Mathematics, 19.10.2020 03:01 cschuessler3

Solve and show the steps to the picture attached

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Answer from: vanessam16

The image of point (2, 4) after transformation is (-2, 13) ⇒ D

Step-by-step explanation:

Let us revise some transformation

Translation right-left OR up-down

If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h) ⇒ add x-coordinate of every point by hIf the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h) ⇒ subtract x-coordinate of every point by hIf the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k ⇒ add y-coordinate of every point by kIf the function f(x) translated vertically down by k units, then its image is g(x) = f(x) - k ⇒ subtract y-coordinate of every point by k

A vertical stretching and a vertical compression (or shrinking)

If m > 1, the graph of y = m • f(x) is the graph of f(x) vertically stretched by factor m. ⇒ multiply every y-coordinate by mIf 0 < m < 1 (a fraction), the graph of y = m • f(x) is the graph of f(x) vertically shrunk (or compressed) by factor m ⇒ multiply every y-coordinate by m

Let us use these rules to solve the question.

∵ Point (2, 4) lies on y = x²

∵ The image of y = x² is y = 3(x + 4)²+1

→ The rules of transformation is y = m(x + h)² + k

∵ m is the scale factor of a vertical stretched

∵ m = 3

→ By using the 5th rule above

∴ The y-coordinate of point (2, 4) should multiply by 3

∴ The image of the point is (2, 4 × 3) = (2, 12)

∵ h is the horizontal translation to the left

∵ h = 4

→ By using the 2nd rule above

∴ The x-coordinate of point (2, 12) should subtract by 4

∴ The image of the point is (2 - 4, 12) = (-2, 12)

∵ k is the vertical translation up

∵ k = 1

→ By using the 3rd rule above

∴ The y-coordinate of point (-2, 12) should add by 1

∴ The image of the point is (-2, 12 + 1) = (-2, 13)

∴ The image of point (2, 4) after transformation is (-2, 13)

Answer from: Quest

Arhombus is a quadrilateral.

Answer from: Quest

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

$\begin{bmatrix}1 & 0 & 0& |5 \\ 0& 2& 0& |8\\ 0& 0& 3& |9\end{bmatrix}$

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

$\begin{bmatrix}1 & 0 & 0& |5 \\ 0& 1& 0& |4\\0& 0& 1& |3\end{bmatrix}$

What is the next step in solving this augmented matrix using gauss-jordan elimination method

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