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lisov135 [29]
3 years ago
6

(PLEASE!!!!) The congruency of MNO and XYZ can be proven using a reflection across the line bisecting OZ. However, this congruen

cy can also be proven using geometric postulates, theorems, and definitions. Prove that the triangles are congruent using a two-column proof and triangle congruency theorems.

Mathematics
2 answers:
jeka943 years ago
7 0

Hello! I had this same question on a test, so I am going to share the answers that I were told are 100% correct!

1: Given

2: Given

3: Given

4: Definition of congruence

5: Reflexive Property

6: Addition property

7: Segment addition postulate

8: Definition of congruence

9: AAS Congruency theorem

Of course, some tests are worded differently, so some extra reading is required. However, I hope this helps, good luck! :)

finlep [7]3 years ago
6 0

Explanation:

Only the reasons need be given here, as the statements are already given in your figure.

  1. Given
  2. Given
  3. Given
  4. Definition of congruent line segments
  5. Symmetric property of congruence
  6. Addition and substitution properties of equality*
  7. Segment addition theorem
  8. Definition of congruent line segments
  9. AAS congruence postulate

_____

* The addition property says if A=B, then A+C=B+C. The substitution property further says if C=D, then A+C=B+D (D can be substituted for C). IMO, both properties are needed together to get from A=B and C=D to A+B=C+D.

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Answer:

You need more information. But typically multiplly by 100 so .1 would be 10 %

Step-by-step explanation:


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RideAnS [48]

\sf{Given : 3tanx + 7 = \dfrac{2}{(1 - sinx)(1 + sinx)}}

We know that : (a - b)(a + b) = a² - b²

\implies \sf{3tanx + 7 = \dfrac{2}{1 - sin^2x}}

We know that : 1 - sin²x = cos²x

\implies \sf{3tanx + 7 = \dfrac{2}{cos^2x}}

\sf{\bigstar \ \ We \ know \ that : \boxed{\sf{\dfrac{1}{cos^2x} = sec^2x}}}

\implies \sf{3tanx + 7 = 2sec^2x}

We know that : sec²x = 1 + tan²x

\implies \sf{3tanx + 7 =2(1 + tan^2x)}

\implies \sf{2 + 2tan^2x - 3 tanx - 7 = 0}

\implies \sf{2tan^2x - 3 tanx - 5 = 0}

\implies \sf{2tan^2x -  5tanx + 2tanx - 5 = 0}

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First of all, let's note the sales tax rates in each town. In Washington, we know it's 6%. In the town in Virginia, it's 5%. In the town in Maryland, it's 9%.

Let's figure out the total taxes in every town by applying the sales tax rate for each town.

To add percents to a whole number, we always multiply using 0.XX (example: to add 1% to a the number 100, we would multiply 100*0.01 and get the answer 1. We'd then add the 1 to the original number, 100, and get 101.)


In this case, we need to multiply the $1000 by the sales tax in Washington, 6%.

1000 x 0.06 = 60. Now, we add the 60 to the original number (1000), and get 1060. Now we know the total tax in Washington on the computer will be $60, and the total price we will pay is $1060.00


For Virginia, the sales tax is 5%. Let's add the 5% using the same method we used in the equation above.

1000 x 0.05 = 50. Now, add the 50 to the original 1000, and we get 1050. Now we know that the total tax in Virginia is going to be $50, and the total price that we'll pay in Virginia is $1050.00.


On to the final town, Maryland. In Maryland, the sales tax rate is 9%. Let's use the same formula again.

1000 * 0.09 = 90. Now that we have the 90, we add it to the original 1000, and we get 1090. In Maryland the total sales tax will be $90, and the total price we'll pay is $1090.00.


Now, let's complete the question by answering the 3 parts.


To spend the least amount total Amir should buy the computer in Virginia ($1050.00).

Amir would pay the most sales tax in Maryland ($90.00).

Amir would pay $60 sales tax in Washington, DC.


I hope this answer was in depth enough to help you out so that you can do this on your own in the future. :)

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