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ICE Princess25 [194]
3 years ago
14

triangle abc is shown in the diagram. the lengths of the sides are in terms of the variable n, where n>4. Complete the inequa

lity

Mathematics
2 answers:
erik [133]3 years ago
7 0

Answer:

In the first box, B; in the second box, A; and in the third box, C.

Step-by-step explanation:

The sides marked on the triangle would be ranked in order from least to greatest as

n+3, 2n, 3n-2.

This is because for numbers greater than 3 (we are told that n is greater than or equal to 4), adding 3 to a number is less than multiplying it by 2.

Multiplying a number by 2 is less than multiplying a number by 3 then subtracting 2.

To test, use 4:

n+3 = 4+3 = 7; 2n = 2(4) = 8; 3n-2 = 3(4)-2 = 12-2 = 10.

The angles associated with these sides are across from them.  The angle across from the side marked n+3, AC, is angle B.  The angle across from the side marked 2n, BC, is angle A.  The angle across from the side marked 3n-2, AB, is angle C.

BaLLatris [955]3 years ago
4 0
If n>4, then n+3<2n<3n-2 (n+3<2n is true because this unequality is equivalent to 3<n and 2n<3n-2 is also true because this unequality is equivalent to 2<n). Hence, the side AC is the smallest one and the side AB is the biggest one.
The largest side is opposite the largest angle, the medium side is opposite the medium angle and the smallest side is opposite the smallest angle.

Then, m∠B<m∠A<m∠C.
Answer: m∠B<m∠A<m∠C.

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If a rectangle is altered by increasing its length by 20 percent and its width by 10 percent, its area increases by a percent. W
aleksklad [387]

Answer:

D

Step-by-step explanation:

Remember that the formula for the area of a rectangle is:

A=lw

Where l is the our length and w is our width.

If we increase our length by 20%, this means that we add 20% or 0.2 of our old length to our old length. So, our new length will be:

l_{new}=l+.2l

Combine like terms:

l_{new}=1.2l

Similarly, if we increase our width by 10%, this means that we add 10% or 0.1 of our old width to our old width. So, our new width is:

w_{new}=0.1w+w

Combine like terms:

w_{new}=1.1w

Therefore, our new area will be:

A_{new}=(l_{new})(w_{new})

Substitute 1.2l and 1.1w. This yields:

A_{new}=1.2l(1.1w)

Multiply:

A_{new}=1.32lw

Our old area is:

A_{old}=lw

So, our area increased by a factor of 1.32.

This is the same as 32% of our old area.

So, our answer is D.

And we're done!

5 0
3 years ago
Surface area is always measured in square units.<br><br> True<br> False
OLEGan [10]
<h3>Answer: True</h3>

Often we replace "units" with something like "feet" or "meters"

examples: square feet, square meters, square yards, etc

The "square" refers to the idea that any surface area can be unwrapped and lay flat, then you can break the area of that flat figure into smaller squares. A good example of this is a dice has 6 faces and each face is a square itself, so the total surface area is the sum of all the 6 square areas.

6 0
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suter [353]
C=100.I used the Pythagorean theorem just in case next time you run into this problem. 

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Step-by-step explanation:

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Step-by-step explanation:

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6 0
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