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ELEN [110]
3 years ago
14

What is 635/72=-5/2(-11/4+x)

Mathematics
1 answer:
Ahat [919]3 years ago
5 0

635/72=-5/2(-11/4+x)

distribute

635/72 = -5/2 * -11/4 - 5/2x

635/72 = 55/8 -5/2 x

multiply each side by 72 to clear the fractions

72*635/72 = 72*(55/8 - 5/2 x)

distribute

635 = 72* 55/8 - 72* 5/2 x

635 = 495 - 180x

subtract 495 from each side

140 = -180 x

divide by -180

-140/180 = x

-14/18 =x

-7/9 =x

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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
Find the value of x.
Leona [35]

This is an isosceles triangle. Therefore, at the base we have congruent angles (look at the picture).

We have the equation:

(5x + 13)° + (3x + 7)° = 180°

5x + 13 + 3x + 7 = 180    <em>combine like terms</em>

(5x + 3x) + (13 + 7) = 180

8x + 20 = 180     <em>subtract 20 from both sides</em>

8x = 160      <em>divide both sides by 8</em>

<h3>x = 20</h3>

3 0
3 years ago
Find X please help me with test corrections due midnight tonight!<br>If HBN is congruent to LYR.
kkurt [141]

Step-by-step explanation:

here's the solution: -

if the given triangles are similar, then their corresponding sides will be in proportion, so

=》

\frac{x}{14}  =  \frac{x + 11}{21}

( by cross multiplication )

=》

21x = 14x + 154

=》

21x - 14x = 154

=》

7x = 154

=》

x =  \frac{154}{7}

=》

x = 22

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Step-by-step explanation:

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