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3 years ago

Explain which theorems definitions or combinations of both can be used to prove that alternate exterior angles are congruent

Mathematics

2 answers:

My name is Ann [436]3 years ago

8 0

Answer:

You can prove that and are congruent using the same method. The converse of this theorem is also true; that is, if two lines and are cut by a transversal so that the alternate exterior angles are congruent.

Step-by-step explanation:

Licemer1 [7]3 years ago

6 0

Answer:

As mentioned in the explanation steps.

Step-by-step explanation:

The following theorem is helpful to prove that the alternate exterior angles are congruent.

If two lines lie in the same plane and parallel to each other. A traversal line intersect these parallel lines at different points, then the alternate exterior angles must be same.

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) Use the Laplace transform to solve the following initial value problem: y′′−6y′+9y=0y(0)=4,y′(0)=2 Using Y for the Laplace tra

artcher [175]

Answer:

$y(t)=2e^{3t}(2-5t)$

Step-by-step explanation:

Let Y(s) be the Laplace transform Y=L{y(t)} of y(t)

Applying the Laplace transform to both sides of the differential equation and using the linearity of the transform, we get

L{y'' - 6y' + 9y} = L{0} = 0

(*) L{y''} - 6L{y'} + 9L{y} = 0 ; y(0)=4, y′(0)=2

Using the theorem of the Laplace transform for derivatives, we know that:

$\large\bf L\left\{y''\right\}=s^2Y(s)-sy(0)-y'(0)\\\\L\left\{y'\right\}=sY(s)-y(0)$

Replacing the initial values y(0)=4, y′(0)=2 we obtain

$\large\bf L\left\{y''\right\}=s^2Y(s)-4s-2\\\\L\left\{y'\right\}=sY(s)-4$

and our differential equation (*) gets transformed in the algebraic equation

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0$

Solving for Y(s) we get

$\large\bf s^2Y(s)-4s-2-6(sY(s)-4)+9Y(s)=0\Rightarrow (s^2-6s+9)Y(s)-4s+22=0\Rightarrow\\\\\Rightarrow Y(s)=\frac{4s-22}{s^2-6s+9}$

Now, we brake down the rational expression of Y(s) into partial fractions

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4s-22}{(s-3)^2}=\frac{A}{s-3}+\frac{B}{(s-3)^2}$

The numerator of the addition at the right must be equal to 4s-22, so

A(s - 3) + B = 4s - 22

As - 3A + B = 4s - 22

we deduct from here

A = 4 and -3A + B = -22, so

A = 4 and B = -22 + 12 = -10

It means that

$\large\bf \frac{4s-22}{s^2-6s+9}=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

and

$\large\bf Y(s)=\frac{4}{s-3}-\frac{10}{(s-3)^2}$

By taking the inverse Laplace transform on both sides and using the linearity of the inverse:

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}$

we know that

$\large\bf L^{-1}\left\{\frac{1}{s-3}\right\}=e^{3t}$

and for the first translation property of the inverse Laplace transform

$\large\bf L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=e^{3t}L^{-1}\left\{\frac{1}{s^2}\right\}=e^{3t}t=te^{3t}$

and the solution of our differential equation is

$\large\bf y(t)=L^{-1}\left\{Y(s)\right\}=4L^{-1}\left\{\frac{1}{s-3}\right\}-10L^{-1}\left\{\frac{1}{(s-3)^2}\right\}=\\\\4e^{3t}-10te^{3t}=2e^{3t}(2-5t)\\\\\boxed{y(t)=2e^{3t}(2-5t)}$

5 0

3 years ago

Rob spent $38 on shirts. Tee shirts cost $4 and long sleeve shirts cost $5. If he bought a total of 8 then how many of each kind

KATRIN_1 [288]

Answer:

2 long sleeve and then 7 short sleeve

3 0

3 years ago

Pleasaaaaseee answer the all for BRAINLEST answer and thanks

kow [346]

X=2/4=1/2
s=1 1/2
r= 1/2
y= 2/7
w= 1 2/3
p=2/5
Hope this works i can't see the others ok?

3 0

3 years ago

Pls can someone pls help me <br> Please show your work

Lana71 [14]

Answer:

x = 8

I dunno what the question is in the first place, but I assume you are solving for x.

Step-by-step explanation:

The two given angles are equivalent because they are parallel and they have a line that intersects.

The line creates two angles on each side of each line, which is 120 or 60 because there are 180 degs on a straight line.

The obtuse side is 120, and the -8 + 16x is also on an obtuse angle, showing that they are equal.

120 = -8 + 16x

128 = 16x

8 = x

x = 8

7 0

2 years ago

reid ate 1/4 of the pumpkin pie vince ate 1/3 of the same pie how mutch of the pie was left after reid and vince ate their piece

Tcecarenko [31]

1 - 1/4 - 1/3

=12/12 - 3/12 - 4/12

=12/12 - 7/12

=5/12

4 0

3 years ago

Read 2 more answers