Mathematics, 30.10.2019 09:31 mouna45

Find the range of possible values for a measurement of 36

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Answer from: flax05

Let side a = 5. Let side b = 9. Then the triangle has

sides

a=5, b=9, and c=?. Any side of a triangle must be less

than the other two sides added together, so

a < b+c, b < a+c, and c < a+b

Substituting:

5 < 9+c, 9 < 5+c, and c < 5+9

Solving all three for c:

-4 < c, 4 < c, c < 14

The first one is of course true, so ignore it.

Put the second and third together and get

4 < c < 14

That's it. c must be more than 4 and less than 14.

2. 7 and 14

Let side a = 7. Let side b = 14. Then the triangle

has sides

a=7, b=14, and c=?. Any side of a triangle must be less

than the other two sides added together, so

a < b+c, b < a+c, and c < a+b

Substituting:

7 < 14+c, 14 < 7+c, and c < 7+14

Solving all three for c:

-7 < c, 7 < c, c < 21

The first one is of course true, so ignore it.

Put the second and third together and get

7 < c < 21

That's it. c must be more than 7 and less than 21.

3. 8 and 13

Let side a = 8. Let side b = 13. Then the triangle

has sides

a=8, b=13, and c=?. Any side of a triangle must be less

than the other two sides added together, so

a < b+c, b < a+c, and c < a+b

Substituting:

8 < 13+c, 13 < 8+c, and c < 8+13

Solving all three for c:

-5 < c, 5 < c, c < 21

The first one is of course true, so ignore it.

Put the second and third together and get

5 < c < 21

That's it. c must be more than 5 and less than 21.

4. 10 and 12

Let side a = 10. Let side b = 12. Then the triangle

has sides

a=10, b=12, and c=?. Any side of a triangle must be less

than the other two sides added together, so

a < b+c, b < a+c, and c < a+b

Substituting:

10 < 12+c, 12 < 10+c, and c < 10+12

Solving all three for c:

-2 < c, 2 < c, c < 22

The first one is of course true, so ignore it.

Put the second and third together and get

2 < c < 22

That's it. c must be more than 2 and less than 22.

They are all done the same way. You can do the other half

by yourself.

Answer from: Quest

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed

Answer from: Quest

step-by-step explanation:

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