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3 years ago

How to find if a triangle is acute or obtuse with side lengths?

1 answer:

8 0

You would have to determine if the following lengths make an acute, right or obtuse triangle. Plug in each set of lengths into the Pythagorean Theorem.

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Which expression is equivalent to...? Screenshots attached, please help.

BaLLatris [955]

For this case we must simplify the following expression:

$\sqrt [3] {64 * a ^ 6 * b ^ 7 * c ^ 9}$

We rewrite:

$64 = 4 ^ 3\\a ^ 6 = (a ^ 2) ^ 3\\b ^ 6 * b = ((b ^ 2) ^ 3 * b)\\c ^ 9 = (c ^ 3) ^ 3$

So:

$\sqrt [3] {4 ^ 3 * (a ^ 2) ^ 3 * (b ^ 2) ^ 3 * b * (c ^ 3) ^ 3} =\\\sqrt [3] {4 * a ^ 2 * b ^ 2 * c ^ 3) ^ 3 * b} =$

By definition of properties of powers and roots we have:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

So:

$4a ^ 2b ^ 2 c ^ 3 \sqrt [3] {b}$

Answer:

Option B

3 0

2 years ago

John and Belinda played a nine holes of golf. John's score was 10 less than two times Belinda's score. If Johns score was 54 str

polet [3.4K]

Answer:

Belinda's score is 32 strokes.

Step-by-step explanation:

Let the score of John be "x" and Belinda be "y".

It is given that, in the game of golf, John's score was 10 less than two times Belinda's score.

Also, John's score is 54 strokes.

The above equation can be written as ;

$x = 2(y) -10$

Here, x = 54,

$54 = 2(y) -10$

$64 = 2(y)$

$y = 32$

Thus, Belinda's score is 32 strokes.

6 0

2 years ago

Express the perimeter of the triangle as a polynomial.

Tcecarenko [31]

The perimeter is just the sum of all of the side lengths.

p=3x+4+x-10+5x-2

p=9x-8

7 0

2 years ago

Read 2 more answers

Find the remaining factors of x^3+6x^2-4x+3 given (x+2)

satela [25.4K]

Answer:

y=(x+6)(x−2)(x+2)

Step-by-step explanation:

4 0

1 year ago

2 planes leave the airport at the same time. their speeds are 140 mph and 170 mph and the angle between their courses is 25 degr

Damm [24]

Answer:

183.27miles

Step-by-step explanation:

Note that we are considering two planes.

Plane 1

Speed = 140 mph

Time = 2.5 hours

Distance = ?

Speed = distance/time

140 mph = distance/2.5hrs

Distance = 140×2.5

= 350miles

Plane 2

Speed = 170 mph

Time = 2.5 hours

Distance = ?

Speed = distance/time

170 mph = distance/2.5hrs

Distance = 170×2.5

= 425miles

The angle between side is 25 degree

From cosine rule

c^2 = a^2 + b^2 − 2abcos(tetha)

Where a = 350

b = 425miles

c^2 = 350^2+425^2-2(350×425)(cos25)

c^2 = 122500+180625-297500(0.906)

c^2 = 303125-269535

c^2 = 33590

C = √33590

C = 183.27miles

The distance they flew apart after 2.5hrs is 183.27miles

5 0

2 years ago