What is the name of an interior angle of a triangle that is not adjacent to a given exterior of the triangle

Mathematics

1 answer:

d1i1m1o1n [39]3 years ago

6 0

Definition of an exterior angle

At each vertex of a triangle, an exterior angle of the triangle may be formed by extending ONE SIDE of the triangle. See picture below.

Calculating the Angles

We can use equations to represent the measures of the angles described above. One equation might tell us the sum of the angles of the triangle. For example,

x + y + z = 180

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-2x+5=4x-7 solve for x. Show all work

Neko [114]

Answer:

2=x

Step-by-step explanation:

-2x+5=4x-7

+2x +2x

5=6x-7

+7 +7

12=6x

2=x

7 0

3 years ago

Read 2 more answers

The mass of the particles that a river can transport is proportional to the sixth power of the speed of the river. A certain riv

kari74 [83]

The river flows at 2 miles per hour. This is the speed of the current, or the speed at which the water itself is moving.

The mass of the particles moving in river is proportional to the sixth power of 2, or $2^6 = 64$ miles per hour. So, if x is the mass of the particle, then the speed is modeled by an inverse relationship $x * 2^6 = k$ , for some constant k.

For particles that are 15 times the usual mass, the speed of the river itself must increase for the particles to travel at the same speed as before. The mass of the particles is still proportional to the sixth power of the speed of the river, but the speed of the river can no longer be 2 miles per hour. It is some speed y, which we are solving for.

So, the key here is proportional. We can set up two proportions and cross multiply.

$\dfrac{x}{2^6} = \dfrac{15x}{y^6} \\ (x)(y^6)=(2^6)(15x)$

Cancelling our x's (because we don't need to solve for them), we have

$y^6 = 15(2^6) = 15(64)=960$

To solve for y, we must take the sixth root of both sides, or raise both sides to the one-sixth power.

$\sqrt[6]{y^6} = \sqrt[6]{960}$

Using a calculator, we see that $\sqrt[6]{960} = 3.14 \ miles \ per \ hour$ .