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Salsk061 [2.6K]
3 years ago
8

In triangle xyz, z2 = x2 + y2. triangle xyz has sides x, qy, z opposite to the corresponding vertices x, y, z which equation is

true about the measure of the angles of the triangle? the measure of angle xyz is equal to 100 degrees the measure of angle xzy is equal to 90 degrees the measure of angle xyz plus the measure of angle yxz is equal to 80 degrees the measure of angle xyz plus the measure of angle yxz is equal to 70 degrees

Mathematics
2 answers:
Mrac [35]3 years ago
6 0

{\text{In triangle XYZ}},{\text{ square of one side is equal to the sum of squares of other two sides, }} \hfill \\ {\text{,i}}{\text{.e}}{\text{., if triangle XYZ has sides of measure }}x\,{\text{unit, }}y\,{\text{unit and }}z\,{\text{unit}} \hfill \\ {\text{opposite to the corresponding vertices }}X,{\text{ }}Y\,{\text{and }}Z\,{\text{respectively, then}} \hfill \\ {z^2} = {x^2} + {y^2} \hfill \\ {\text{Since, the given triangle satisfying the condition of Pythagoras theorem, }} \hfill \\{\text{thus, the given triangle would be a right angled triangle and thereby the measure}} \hfill \\{\text{of one angle of triangle will be a right angle say at vertex Z}}{\text{.}} \hfill \\\Rightarrow m\left( {\angle Z} \right) = 90^\circ  \hfill \\\Rightarrow m\left( {\angle XZY} \right) = 90^\circ  \hfill \\{\text{Thus,the measure of angle XZY is equal to }}90{\text{ }}degrees. \hfill \\

insens350 [35]3 years ago
3 0

Answer:

Measurement of XZY=90 degrees!

Step-by-step explanation:

I got it correct on my test :)

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The 12th term of a sequence is 41 and the 15th term is 140. What is the nth term?
OLga [1]
An= mth term.
an=a₁+(n-1)*d

a₁₂=41
a₁₅=140

a₁₂=41
41=a₁+(12-1)*d
41=a₁+11d 
a₁+11d=41    (1)

a₁₅=140
140=a₁+(15-1)*d
140=a₁+14d 
a₁+14d=140    (2)

With the equiations (1) and (2)  build a system of equations
a₁+11d=41
a₁+14d=140

we solve it.
-(a₁+11d=41)
  a₁+14d=140
--------------------
       3d=99  ⇒d=99/3=33

a₁+11d=41
a₁+(11*33)=41
a₁+363=41
a₁=41-363=-322

an=a₁+(n-1)*d
an=-322+(n-1)*33
an=-322+33n-33
an=-355+33n

an=-355+33n

To check:
a₁₂=-355+33*12=-355+396=41
a₁₅=-355+33*15=-355+495=140.
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