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2 years ago

8

if we just passed a sign which says that harrison is 25 miles away and turkey is 40 miles ahead, how far will we have to go to b

e halfway between turkey and harriso

1 answer:

Tatiana [17]2 years ago

4 0

Answer:

<em>You will need to go 7.5 miles to be halfway between Harrison and Turkey</em>

Step-by-step explanation:

If you see a sign saying that Harrison is 25 miles away and that Turkey is 40 miles ahead, then the distance from Harrison to Turkey must be 40 miles - 25 miles = 15 miles.

If you drive up to be halfway between Harrison and Turkey, then you need to travel 15/2 = 7.5 miles.

You will need to go 7.5 miles to be halfway between Harrison and Turkey

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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:

A problem to determine the range of a function brainly.com/question/3852778
A problem to determine the vertex of a curve brainly.com/question/1286775
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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Answer: 1) x> -21

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2 years ago

Which unit rates would be appropriate for describing the speed of cars in a race?

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Miles per hours and feet per second.

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3 years ago

Sravya earns $42,820 per year in take home pay. What is the most money a housing expert would advise her to spend on a monthly m

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Step-by-step explanation:

the most money a housing expert would advise her to spend on a monthly mortgage payment would be 1,645

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2 years ago

I NEED THIS ASAP, PLEASE HELP!!!

WINSTONCH [101]

Answer: 22.5 ; 5 ; 14

Step-by-step explanation:

Given the dataset:

{20,22,23,24,26,26,28,29,30}

The lower quartile (Q1) = 1/4(n + 1)th term

Where n = number of observations, n = 9

Q1 = 1/4 (9 + 1)th term

Q1 = 1/4(10) = 2.5

We average the 2nd and 3rd term:

(22 + 23) / 2

45 / 2 = 22.5

B) The interquartile range(IQR) of the dataset :

{62,63,64,65,67,68,68,68,69,74}

IQR = Q3 - Q1

The lower quartile (Q1) = 1/4(n + 1)th term

Where n = number of observations, n = 10

Q1 = 1/4 (10 + 1)th term

Q1 = 1/4(11) = 2.75 term

We take the average of the 2nd and 3rd term:

(63 + 64) / 2

45 / 2 = 63.5

The upper quartile (Q3) = 3/4(n + 1)th term

Where n = number of observations, n = 10

Q3 = 3/4 (10 + 1)th term

Q3 = 3/4(11) = 8.25 term

We take the average of the 8th and 9th term:

(68 + 69) / 2

137 / 2 = 68.5

IQR = Q3 - Q1

IQR = 68.5 - 63.5

IQR = 5

C) give the dataset :

{7,8,8,9,10,12,13,15,16}

The upper quartile (Q3) = 3/4(n + 1)th term

Where n = number of observations, n = 9

Q3 = 3/4 (9 + 1)th term

Q3 = 3/4(10) = 7.5 term

We take the average of the 7th and 8th term:

(13 + 15) / 2

28 / 2 = 14

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3 years ago