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tino4ka555 [31]
3 years ago
10

leah found that 25% of the students in her class prefer ice cream for dessert. if there are 24 students in her class, how many p

erfer ice cream as dessert?
Mathematics
1 answer:
Nataliya [291]3 years ago
5 0
<span><span>1.       </span>Leah found that 25% of the students in her class prefer ice cream for dessert
=> Now, if she has 24 students in her class. Let’s find out how many of her students prefer ice cream for dessert.
=> 24 students = is the 100% of the number of student.
Now, 25% of it preferred ice cream as dessert. Lets solve
=> 25% / 100% = .25
Now, multiply this decimal with the value of our 100%
=> 24 * .25
=> 6, thus 6 of her students prefer ice cream for dessert.</span>



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\text{Given that,}\\\\5x-4x^2 +3 \\\\\text{When}~ x = -1,\\\\~~~5(-1) -4(-1)^2 +3 \\\\=-5-4(1)+3\\\\=-5-4+3\\\\=-5-1\\\\=-6

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<h3>Answer: Choice D)  31.2 miles</h3>

This value is approximate.

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

Explanation:

Let's focus on the 48 degree angle. This angle combines with angle ABC to form a 90 degree angle. This means angle ABC is 90-48 = 42 degrees. Or in short we can say angle B = 42 when focusing on triangle ABC.

Now let's move to the 17 degree angle. Add on the 90 degree angle and we can see that angle CAB, aka angle A, is 17+90 = 107 degrees.

Based on those two interior angles, angle C must be...

A+B+C = 180

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149+C = 180

C = 180-149

C = 31

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

To sum things up so far, we have these known properties of triangle ABC

  • angle A = 107 degrees
  • side c = side AB = 24 miles
  • angle B = 42 degrees
  • angle C = 31 degrees

Let's use the law of sines to find side b, which is opposite angle B. This will find the length of side AC (which is the distance from the storm to station A).

b/sin(B) = c/sin(C)

b/sin(42) = 24/sin(31)

b = sin(42)*24/sin(31)

b = 31.1804803080182 which is approximate

b = 31.2 miles is the distance from the storm to station A

Make sure your calculator is in degree mode.

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