The binomial (2 · x + y)⁷ in expanded form by 128 · x⁷ + 448 · x⁶ · y + 672 · x⁵ · y² + 560 · x⁴ · y³ + 280 · x³ · y⁴ + 84 · x² · y⁵ + 14 · x · y⁶ + y⁷.
<h3>How to expand the power of a binomial</h3>
Herein we have the seventh power of a binomial, whose expanded form can be found by using the binomial theorem and Pascal's triangle. Hence, we find the following expression for the expanded form:
(2 · x + y)⁷
(2 · x)⁷ + 7 · (2 · x)⁶ · y + 21 · (2 · x)⁵ · y² + 35 · (2 · x)⁴ · y³ + 35 · (2 · x)³ · y⁴ + 21 · (2 · x)² · y⁵ + 7 · (2 · x) · y⁶ + y⁷
128 · x⁷ + 448 · x⁶ · y + 672 · x⁵ · y² + 560 · x⁴ · y³ + 280 · x³ · y⁴ + 84 · x² · y⁵ + 14 · x · y⁶ + y⁷
Then, the binomial (2 · x + y)⁷ in expanded form by 128 · x⁷ + 448 · x⁶ · y + 672 · x⁵ · y² + 560 · x⁴ · y³ + 280 · x³ · y⁴ + 84 · x² · y⁵ + 14 · x · y⁶ + y⁷.
To learn more on binomials: brainly.com/question/12249986
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<h3>
Answer:</h3>
The transformation is a rotation.
<h3>
Step-by-step explanation:</h3>
The incorrect answers can be ruled out as follows:
- dilation would change the size, but not the directions of the lines
- reflection would change the DEF ordering from clockwise to counterclockwise
- translation would move the figure, but not change the directions of the lines
The image is the same size as the original. Each of the sides of the triangle is moved through the same angle. The transformation is a rotataion.
The center of rotation can be found as the point of intersection of the perpendicular bisectors of DD', EE' and FF'
Here is the answer, I think.
Answer:
g(n) =0.05*2ⁿ
Step-by-step explanation:
For each fold, the thickness increases by a factor of 100%. With that in mind, as consecutive folds are made, thickness will grow exponentially. If the initial thickness is 0.05, the thickness 'g' as a function of the number of folds 'n' can be described by:
Assuming infinite folds are possible, the thickness is given by g(n) =0.05*2ⁿ.
