Answer the question in the image

Complete the description of the piecewise function graphed below. Use interval notation to indicate intervals.

Gemiola [76]

Answer:

{ -2 if x ∈ -4 < x < -3

{ -5 if x ∈ -3 ≤ x < 2

[ 5 if x ∈ 2 ≤ x < 5

Step-by-step explanation:

From the graph, we have;

{ -2 if x ∈ -4 < x < -3

For the next inequality line at y = -5, we have;

1) The inequality line, starts with an open circle on the left at x = -3, which is equivalent to less than or equal to symbol, ≤ as -3 ≤ x because the point x =-3 is the left boundary. The inequality line extends to the point x = 2, where we have a closed circle (on the right), which is equivalent to a x ≤ 2 with the 2 on the right hand side because, the 2 is the right boundary of the inequality

2) The inequality can be summarized as starting from x = -3 extends to x = 2

3) As stated in point 1) the point x = 3, we have -3 ≤ x and at point x = 2, we have x ≤ 3 which can be combined as -3 ≤ x < 2, to give;

{ -5 if x ∈ -3 ≤ x < 2

For the next inequality line at y = 5, we have;

1) The inequality line, starts with an open circle on the left at x = 2, which is equivalent to less than or equal to symbol, ≤ as 2 ≤ x because the point x =2 is the left boundary. The inequality line extends to the right to reach point x = 5, where we have a closed circle (on the right), which is equivalent to a x ≤ 5 inequality, with the 5 on the right hand side because, the 5 is the right boundary of the inequality

2) The inequality can be summarized as starting from x = 2 extends to x = 5

3) As stated in point 1) the point x = 2, we have 2 ≤ x and at point x = 5, we have x ≤ 5 which can be combined as 2 ≤ x < 5, to give;

[ 5 if x ∈ 2 ≤ x < 5.

7 0

3 years ago

-2x+y=1 and y=-x+4 What is x?

Vikentia [17]

When -2x+y=1 and y=-x+4, x = 1

4 0

3 years ago

Name all the corresponding congruent angles and sides? Then complete the triangle congruence statement?

Flura [38]

Answer:

Angle A = Angle Y

Angle B = Angle Z

Angle C = Angle X

AB = YZ

AC = YX

BC = ZX

Triangle ABC = Triangle YZX

Step-by-step explanation:

Find this by looking at the corresponding parts on the other triangle. They have the same marking on them. Make sure that when answering for segments or triangles that the order is the same on both sides.

6 0

3 years ago

Find the area of this parallelogram.

Grace [21]

Answer: A
i hope it helped

3 0

3 years ago

The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:

denis23 [38]

Part A) x-intercepts simply show that when the value of the function is zero. Vertex coordinates show that when the function obtains its maximum value. When x=50, function obtains its maximum value and it's 75. The function is increasing in the interval (0, 50) and decreasing in the interval (50, 100). In regard to the height and distance of the tunnel, these numbers show that decreasing and increasing intervals are symmetric. Each number from the intervals has its own pair in the corresponding interval and they are located in the same distance from the midpoint (50,75)

Part B) In order to calculate the average rate of change, we can first write the function. Using the information about the x-intercept and the vertex coordinates, we find that our function is $f(x)=-0.03x^{2}+3x$ .
Plugging 15 and 35 in x, we can find the values of the function, i.e.
$f(15)=38.25$ and $f(35)=68.25$ .
Then, the average change is $\frac{68.25-38.25}{35-15}=1.5$

4 0

3 years ago

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