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zheka24 [161]
3 years ago
5

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

Mathematics
1 answer:
Setler [38]3 years ago
6 0

Answer:

-m+3

Step-by-step explanation:

4 - 3m - 1 + 2m

4-1-m

-m+3

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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 <em>original</em> polygon is highlighted in <em>red</em> and the image is highlighted in <em>blue</em>.

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 <em>original</em> polygon is highlighted in <em>red</em> and the image is highlighted in <em>blue</em>.

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 <br><br> 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
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