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Svetach [21]
3 years ago
8

Is PQR = XYZ? If so, name which similarity postulate or theorem applies.

Mathematics
2 answers:
Aleonysh [2.5K]3 years ago
7 0

We have to determine if triangle PQR is similar to triangle XYZ or not.

To determine if the two triangles are similar, we use three postulates

AA, SSS, SAS.

AA means two angles must be equal in both triangles.

From picture we can see that only one angle is given so we can't be sure about other angles.


SSS means all sides are in same ratio but we have been given value of only one side. So that is also not applicable.


SAS means ratio of two sides from both traingles is equal and both triangles share a common angle but that is also not the given case.


Hence final answer is D. "Cannot be determined".

8_murik_8 [283]3 years ago
5 0

Answer:

cannot be determined (apex)

Step-by-step explanation:


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Simplify (x3 +  3x2 + 5x – 4) –  (3x3 – 8x2 – 5x + 6)

The first thing I have to do is take that "minus" sign through the parentheses containing the second polynomial. Some students find it helpful to put a "1" in front of the parentheses, to help them keep track of the minus sign.

Here's what the subtraction looks like, when working horizontally:

(x3 + 3x2 + 5x – 4) – (3x3 – 8x2 – 5x + 6)

(x3 + 3x2 + 5x – 4) – 1(3x3 – 8x2 – 5x + 6)

(x3 + 3x2 + 5x – 4) – 1(3x3) – 1 (–8x2) – 1(–5x) – 1(6)

x3 + 3x2 + 5x – 4 – 3x3 + 8x2 + 5x – 6

x3 – 3x3 + 3x2 + 8x2 + 5x + 5x – 4 – 6

–2x3 + 11x2 + 10x –10

And here's what the subtraction looks like, when going vertically:

x

3

−(3x

3

​

 

+3x

2

−8x

2

​

 

+5x

−5x

​

 

−4

+6)

​

​

In the horizontal addition (above), you may have noticed that running the negative through the parentheses changed the sign on each and every term inside those parentheses. The shortcut when working vertically is to not bother writing in the subtaction sign or the parentheses; instead, write the second polynomial in the second row, and then just flip all the signs in that row, "plus" to "minus" and "minus" to "plus".

\

x

3

–3x

3

−2x

3

​

 

+3x

2

+8x

2

+11x

2

​

 

+5x

+5x

+10x

​

 

−4

–6

−10

​

​

Either way, I get the answer:

–2x3 + 11x2 + 10x – 10

4 0
3 years ago
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