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Verizon [17]
2 years ago
10

HELP ASAP THIS IS DUE RIGHT NOW

Mathematics
1 answer:
mars1129 [50]2 years ago
7 0

Slime was a toy product manufactured by Mattel, sold in a plastic trash can and introduced in February 1976. It consisted of a non-toxic viscous, squishy and oozy green or other color material made primarily from guar gum.

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A. 14 (7x2=14)

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Pls help me with my math
givi [52]

Answer:

The definition for the given piecewise-defined function is:   \boxed{\displaystyle\sf\ Option\:D:\:\: f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}.

Step-by-step explanation:

<h3>General Concepts:</h3>
  • Piecewise-defined functions.
  • Interval notations.

<h3>What is a piecewise-defined function?</h3>

A piecewise-defined function represents specific rules over different intervals of the domain.  

<h3>Symbols used in expressing interval notations:</h3>

Open interval: This means that the endpoint is <em>not</em> included in the interval.

We can use the following symbols to indicate the <u>exclusion</u> of endpoints in the interval:

  • Left or right parenthesis, "(  )" (or both).
  • Greater than (>) or less than (<) symbols.
  • Open dot "\circ" is another way of expressing the exclusion of an endpoint in the graph of a piecewise-defined function.

Closed interval: This implies the inclusion of endpoints in the interval.

We can use the following symbols to indicate the <u>inclusion</u> of endpoints in the interval:

  • Open- or closed brackets (or both), "[  ]."
  • Greater than or equal to (≥) or less than or equal to (≤) symbols.
  • Closed circle or dot, "•" is another way of expressing the <em>inclusion</em> of the endpoint in the graph of a piecewise-defined function.  

<h2>Determine the appropriate function rule that defines different parts of the domain.  </h2>

The best way to determine which piecewise-defined function represents the graph is by observing the <u>endpoints</u> and <u>orientation</u> of both partial lines.

  • Open circle on (-1, 2):  The graph shows that one of the partial lines has an <em>excluded</em> endpoint of (-1, 2) extending towards the <u>right</u>. This implies that its domain values are defined when x > -1.
  • Closed circle on (-1, 1): The graph shows that one of the partial lines has an <em>included</em> endpoint of (-1, 1) extended towards the <u>left</u>. Hence,  its domain values are defined when x ≤ -1.

Based on our observations from the previous step, we can infer that x > -1 or x ≤ -1 apply to piecewise-defined functions A or D. However, only one of those two options represent the graph.

<h2>Solution:</h2><h3>a) Test option A:</h3>

    \boxed{\displaystyle\sf Option\:A)\:\:\:f(x) = \begin{cases}\displaystyle\sf\ 2x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ x + 4 & \sf\:{if\:\:x > -1}\end{cases}}

<h3>Piece 1: If x ≤ -1, then it is defined by f(x) = 2x + 2. </h3>

We must choose a domain value that falls within the interval of x ≤ -1 whose output is included is included in the graph of the partial line with a <u>closed dot</u>.

Substitute x = -2 into f(x) = 2x + 2:  

  • f(x) = 2x + 2
  • f(-2) = 2(-2) + 2
  • f(-2) = -4 + 2
  • f(-2) = -2  ⇒  <em>False statement</em>.

⇒ The output value of f(-2) = -2 is <u>not</u> included in the graph of the partial line whose endpoint is at (-1, 1).

<h3>Piece 2: If x > -1, then it is defined by f(x) = x + 4. </h3>

We must choose a domain value that falls within the interval of x > -1 whose output is included in the graph of the partial line with an <u>open dot</u>.

Substitute x = 0 into  f(x) = x + 4:

  • f(x) = x + 4
  • f(0) = (0) + 4
  • f(0) = 4  ⇒  <em>True statement</em>.

⇒ The output value of f(0) = 4 <u>is</u> included in the graph of the partial line whose endpoint is at (-1, 2).

Conclusion for Option A:

Option A is not the correct piecewise-defined function because one of the pieces, f(x) = 2x + 2, does not specify the interval (-∞, -1].

<h3>b) Test option D:</h3>

    \boxed{\displaystyle\sf Option\:D)\:\:\:f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}

<h3>Piece 1:  If x ≤ -1, then it is defined by f(x) = x + 2. </h3>

We must choose a domain value that falls within the interval of x ≤ -1 whose output is included is included in the graph of the partial line with a <u>closed dot</u>.

Substitute x = -2 into f(x) = x + 2:

  • f(x) = x + 2
  • f(-2) = (-2) + 2
  • f(-2) = 0  ⇒  <em>True statement</em>.

⇒ The output value of f(-2) = 0 <u>is</u> included the graph of the partial line whose endpoint is at (-1, 1).

<h3>Piece 2: If x > -1, then it is defined by f(x) = 2x + 4.</h3>

We must choose a domain value that falls within the interval of x > -1 whose output is included is included in the graph of the partial line with an <u>open dot</u>.

Substitute x = 0 into f(x) = 2x + 4:

  • f(x) = 2x + 4
  • f(0) = 2(0) + 4
  • f(0) = 0 + 4 = 0  ⇒  <em>True statement</em>.

⇒ The output value of f(0) = 4 <u>is</u> included in the graph of the partial line whose endpoint is at (-1, 2).  

<h2>Final Answer: </h2>

We can infer that the piecewise-defined function that represents the graph is:

\boxed{\displaystyle\sf\ Option\:D:\:\: f(x) = \begin{cases}\displaystyle\sf\ x + 2 & \sf\:{if\:\:x \leq -1} \\\displaystyle\sf\ 2x + 4 & \sf\:{if\:\:x > -1}\end{cases}}.

________________________________________

Learn more about piecewise-defined functions here:

brainly.com/question/26145479

8 0
2 years ago
A multiple-choice question has 3 options. What is the percentage that you will choose the WRONG option?
sukhopar [10]

Answer:

66%

Step-by-step explanation: 2/3 is .66666666666666...

4 0
3 years ago
A cylinder and a cone have the same volume. The cylinder has a radius of 2 inches and a hieght of 3 inches. The cone has a radiu
arlik [135]

The height of the cone is inches, if the cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.

Step-by-step explanation:

The given is,

          A cylinder and a cone have the same volume

          Cylinder has a radius 2 inches and height of 3 inches.

          Cone has a radius of 3 inches

Step:1

           For Cylinder'

           Formula to calculate the volume of cylinder is,

                        V = \pi r^{2} h..................................................(1)

          where,

                      r - 2 inches

                      h - 3 inches

         From the equation (1)

                           = \pi × 2^{2} × 3

                           = 37.70

                        V = 37.70 cubic inches

Step:2

         For cone,

         Formula to calculate the volume of cone is,

                     V = \pi r^{2} \frac{h}{3}..................................................(2)

         From the statement,

                      cylinder and a cone have the same volume

                      V_{cylinder} = V_{cone}

                          37.70 = \pi × 3^{2} × \frac{h}{3}

                          37.70 = 9.42478 × h

Height of the cone, h = 4 inches

Result:

            Thus the height of the cone is 4 inches, if a cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.

4 0
2 years ago
How do find the volume of 20cm and 30cm and 45cm
saw5 [17]
What 3D figure/shape is it?
7 0
2 years ago
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