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snow_tiger [21]
3 years ago
6

What are the coordinates of point P on a directed line segment from R to Q such that P is 5/6 the length of the line segment.

Mathematics
1 answer:
Black_prince [1.1K]3 years ago
7 0

Answer:

P = [-3/5,2.33]

Step-by-step explanation:

Given

See attachment for line segment RQ

P = \frac{5}{6} of RQ

Required

The coordinates of P

Using line segment ratio formula, we have:

P = [\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n}]

If P is at:

P = \frac{5}{6}

Then:

m : n = \frac{5}{6} :  1 -\frac{5}{6}

Solve

m : n = \frac{5}{6} :  \frac{6-5}{6}

m : n = \frac{5}{6} :  \frac{1}{6}

Multiply by 6

m : n = \frac{5}{6} *6:  \frac{1}{6} * 6

m : n = 5 : 1

By comparison

m=5\ \& n = 1

From the attached line segment

R(x_1,y_1) = (4,-1)

Q(x_2,y_2) = (-5,3)

So, we have:

P = [\frac{5*-5 + 1*4}{5+1},\frac{5*3 + 1*-1}{5+1}]

P = [\frac{-25 + 4}{6},\frac{15 -1}{6}]

P = [\frac{-21}{6},\frac{14}{6}]

P = [-3/5,2.33]

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First, find the least common denominator (LCD) of the two fractions.
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Third, simplify. The denominators are now the same. / Your problem should look like: \frac{9}{16} + \frac{8}{16}
Fourth, join the denominators. / Your problem should look like: \frac{9+8}{16}
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3 years ago
A fish swims upstream a distance of 16 miles in a river with a current of 3 miles per hour. The fish returns swimming
arlik [135]

Answer:

9 mph = the speed in still water

Step-by-step explanation:

Let r = the speed in still water

Then the speed going down stream is r + 3

and the speed going upstream is r - 3

d = rt   or t = d/r

time going downstream is 16/(r + 3) and time going upstream is 16/(r - 3)

The total time was 4 hours, so

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Then 16(r - 3) + 16(r + 3) = 4(r + 3)(r - 3)

         16r - 48 + 16r + 48 = 4r^{2} - 36

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         4r^{2} - 32r - 36 = 0

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7 0
3 years ago
Kathy is baking cakes.if each cake requires 1/12 of a teaspoon of vanilla,and she has 9/12 of a teaspoon, how many cakes can she
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3 0
3 years ago
Read 2 more answers
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padilas [110]

Answer:

  • largest: R
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Step-by-step explanation:

The slope of the graph at x=0 is related to the value of b. It is also proportional to the value of <em>a</em>, which is the same for all but curve B. The red curve R has the largest slope at x=0, (much larger than 3/4 the slope of curve B), so curve R has the greatest value of <em>b</em>.

Similarly, the smallest value of <em>b</em> will correspond to the curve with the smallest (most negative) slope. That would be curve K. Curve K has the smallest value of <em>b</em>.

7 0
3 years ago
How can we ensure that we choose a sample of students that is representative of all 8:00 am classes that take place on a given m
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By using a sampling technique  we ensure that we choose a sample of students that is representative of all 8:00 am classes.

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explanation;

we conclude the

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