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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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Answer:

<em>The correct option is:  C. x=6\sqrt{3}, y=12</em>

Step-by-step explanation:

The two angles of the triangle are given as 60° and 60°

As the sum of all three angle in any triangle is always 180°, so the measure of the third angle will be: 180°-(60°+60°) = 180° - 120° = 60°

Now each angle of the triangle is 60°, it means the triangle is equilateral.

The base of the triangle is given as 12. So, the length of each side will be 12.

That means, the value of y=12

Now in the left right triangle.....

Sin(60)=\frac{x}{y} \\ \\ \frac{\sqrt{3}} {2}=\frac{x}{12} \\ \\ 2x=12\sqrt{3} \\ \\ x=6\sqrt{3}

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Answer in factored form x^2+11x+7
KATRIN_1 [288]
X² <span>+ 11x + 7

because 7 is a prime number, this doesn't factor prettily. you'll want to use the quadratic formula; if you aren't familiar with it, i'd either research it or look it up in your textbook, because it's clunky and not easily understood in this format:

(-b </span>± √((b)² - 4ac))/(2a)

in your equation x² + 11x + 7 ... a = 1, b = 11, and c = 7. what you do is you take the coefficients of every term, then plug it into your equation:
(-11 ± √((11)² - 4(1)(7))/(2(1))

not pretty, i know. but, regardless, you can simplify it:
(-11 ± √((11)² - 4(1)(7))/(2(1))
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and you can't simplify it further. -11 isn't divisible by 2, and 93 doesn't have a perfect square that you can take out from beneath the radical. the ± plus/minus symbol indicates that you have 2 answers, so you can write them out separately:

(x - (-11 - √93)/2) and (x + (-11 - √93)/2)

they look confusing, but those are your two factors. they can be simplified just slightly by changing the signs in the middle due to the -11:

(x + (11 + √93)/2) (x - (11 - √93)/2)

and how these would read, just in case the formatting is too confusing for you: x plus the fraction 11 + root 93 divided by 2. the 11s and root 93s are your numerator, 2s are your denominator.
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