Given: The coordinates of the original rectangle are (8, 6), (4, 6), (8, −4), and (4, −4). We know that the coordinates of the image after dilation from the origin by a scale factor of k is given by:_

$(xy)\rightarrow(kx,ky)$

Then, the coordinates of the image after dilation from the origin by a scale factor of 1.5 are given by:_

(8, 6)→ $(8\times1.5,6\times1.5)=(12,9)$

(4, 6)→ $(4\times1.5,6\times1.5)=(6,9)$

(8, −4) → $(8\times1.5,-4\times1.5)=(12,-6)$

(4, −4)→ $(4\times1.5,-4\times1.5)=(6,-6)$

Hence, the coordinates of the image after dilation from the origin by a scale factor of 1.5 are (12,9), (6,9), (12,-6) and (6,-6).

3 0

4 years ago

The following data was collected from the manufacturing of an auto component. It represents the diameter (in mm) of that compone

kari74 [83]

Answer:

14.6

Step-by-step explanation:

(A). STEP ONE: Calculate the mean

(1). Row one = (10 + 12 + 12 + 14 ) = 48/4 = 12.

(2). Row Two: (12 + 11 + 13 + 16 ) = 52/4 = 13.

(3). Row three : (11 + 13 + 14 + 14)/4 = 13.

(4). Row four: (11 + 10 + 7 + 8)/4 = 36/4 = 9.

(5). Row five: (13 +12 + 14 + 13)/4 = 52/4 = 13.

(B). STEP TWO:

- determine the maximum and minimum value for each row.

- for each row, maximum - minimum.

Maximum values for each row:

Row one = 14, row two= 16, row three = 14, row four = 11 and row five = 14.

Minimum value for each row:

Row one = 10, row two = 11, row three = 11, row four =7 and row five = 12.

DIFFERENCES in each row :

row one = 14 - 10 = 4, row two = 16 - 11 = 5, row three = 14 - 11 = 3, row four = 11 - 7 = 4 and row five = 14 -12 = 2.

(C). STEP THREE: Calculate the mean of all the rows = 60/5 = 12.

(D). STEP FOUR : Calculate the Average Range = 18/5 = 3.6.

(E). STEP FIVE : Calculate the UCL.

A = Average rage × 0.729 = 3.6 × 0.729.

B = overall mean = 12.

UCL = A + B = 14.6.

7 0

3 years ago

Determine the slope of the line that passes through the points (-4, 6) and (0,4).

gavmur [86]

Answer:

B.) $m=-\frac{1}{2}$

Step-by-step explanation:

use the slope rule

$\frac{rise}{run} \\\\\\frac{y2-y1}{x2-x1}$

Fill in values

$\frac{4-6}{0-(-4)}$

Simplify

$\frac{-2}{4}\\-\frac{2}{4}$

Simplify further

$m=-\frac{1}{2}$

Done.

3 0

3 years ago

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