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Anuta_ua [19.1K]
3 years ago
12

How do i simplify this?

Mathematics
1 answer:
laiz [17]3 years ago
7 0

I know only this

hope this works

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Is the triangle obtuse, acute, equilateral or right?
Stells [14]

9514 1404 393

Answer:

  obtuse

Step-by-step explanation:

The law of cosines tells you ...

  b² = a² +c² -2ac·cos(B)

Substituting for a²+c² using the given equation, we have ...

  b² = b²·cos(B)² -2ac·cos(B)

We can subtract b² to get a quadratic in standard form for cos(B).

  b²·cos(B)² -2ac·cos(B) -b² = 0

Solving this using the quadratic formula gives ...

  \cos(B)=\dfrac{-(-2ac)\pm\sqrt{(-2ac)^2-4(b^2)(-b^2)}}{2b^2}\\\\\cos(B)=\dfrac{ac}{b^2}\pm\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}

The fraction ac/b² is always positive, so the term on the right (the square root) is always greater than 1. The value of cos(B) cannot be greater than 1, so the only viable value for cos(B) is ...

  \cos(B)=\dfrac{ac}{b^2}-\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}

The value of the radical is necessarily greater than ac/b², so cos(B) is necessarily negative. When cos(B) < 0, B > 90°. The triangle is obtuse.

4 0
3 years ago
Read 2 more answers
Explain how the segment addition postulate can be modeled using a real-world object
IgorC [24]

To determine the length of AB, one must subtract BC from AC. If the length of AC is 18 and the length of BC is 4, then using this formula yields 18 - 4 = 14, so the length of AB is 14.

This postulate also allows a line segment that has only two known points to be broken into two line segments with the addition of a third point in between the endpoints. This is useful for proofs in geometry and analysis.


6 0
3 years ago
Read 2 more answers
The expression 2y+3y2−5y+y2simplifies to 4y2−3y <br> true or false
Mumz [18]

Answer:

False?

Step-by-step explanation:

I'm pretty sure it's false because wouldn't it simplify to 5y? Sorry if I'm wrong. :)

8 0
3 years ago
Find a radius of a circle the length of which is 24π cm.
Juli2301 [7.4K]

Answer:

12

Step-by-step explanation:

Length of a circle = circumference = 2πr = 24π

                                            Radius (r) = 24π/2π

                                                             = 12cm

3 0
2 years ago
A company wants to decrease their energy use by 10%. If their electric bill is currently $1,900 a month, what will their bill be
NemiM [27]

Answer:

A. $1,710

B. Yes, probably.

Step-by-step explanation:

Assuming that a 10% decrease in energy use leads to a 10% decrease in the electric bill:

We'll want to find the value which is 10% less than the original value, i.e., the bill cost which is 90% of the original bill.

90% = 0.9

Since the original bill was $1900, we can just multiply 1900 by 0.9:

1900*0.9=1710

Answer: A bill of $1,710 would equal a 10% decrease.

Since $1,672 is less than that, then they have decreased their energy use by more than 10% which is likely a success.

Answer: Yes, probably.

5 0
3 years ago
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