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vivado [14]
3 years ago
8

Which of the following is the graph of y=1/2X ?

Mathematics
2 answers:
ivanzaharov [21]3 years ago
8 0
Where’s the graph?????
anygoal [31]3 years ago
7 0

Answer:

C on edgenuity

Step-by-step explanation:

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Which correctly describes how the graph of the inequality 6y − 3x > 9 is shaded? -Above the solid line
baherus [9]

The statement which correctly describes the shaded region for the inequality is \fbox{\begin\\\ Above the dashed line\\\end{minispace}}

Further explanation:

In the question it is given that the inequality is 6y-3x>9.  

The equation corresponding to the inequality 6y-3x>9 is 6y-3x=9.

The equation 6y-3x=9 represents a line and the inequality 6y-3x>9 represents the region which lies either above or below the line 6y-3x=9.

Transform the equation 6y-3x=9 in its slope intercept form as y=mx+c, where m represents the slope of the line and c represents the y-intercept.  

y-intercept is the point at which the line intersects the y-axis.  

In order to convert the equation 6y-3x=9 in its slope intercept form add 3x to equation 6y-3x=9.  

6y-3x+3x=9+3x

6y=9+3x

Now, divide the above equation by 6.  

\fbox{\begin\\\math{y=\dfrac{x}{2}+\dfrac{1}{2}}\\\end{minispace}}

Compare the above final equation with the general form of the slope intercept form \fbox{\begin\\\math{y=mx+c}\\\end{minispace}}.  

It is observed that the value of m is \dfrac{1}{2} and the value of c is \dfrac{3}{2}.

This implies that the y-intercept of the line is \dfrac{3}{2} so, it can be said that the line passes through the point \fbox{\begin\\\ \left(0,\dfrac{3}{2}\right)\\\end{minispace}}.

To draw a line we require at least two points through which the line passes so, in order to obtain the other point substitute 0 for y in 6y=9+3x.  

0=9+3x

3x=-9

\fbox{\begin\\\math{x=-3}\\\end{minispace}}  

This implies that the line passes through the point \fbox{\begin\\\ (-3,0)\\\end{minispace}}.  

Now plot the points (-3,0) and \left(0,\dfrac{3}{2}\right) in the Cartesian plane and join the points to obtain the graph of the line 6y-3x=9.  

Figure 1 shows the graph of the equation 6y-3x=9.

Now to obtain the region of the inequality 6y-3x>9 consider any point which lies below the line 6y-3x=9.  

Consider (0,0) to check if it satisfies the inequality 6y-3x>9.  

Substitute x=0 and y=0 in 6y-3x>9.  

(6\times0)-(3\times0)>9  

0>9

The above result obtain is not true as 0 is not greater than 9 so, the point (0,0) does not satisfies the inequality 6y-3x>9.  

Now consider (-2,2) to check if it satisfies the inequality 6y-3x>9.  

Substitute x=-2 and y=2 in the inequality 6y-3x>9.  

(6\times2)-(3\times(-2))>9  

12+6>9  

18>9  

The result obtain is true as 18 is greater than 9 so, the point (-2,2) satisfies the inequality 6y-3x>9.  

The point (-2,2) lies above the line so, the region for the inequality 6y-3x>9 is the region above the line 6y-3x=9.  

The region the for the inequality 6y-3x>9 does not include the points on the line 6y-3x=9 because in the given inequality the inequality sign used is >.

Figure 2 shows the region for the inequality \fbox{\begin\\\math{6y-3x>9}\\\end{minispace}}.

Therefore, the statement which correctly describes the shaded region for the inequality is \fbox{\begin\\\ Above the dashed line\\\end{minispace}}

Learn more:  

  1. A problem to determine the range of a function brainly.com/question/3852778
  2. A problem to determine the vertex of a curve brainly.com/question/1286775
  3. A problem to convert degree into radians brainly.com/question/3161884

Answer details:

Grade: High school

Subject: Mathematics  

Chapter: Linear inequality

Keywords: Linear, equality, inequality, linear inequality, region, shaded region, common region, above the dashed line, graph, graph of inequality, slope, intercepts, y-intercept, 6y-3x=9, 6y-3x>9, slope intercept form.

4 0
3 years ago
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Choose the correct simplification of the expression (3x)^4.
Y_Kistochka [10]
The exponent 4 needs to be applied to both 3 and x, so we would have:
3 * 3 * 3 * 3 * x^4.
9 * 9 * x^4.
81x^4
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2 years ago
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At a meeting, there were 18 men and 24 women. What is the ratio of men to women at the meeting?
sergey [27]

Answer:

men = 12

women = 8

Step-by-step explanation:

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2 years ago
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Identify the number of moles of each element present in one mole of NH NO3.
Sergio039 [100]

Answer:

no se jejfjekqkznbeoqnzne

7 0
2 years ago
A semicircle is attached to the side of a rectangle as shown.
laiz [17]

Answer:

58.8\ mm^2

Step-by-step explanation:

we know that

The area of the figure is equal to the area of rectangle plus the area of semicircle

step 1

Find the area of rectangle

The area of rectangle is equal to

A=bh

where

b=9\ mm\\h=3\ mm

substitute

A=(9)(3)=27\ mm^2

step 2

Find the area of semicircle

The area of semicircle is equal to

A=\frac{1}{2}\pi r^{2}

we have

r=9/2=4.5\ mm ---> the radius is half the diameter

\pi =3.14

substitute

A=\frac{1}{2}(3.14) (4.5)^{2}

A=31.8\ mm^2

step 3

Find the area of the figure

A=27+31.8=58.8\ mm^2

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3 years ago
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