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solmaris [256]
3 years ago
11

Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the g

raph of the following inequality:
y > one half x + 2 (5 points)


The origin is not included in the shaded region and the shaded area is above the line.

The origin is not included in the shaded region and the shaded area is below the line.

The origin is included in the shaded region and the shaded area is above the line.

The origin is included in the shaded region and the shaded area is below the line.

Mathematics
1 answer:
just olya [345]3 years ago
3 0

Answer:

The correct option is

The origin is included in the shaded region and the shaded area is below the line.

Step-by-step explanation:

Y>3/2x + 2

Put x=0

Y= 2

(0,2)

Put y=0

X= -4/3

(-4/3,0)

See attached picture for the sketch

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Find the slope of the line.
pickupchik [31]
There are several ways to do this.
I'll show you two methods.

1) Pick two points on the line and use the slope formula.
Look for two points that are easy to read. It is best if the points are on grid line intersections. For example, you can see points (-4, -1) and (0, -2) are easy to read.
Now we use the slope formula.

slope = m = (y2 - y1)/(x2 - x1)

Call one point (x1, y1), and call the other point (x2, y2).
Plug in the x1, x2, y1, y2 values in the formula and simplify the fraction.

Let's call point (-4, -1) point (x1, y1).
Then x1 = -4, and y1 = -1.
Let's call point (0, -2) point (x2, y2).
Then x2 = 0, and y2 = -2.

Plug in values into the formula:

m = (y2 - y1)/(x2 - x1) = (-2 - (-1))/(0 - (-4)) = (-2 + 1)/(0 + 4) = -1/4

The slope is -1/4

2) Pick two points on the graph and use rise over run.
The slope is equal to the rise divided by the run.
Run is how much you go up or down.
Rise is how much you go right or left.

Pick two easy to read points.
We can use the same points we used above, (-4, -1) and (-0, -2).
Start at point (0, -2).
How far up or down do you need to go to get to point (-4, -1)?
Answer: 1 unit up, or +1.
The rise is +1.
Now that we went up 1, how far do you go left or right top go to point (-4, -1)?
Answer: 4 units to the left. Going left is negative, so the run is -4.
Slope = rise/run = +1/-4 = -1/4

As you can see we got the same slope using both methods.
6 0
3 years ago
If f(x) = x^2 +1, and g(x) = x - 2, find [fºg)(x).<br> PLEASE HELP
dem82 [27]

Answer:

A.

Step-by-step explanation:

8 0
2 years ago
can someone please help me with this question!!
valkas [14]

Answer:

B' (-4, -4)

Step-by-step explanation:

When you dilate from the origin, you multiply the coordinate points by the scale factor.

B (-1, -1) × 4 = B' (-4, -4)

I hope this helps :))

7 0
3 years ago
What is the graph of the function f(x) = the quantity of x plus 2, all over x minus 3
lisabon 2012 [21]
Go to desmos.com its a free graphing calculator site. type in (x+2)/(x-3)

it'll show you the graph

6 0
2 years ago
Holly wants to save money for an emergency. Holly invests $1,100 in an account that pays an interest rate of 8.75%. How many yea
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