh
Naya [18.7K]

Answer:

5

Step-by-step explanation:

You <em>multiply</em> the number of people by the number of each slices each person gets. Which is 100; 50x2.

Each cake has 20 slices so you <em>divide</em> 100 by 20. Which equals 5.

It would take 5 cakes to feed all 50 people 2 slices each.

<em>Hope this helps</em>. :)

3 0
3 years ago
A car travels at an average speed of 60 mph on a trip what is the car speed in feet per second
kotegsom [21]

Answer:   88 Feet Per Second



Step-by-step explanation:  

Firstly you need to know 3 things:  

> 60 mph = 60 Miles Per Hour  

> 1 Hour = 60 mins = 60*60 = 3600 seconds  

> 1 Mile = 5280 feet  

Next you can change the miles to feet and hours to seconds.  

60 mi/ 1 hour = 60*5280/ 3600 = 316800ft/ 3600sec  

Now time to reduce that big fraction! (Or in this case just divide by 3600 sec)  

316800ft/ 3600sec  

= 88ft/1sec  

= 88 Feet Per Second  

Hope that helps!


5 0
3 years ago
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