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Vesnalui [34]
2 years ago
15

| 15. Aliyah runs approximately 5.4 miles per hour.

Mathematics
1 answer:
miss Akunina [59]2 years ago
6 0

Answer: 33.33 minutes longer.

Step-by-step explanation :

We need to remember the following formula:

 t=\frac{d}{V}

Where "t" is the time, "d" is the distance and "V" is the speed.

We know that she runs approximately 5.4 miles per hour, then:

V=5.4\ \frac{mi}{h}

Since she plans to run 9 miles on Tuesday, her run's time on Tuesday will be:

t_1=\frac{9\ mi}{5.4\ \frac{mi}{h}}\\\\t_1=\frac{5}{3}\ h

Making the conversion from hours to minutes, we get:

(\frac{5}{3}\ h)(\frac{60\ min}{1\ h})=100\ min

Since she plans to run 12 miles on Thursday, her run's time on that day will be:

t_2=\frac{12\ mi}{5.4\ \frac{mi}{h}}\\\\t_2=\frac{20}{9}\ h

Making the conversion from hours to minutes, we get:

(\frac{20}{9}\ h)(\frac{60\ min}{1\ h})=133.33\ min

Finally in order to find how many longer will her run be on Thursday compared to Tuesday, we need to make the following subtraction:

t_2-t_1=133.33\ min-100\ min=33.33\ min

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Use the Midpoint Formula three times to find the three points that divide the line segment joining (x1, y1) and (x2, y2) into fo
fredd [130]
We are given points A(x_1,y_1) and B(x_2,y_2). 

We first find the midpoint M, of AB, which divides the segment AB into 2 equal parts, 

then we find the midpoint N of AM, and midpoint K of MB.

Thus each of the half parts is divided into 2 equal parts. The whole segment is divided into 4 equal parts.




The coordinates of M, N and K are found as follows:


the coordinates of M are: ( \frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})


the coordinates of N are: 

\displaystyle{( \frac{x_1+\frac{x_1+x_2}{2}}{2} , \frac{y_1+\frac{y_1+y_2}{2}}{2})=( \frac{\frac{2x_1+x_1+x_2}{2}}{2} , \frac{\frac{2y_1+y_1+y_2}{2}}{2})

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6 0
2 years ago
Find the equation of the line which passes through (−2, 3) and the point of intersection of the lines x + 2y=0 and 2x − y − 12=0
Alik [6]

Answer: y = 0.794*x + 4.588

Step-by-step explanation:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case the points are:

(-2, 3) and the intersection of the lines:

x + 2y = 0

2x - y - 12  = 0

To find the intersection of those lines, we can first isolate one variable in one side of each equality, i will isolate the variable y.

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Now we can write:

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Solving this we can find the value of x at which both lines intersect.

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Now we can find the slope of our equation.

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then we have:

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3 + 1.588 = b = 4.588

Then the equation is:

y = 0.794*x + 4.588

3 0
2 years ago
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