Combine like terms: 4 - 3m

Graph the polygon and its image after a dilation centered at C(1,1)

Grace [21]

Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.

DIlations are defined by the follwing operation:

$P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]$ (1)

Where:

$O(x,y)$ - Center of dilation.
$k$ - Dilation factor.
$P(x,y)$ - Original point of the polygon.
$P'(x,y)$ - Dilated point of the polygon.

If we know that $O(x,y) = (1,1)$ , $k = 0.5$ , $J(x,y) = (3,1)$ , $K(x,y) = (5, -3)$ , $L(x,y) = (5,5)$ and $M(x,y) = (3,7)$ , then the coordinates of the new polygon are:

$J'(x,y) = (1,1) + 0.5\cdot [(3,1)-(1,1)]$

$J'(x,y) = (1,1)+0.5\cdot (2,0)$

$J'(x,y) = (1,1) +(1,0)$

$J'(x,y) = (2,1)$

$K'(x,y) = (1,1) + 0.5\cdot [(5,-3)-(1,1)]$

$K'(x,y) = (1,1) +0.5\cdot (4,-4)$

$K'(x,y) = (1,1) +(2,-2)$

$K'(x,y) = (3,-1)$

$L'(x,y) = (1,1) + 0.5\cdot [(5,5)-(1,1)]$

$L'(x,y) = (1,1) + 0.5\cdot (4,4)$

$L'(x,y) = (1,1) + (2,2)$

$L'(x,y) = (3,3)$

$M'(x,y) = (1,1) + 0.5\cdot [(3,7)-(1,1)]$

$M'(x,y) = (1,1) +0.5\cdot (2,6)$

$M'(x,y) = (1,1) +(1,3)$

$M'(x,y) = (2,4)$

Now we proceed to present the graphs of the polygon and its image with the help of a graphing tool. The original polygon is highlighted in red and the image is highlighted in blue.

We kindly invite to check this question on dilations: brainly.com/question/13176891

6 0

3 years ago

What is the equation of this line in slope intercept form? 2x+y=−19

Zina [86]

Isolate y by subtracting 2x from both sides
Your answer is: y= -2x-19

4 0

3 years ago

he gas mileage for a certain model of car is known to have a standard deviation of 4 mi/gallon. A simple random sample of 49 car

charle [14.2K]

Answer:

c) (26.295, 28.705)

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.965}{2} = 0.0175$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.0175 = 0.9825$ , so $z = 2.11$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.11\frac{4}{\sqrt{49}} = 1.205$

The lower end of the interval is the sample mean subtracted by M. So it is 27.5 - 1.205 = 26.295 mi/gallon

The upper end of the interval is the sample mean added to M. So it is 27.5 + 1.205 = 28.705 mi/gallon

So the correct answer is:

c) (26.295, 28.705)

5 0

4 years ago

2. angle ABE = angle MNP Write another valid congruency statement:

Free_Kalibri [48]

Given:

$\Delta ABE\cong \Delta MNP$

To find:

The congruent angles and sides, then find the another valid congruency statement.

Solution:

We have,

$\Delta ABE\cong \Delta MNP$

We know that, corresponding parts of congruent triangles are congruent (CPCTC).

Using CPCTC, we get

Angles:

$\angle A\cong \angle M$

$\angle B\cong \angle N$

$\angle E\cong \angle P$

Sides:

$AB\cong MN$

$BE\cong NP$

$AE\cong MP$

The another congruent statement is $\Delta BEA\cong \Delta NPM$ .

Therefore, the required table is

Angles Sides

$\angle A\cong \angle M$ $AB\cong MN$

$\angle B\cong \angle N$ $BE\cong NP$

$\angle E\cong \angle P$ $AE\cong MP$

The another congruent statement is $\Delta BEA\cong \Delta NPM$ .

4 0

3 years ago

Please answer fast!!!!!!!!!!!!!!!!!!!!!!

nadezda [96]

Answer:

y = -2x + 6 and y = 1/3x - 7

Step-by-step explanation:

For A, using rise over run, you can count 2 units up and 1 unit left of any given point to get to the next point. Because left is the negative direction on a graph, the 1 unit is negative. To calculate slope, divide the rise (2) over the run (-1) and substitute the slope as m into y = mx + b. In the formula, b is the y-intercept (where the line crosses the x axis). The y-intercept of A is 6, so replace b in the formula with 6:

y = -2x + 6

The slope of B is 1/3 and the y intercept is -7, so substitute those values into the formula again to get the answer for B:

y = 1/3x - 7

6 0

3 years ago

Combine like terms: 4 - 3m - 1 + 2m