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lesantik [10]
3 years ago
11

If a polygon has a vertex at (161, -329) and it is translated 168 units to the right, what are the coordinates of that vertex's

new location? Type your answer as an ordered pair, like this example: (-12, 34).
Mathematics
1 answer:
bearhunter [10]3 years ago
5 0
Vertex of the polygon is (161, -329)

The new vertex is shifted 168 units to the right. A horizontal shift can be achieved be adding or subtracting the number from the x-coordinate. A change in the y coordinate brings the vertical shift. So in this case the x-component will change only and y component will be the same.

A shift towards right means, the value of x component is increase as x gets larger as we move towards right on the graph. So moving 168 units to the right, we will get the following vertex (329 , -329)

Thus, the new vertex of the polygon will be at the point (329, -329)
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Here's the question. ​
OleMash [197]

Answer:

The value of T₂₀ - T₁₅ is <u>-20</u>.

Step-by-step explanation:

<u>Given</u> :

  • >> If for an A.P, d = -4

<u>To</u><u> </u><u>Find</u> :

  • >> T₂₀ - T₁₅

<u>Using Formula</u> :

General term of an A.P.

\star{\small{\underline{\boxed{\sf{\red{ T_n = a  + (n - 1)d}}}}}}

  • >> Tₙ = nᵗʰ term
  • >> a = first term
  • >> n = no. of terms
  • >> d = common difference

<u>Solution</u> :

Firstly finding the A.P of T₂₀ by substituting the values in the formula :

{\dashrightarrow{\pmb{\sf{ T_n = a  + (n - 1)d}}}}

{\dashrightarrow{\sf{ T_{20} = a  + (20 - 1) d}}}

{\dashrightarrow{\sf{ T_{20} = a  + (19)d}}}

{\dashrightarrow{\sf{ T_{20} = a  + 19  \times d}}}

{\dashrightarrow{\sf{ T_{20} = a  + 19d}}}

{\star \: {\underline{\boxed{\sf{\pink{ T_{20} = a  + 19d}}}}}}

Hence, the value of T₂₀ is a + 19d.

\rule{190}1

Secondly, finding the A.P of T₁₅ by substituting the values in the formula :

{\dashrightarrow{\pmb{\sf{ T_n = a  + (n - 1)d}}}}

{\dashrightarrow{\sf{ T_{15}= a  + (15 - 1) d}}}

{\dashrightarrow{\sf{ T_{15}= a  + (14) d}}}

{\dashrightarrow{\sf{ T_{15}= a  + 14 \times d}}}

{\dashrightarrow{\sf{ T_{15}= a  + 14d}}}

{\star{\underline{\boxed{\sf \pink{ T_{15}= a  + 14d}}}}}

Hence, the value of T₁₅ is a + 14d

\rule{190}1

Now, finding the difference between T₂₀ - T₁₅ :

{\dashrightarrow{\pmb{\sf{T_{20} -  T_{15}}}}}

{\dashrightarrow{\sf{(a + 19d) -  (a + 14d)}}}

{\dashrightarrow{\sf{a + 19d -  a  -  14d}}}

{\dashrightarrow{\sf{a - a + 19d -  14d}}}

{\dashrightarrow{\sf{0+ 19d -  14d}}}

{\dashrightarrow{\sf{19d -  14d}}}

{\dashrightarrow{\sf{5 \times  - 4}}}

{\dashrightarrow{\sf{ - 20}}}

{\star \: \underline{\boxed{\sf{\pink{T_{20} -  T_{15} =  - 20}}}}}

Hence, the value of T₂₀ - T₁₅ is -20.

\underline{\rule{220pt}{3.5pt}}

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Step-by-step explanation:

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Step-by-step explanation:

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