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Finger [1]
3 years ago
5

Which is a true statement about an exterior angle of a triangle

Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
8 0

Answer:

D

Step-by-step explanation:

The exterior angles are out of the triangle at all times and it adds up to make 180 with anyone of the inside angle of the triangle.

The pair also rests on the same flat/straight line and that makes a pair.

Therefore we can say that it is formed by a linear pair/group with one of the interior/inside angles of the triangle.

So, the correct answer would be D.

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Reed uses 8 pieces of glass per square foot to make a stained glass window. How many pieces of glass will he need to make a wind
laiz [17]
To solve the problem posed in the statement we need to know the equivalence between squared foot and squared inches, and that is:
1 square foot = 144 square inches
So Reed uses 8 pieces of glass per 144 squared inches as well.
Now we can use a rule of three, simple and direct proportion to solve the question, it goes like this:
144 squared inches ------> 8 pieces glass
864 squared inches ------> x

x = (864)(8)/144
x = 48
Hence, Reed will use 48 pieces of glass to make a window that is 864 square inches.
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3 years ago
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puteri [66]

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5 0
2 years ago
56 is decreased to 11
nexus9112 [7]

Answer:

56 decreases to 11 because 45 was subtracted from it.

56-45=11


4 0
3 years ago
Read 2 more answers
Solve y ' ' + 4 y = 0 , y ( 0 ) = 2 , y ' ( 0 ) = 2 The resulting oscillation will have Amplitude: Period: If your solution is A
Vlad [161]

Answer:

y(x)=sin(2x)+2cos(2x)

Step-by-step explanation:

y''+4y=0

This is a homogeneous linear equation. So, assume a solution will be proportional to:

e^{\lambda x} \\\\for\hspace{3}some\hspace{3}constant\hspace{3}\lambda

Now, substitute y(x)=e^{\lambda x} into the differential equation:

\frac{d^2}{dx^2} (e^{\lambda x} ) +4e^{\lambda x} =0

Using the characteristic equation:

\lambda ^2 e^{\lambda x} + 4e^{\lambda x} =0

Factor out e^{\lambda x}

e^{\lambda x}(\lambda ^2 +4) =0

Where:

e^{\lambda x} \neq 0\\\\for\hspace{3}any\hspace{3}\lambda

Therefore the zeros must come from the polynomial:

\lambda^2+4 =0

Solving for \lambda:

\lambda =\pm2i

These roots give the next solutions:

y_1(x)=c_1 e^{2ix} \\\\and\\\\y_2(x)=c_2 e^{-2ix}

Where c_1 and c_2 are arbitrary constants. Now, the general solution is the sum of the previous solutions:

y(x)=c_1 e^{2ix} +c_2 e^{-2ix}

Using Euler's identity:

e^{\alpha +i\beta} =e^{\alpha} cos(\beta)+ie^{\alpha} sin(\beta)

y(x)=c_1 (cos(2x)+isin(2x))+c_2(cos(2x)-isin(2x))\\\\Regroup\\\\y(x)=(c_1+c_2)cos(2x) +i(c_1-c_2)sin(2x)\\

Redefine:

i(c_1-c_2)=c_1\\\\c_1+c_2=c_2

Since these are arbitrary constants

y(x)=c_1sin(2x)+c_2cos(2x)

Now, let's find its derivative in order to find c_1 and c_2

y'(x)=2c_1 cos(2x)-2c_2sin(2x)

Evaluating    y(0)=2 :

y(0)=2=c_1sin(0)+c_2cos(0)\\\\2=c_2

Evaluating     y'(0)=2 :

y'(0)=2=2c_1cos(0)-2c_2sin(0)\\\\2=2c_1\\\\c_1=1

Finally, the solution is given by:

y(x)=sin(2x)+2cos(2x)

5 0
3 years ago
Does the value of x make the equation to 0. Why?
natka813 [3]

Answer:

Since there is no value of x that will ever make this a true statement, the solution to the equation above is “no solution”. Be careful that you do not confuse the solution x = 0 with “no solution”. The solution x = 0 means that the value 0 satisfies the equation, so there is a solution.

Step-by-step explanation:

3 0
3 years ago
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