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WARRIOR [948]
3 years ago
14

1. HELP Use front-end estimation to estimate the sum 8.86 + 9.43 + 5.75

Mathematics
1 answer:
marta [7]3 years ago
5 0

Answer:

1. Option D.

2. Option A.

Step-by-step explanation:

1. You need to follow these steps in order to estimate the sum of 8.86 + 9.43 + 5.75:

Step 1: Add the digits in the ones places of the whole numbers (these are: 8, 9 and 5).

Step 2: Round the decimals to the nearest whole number:

0.86\approx 1\\\\0.43\approx0\\\\0.75\approx1

 Step 3: Add them together:

8+9+5+1+0+1=8+9+5+2=24

2. The procedure to estimate  the difference of 83.92-47.23 is:

83.92-\\47.23\\........\\40.00\\\ -4.00\\\ \ + 0.70\\-0.01\\...........\\+36.00\\+0\ 0.69\\..............\\36.69

Rounded to the nearest whole number:

36.69\approx 37

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x=ln(61)/ln(4)

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indicate whether the measures 8, 14, and 16 can be the side lengths of a triangle. if they can, classify the triangle.
Aleksandr-060686 [28]

Answers:  

A triangle is possible.

The triangle is <u>acute</u> and <u>scalene</u>

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

Explanation:

We use the triangle inequality theorem to see if a triangle is possible with these side lengths.

Consider the side lengths a, b, and c. A triangle is possible if and only if the following 3 conditions hold true

  • a+b > c
  • a+c > b
  • b+c > a

Basically pick any two sides. If the sum is larger than the third side, then a triangle is possible.

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

In this case we have: a = 8, b = 14, c = 16. The order of the a,b,c values doesn't really matter.

Then:

  • a+b = 8+14 = 22 which is larger than c = 16. So a+b > c is true.
  • a+c = 8+16 = 24 is larger than b = 14. So a+c > b is true.
  • b+c = 14+16 = 30 is larger than a = 8. So b+c > a is true.

All three inequalities mentioned are true; therefore, <u>a triangle is possible</u> with these side lengths.

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

We'll use those a,b,c values in the converse of the pythagorean theorem to determine what kind of triangle this is. So far we know it's <u>scalene</u> because all three side lengths are different. It would be isosceles if it had exactly two equal sides, and equilateral if all 3 sides were the same length.

a^2+b^2 = c^2\\\\8^2+14^2 = 16^2\\\\260 = 256\\\\

The last equation is false, which tells us this triangle is not a right triangle. It's either acute or obtuse.

Since a^2+b^2 > c^2 is the case here, we can conclude the triangle is <u>acute</u>

If a^2+b^2 < c^2 was the case, then the triangle would be obtuse.

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

Summary:

  • A <u>triangle is possible</u> with side lengths a = 8, b = 14, c = 16.
  • This triangle is <u>scalene</u> and <u>acute</u>
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