What is the x-coordinate of the solution for the system of equations? {y−x=910+2x=−2y Enter your answer in the box. x =
2 answers:
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Answer:
3rd and 4th Options are correct choices.
Step-by-step explanation:
We have been given a graph and we are asked to find which of the given figures demonstrate translation.
Since we know that in translation every point of the object must be moved in the same direction and for the same distance. By translation we can shift a figure in upward, downwards, left and right directions.
Now let us see our given choices one by one.
1. Upon looking at figures represented by 1st option we can see that both figures are mirror images to each other. Since we can get mirror images reflecting the pre-image over an axis of symmetry. So the given figures are result of reflection, therefore, 1st option is not a correct choice.
2. We can see that the figures represented by 2nd option are similar. One figure is smaller and other is larger. Since we get a similar image by dilating our pre-image. Therefore, these figures are result of dilation and 2nd option is not correct indeed.
3. We can see that figures represented by 3rd option are same and these figures are result of shifting. We can see that 1st figure is shifted to right to get the second figure, therefore, 3rd option is a correct choice.
4. The figures represented by 4th option are same and these figures are result of shifting. We can see the figure in the bottom is result of shifting the upper figure downwards and then to right. Therefore, 4th option is a correct choice.
13,207,982,634 x⁵y⁶
Step-by-step explanation:
We understand that in Binomial Theorem, expounding of polynomial functions, we have a rule that also involves the use of Pascal's Triangle to find the Coefficients that will be used to multiply each variable as the polynomial function is multiplied by itself several times;
(3x + 7y)^11 = ₁₁C₀ (3x)¹¹(7y)⁰ + ₁₁C₁ (3x)¹⁰(7y)¹ + ₁₁C₂ (3x)⁹(7y)² + ₁₁C₃ (3x)⁸(7y)³ + ₁₁C₄ (3x)⁷(7y)⁴ + ₁₁C₅ (3x)⁶(7y)⁵ + ₁₁C₆ (3x)⁵(7y)⁶....
The 7th term in our case is;
₁₁C₆ (3x)⁵(7y)⁶
According to the attached Pascals Triangle, the coefficient for our term should be 462, so;
462 (3x)⁵(7y)⁶
= 462 (243x⁵) (117,649y⁶)
= 13,207,982,634 x⁵y⁶
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