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notsponge [240]
3 years ago
11

NEED THE ANSWER ASAP!!

Mathematics
1 answer:
kolezko [41]3 years ago
5 0
68 degrees because they’re vertical angles
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What is the reason for Statement 3 of the two-column proof?
Ivenika [448]

Refer to the attached image.

Given:

The measure of \angle JMK= 52^\circ and \angle KML= 38^\circ.

Also, Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove: \angle JML is a right angle.

Proof:

  Statements                                                                                 Reasons

1. m \angle JMK=52^\circ                                            Given

2. m \angle KML=38^\circ                                           Given

3. m \angle JMK+m \angle KML=m \angle JML  

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. 52^\circ+38^\circ = m \angle JML   Substitution property of equality

5. 90^\circ = m \angle JML                  Simplification

6. \angleJML is a right angle.      Definition of right angle

8 0
3 years ago
If y=e5t is a solution to the differential equation
a_sh-v [17]

Answer:

k = 30, y(t) = C_1e^{5t}+C_2e^{6t}

Step-by-step explanation:

Since y=e^{5t} is a solution, then it must satisfy the differential equation. So, we calculate the derivatives and replace the value in the equation. We have that

\frac{d^2y}{dt^2} = 25 e^{5t},\frac{dy}{dt} = 5e^{5t}

Then, replacing the derivatives in the equation we have:

25e^{5t}-11(5)e^{5t}+ke^{5t}=0 e^{5t}(25-55+k) =0

Since e^{5t} is a positive function, we have that

25-55+k = 0 \rightarrow k = 30.

Now, consider a general solution y(t) = Ae^{rt}, A \in \mathbb{R}, then, by calculating the derivatives and replacing them in the equation, we get

Ae^{rt}(r^2-11r+30)=0

We already know that r=5 is a solution of the equation, then we can divide the polynomial by the factor (r-5) to the get the other solution. If we do so, we get that (r-6)=0. So the other solution is r=6.

Therefore, the general solution is

y(t) = C_1e^{5t}+C_2e^{6t}

8 0
3 years ago
Pedro le dice a María si cambias los billetes de 10 € que tienes por billetes de 5 € y los billetes de 5 € por billetes de 10 €
Bad White [126]

Answer: Maria has 10 bills of 5€ and 10 bills of 10€.

She has a total of 150€.

Step-by-step explanation:

Let be "f" the number of 5€ bills that Maria has and "t" the number of 10€ bills that Maria has.

Set up a system of equations:

\left \{ {{f+t=20} \atop {5f+10t=10f+5t}} \right.

Use the Substitution method to solve the system of equations:

1. Solve for "f" from the first equation:

f=20-t

2. Substitute the equation obtained into the second equation and solve for "t".

Then:

5(20-t)+10t=10(20-t)+5t\\\\100-5t+10t=200-10t+5t\\\\20t-10t=100\\\\t=\frac{100}{10}\\\\t=10

3. Substitute the value of "t" into the equation f=20-t and evaluate:

f=20-10\\\\f=10

Therefore, Maria has 10 bills of 5€ and 10 bills of 10 €.

So the total amount of money she has, is:

Total=10(5)+10(10)=150

She has a total of 150€.

5 0
3 years ago
What is the value of 7x^2 + 3x + 4 when x=2?
Nonamiya [84]

Answer:

38

Step-by-step explanation:

substitute the value of the variable into an equation, then simplify

8 0
3 years ago
Read 2 more answers
How can you tell that −10 and −20 are solutions to this inequality, but 10 is not? 3n − 40 < −5n + 8
pochemuha

Step-by-step explanation:

-10 or -20 satisfies the equation.

But when you substitute 10 in:

30-40<-50+8

-10<-42(wrong)

it's wrong

6 0
3 years ago
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