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RSB [31]
3 years ago
6

I kind of understand this question, but I'm not sure how to answer it directly, can someone help please.

Mathematics
1 answer:
nordsb [41]3 years ago
5 0
So here we use the pythagorean theorem which is a2 + b2 = c2 (“a” squared times “b” squared equals “c” squared) the length from calvins house to the intersection is “a” and the length from phoebes house to the intersection is “b” so in order to find out the length of “c” (calvins house to phoebes house) we need to use the pythagorean theorem

a2 275x275=75,625

b2 113x113 = 12,769

so now that we have figured out what a2 and b2 are let’s add them

75,625 + 12,769 = 88,394

now since we only need to find out the length and not the area we need to find the square root of 88,394

the square root of 88,394 is 297.311 (i cut off the decimal after three places)

the direct length from phoebes house to calvins is 297.311 meters
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Now draw the perpendicular  bisector through the 2 intersections of the arcs. That's  it.
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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.

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you get 2 1/8

so you have about 2 minutes before the timer runs out

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