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aleksklad [387]
2 years ago
10

Jessica has a rectangular poster. The poster is 1.8 meters long and 1.5 meters wide. What is the area of the poster in square ce

ntimeters?
Mathematics
2 answers:
luda_lava [24]2 years ago
8 0
You have to multiply length times width. In this case, the length is 1.8 meters. and the width is 1.5 meters. That would give you a total of 2.7 meters square. They are telling to you to put the answer in centimeters, so you have to change the meters to centimeters, 1 meters = 100 centimeters, so you have to multiply 2.7*100 which would give you an answer of 270 square centimeters. YOU'RE WELCOME :)
enyata [817]2 years ago
3 0
O centimetro quadrado do cartas é 2.70
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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
How do you write 78,621,087 in expanded notation and expanded form?
Inga [223]
70,000,000+8,000,000+600,000+20,000+1,000+80+7 = 78,621,087
4 0
3 years ago
The vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). what is the perimeter and area in square units
ad-work [718]
Check the picture below.

the triangle has that base and that height, recall that A = 1/2 bh.

now as for the perimeter, you can pretty much count the units off the grid for the segment CB, so let's just find the lengths of AC and AB,

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\&#10;\begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&A&(~ 2 &,& 8~) &#10;%  (c,d)&#10;&C&(~ 6 &,& 2~)&#10;\end{array}~~~ &#10;%  distance value&#10;d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}&#10;\\\\\\&#10;AC=\sqrt{(6-2)^2+(2-8)^2}\implies AC=\sqrt{4^2+(-6)^2}&#10;\\\\\\&#10;AC=\sqrt{16+36}\implies AC=\sqrt{52}\implies AC=\sqrt{4\cdot 13}&#10;\\\\\\&#10;AC=\sqrt{2^2\cdot 13}\implies AC=2\sqrt{13}

\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\&#10;\begin{array}{ccccccccc}&#10;&&x_1&&y_1&&x_2&&y_2\\&#10;%  (a,b)&#10;&A&(~ 2 &,& 8~) &#10;%  (c,d)&#10;&B&(~ 16 &,& 2~)&#10;\end{array}\\\\\\&#10;AB=\sqrt{(16-2)^2+(2-8)^2}\implies AB=\sqrt{14^2+(-6)^2}&#10;\\\\\\&#10;AB=\sqrt{196+36}\implies AB=\sqrt{232}\implies AB=\sqrt{4\cdot 58}&#10;\\\\\\&#10;AB=\sqrt{2^2\cdot 58}\implies AB=2\sqrt{58}

so, add AC + AB + CB, and that's the perimeter of the triangle.

8 0
3 years ago
What is g(5) for the sequence g={(6,3), (-4,2), (5,0)}
adelina 88 [10]
G(5) for the sequence g = <span>{(6,3), (-4,2), (5,0)} is 0</span>
7 0
2 years ago
Find the volume of a pyramid with a square base, where the perimeter of the base is 8.6 cm and the height of the pyramid is 8.1
Ymorist [56]

Answer:  12.5 CC

Step-by-step explanation:

V=1/3Bh where B is the area of the base and h is the height

The perimeter of the square base is 8.6 so each side is 2.15 and the area of the base is (2.15)^2 or 4.6225

V=1/3(4.6225)(8.1)=12.5cc

4 0
2 years ago
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