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Helga [31]
2 years ago
9

A is the point (-4,5) and B is the point (5,8). The perpendicular to the line AB at point A crosses the y axis at point C. Find

the coordinates of C.
Mathematics
1 answer:
slamgirl [31]2 years ago
5 0

Answer: Point C is (0, -7)

Step-by-step explanation:

For a general line y = a*x +b

A perpendicular line to this one will have a slope equal to -(1/a)

First, for a line y = a*x + b that passes through points (x₁, y₁) and (x₂, y₂) the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Then for a line that passes through the points A (-4, 5) and B (5, 8) the slope is:

a = (8 - 5)/(5  - (-4))  = 3/9 = 1/3

a = 1/3

Then, a line perpendicular to this one will have the slope:

a' = -(1/(1/3) = -3

Then the perpendicular line is something like:

y = -3*x + b

Now we know that this line passes through point A, then when x = -4, we have y = 5

if we replace these values we get:

5 = -3*(-4) + b

5 = 12 + b

5 - 12  = b

-7 = b

Then our line is:

y = -3*x - 7

This line intersects the y-axis at point C, we know that the y-axis corresponds to x = 0.

Then:

y = -3*0 - 7

y = -7

The point C is (0, -7)

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Answer:

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Step-by-step explanation:

Let x represents temperature and y denotes rate of chirping per minute.

At 106°F, a certain insect chirps at a rate of 67 times per minute.

Take (x_1,y_1)=(106,67)

At 108°F, they chirp 83 times per minute.

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3 0
3 years ago
In tennis, a first serve can be an ace, a fault, or it can be returned. In one match, a tennis player hit 24 aces, which was 25
Anastaziya [24]

Answer:

16 faults

Step-by-step explanation:

<u><em>The correct question is</em></u>

In tennis, a first serve can be an ace, a fault, or it can be returned. In one match, a tennis player hit 24 aces, which was 2/5 of all her first serves. If 1/3 of her first serves were returned, how many of the tennis player's first serves were faults?

Let

x -----> the number of all her first servers

y ----> the number of first services returned

z ---> the number of first services faults

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so

x=24+y+z

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Find out the number of all her first servers

we have that

24=\frac{2}{5}x

Solve for x

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step 2

Find out the number of first services returned

y=\frac{1}{3}x

substitute the value of x

y=\frac{1}{3}(60)=20\ returned

step 3

Find out the number of first services faults

x=24+y+z

we have

x=60\\y=20

substitute and solve for z

60=24+20+z

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6 0
2 years ago
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Answer:

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