Ask question

Ask question

All categories

3 years ago

6

Given: RT || SP, RQ ≅ QP, RP bisects ST at Q Prove: ΔRQT ≅ ΔPQS Tamir is working to prove the triangles congruent using SAS. Aft

er stating the given information, he states that TQ ≅ QS by the definition of segment bisector. Now he wants to state that ∠RQT ≅ ∠PQS. Which reason should he use? alternate interior angles theorem corresponding angles theorem linear pair postulate vertical angles theorem

2 answers:

Hitman42 [59]3 years ago

7 0

The answer is the last one D

Bingel [31]3 years ago

3 0

<span>D. vertical angles theorem</span>

You might be interested in

The wings of the butterfly is 6.7 centimeters what is the wings of the buterfly in millimeters

koban [17]

The wings of the butterfly would be 67 millimeters

4 0

3 years ago

Read 2 more answers

Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

2 years ago

Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estim

bearhunter [10]

Answer:

70.33 feet per second

Step-by-step explanation:

Since, speed of Morris is given is feet per second

lets, convert Aneesha's speed in feet per second.

We know that

1 mile = 5280 feet

1 hour = 60 minutes

1 minute = 60 seconds

thus,

1 hour = 60*60 seconds = 3600 seconds

Now

Aneesha's Speed = 50 miles per hour

to convert miles per hour into feet per second

we will use 1 miles = 5280 feet

1 hour 3600 second

Aneesha's Speed in feet per second = 50*5280 feet/3600 seconds

Aneesha's Speed in feet per second = 73.33 feet per seconds

Given that

Morris is traveling 3 feet per second less than Aneesha

Morris speed = Aneesha's Speed in feet per second - 3 feet per second

Morris speed = (73.33 - 3 ) = 70.33 feet per second

Thus, morris speed is 70.33 feet per second

5 0

4 years ago

Whats 2.48 divided by 0.4?

xxTIMURxx [149]

2.48 / 0.4

Multiply both top and bottom by 10

(2.48 * 10) / (0.4 * 10)

24.8 / 4

6.2

Hope this explains it.

6 0

3 years ago

If y = 3x squared + 4 find the value of y when x = 2

qaws [65]

Answer:

The value of y is 16.

Step-by-step explanation:

You have to substitute x = 2 into the equation :

$y = {3x}^{2} + 4$

Let x = 2,

$y = 3( {2)}^{2} + 4$

$y = 3(4) + 4$

$y = 12 + 4$

$y = 16$

8 0

4 years ago

Read 2 more answers