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Svet_ta [14]
3 years ago
10

Find the coordinates of the orthocenter of triangle ABC with vertices A (2, 0), B (2, 4), and C (6, 0).

Mathematics
1 answer:
ss7ja [257]3 years ago
8 0

9514 1404 393

Answer:

  (2, 0)

Step-by-step explanation:

The orthocenter of a right triangle is the vertex where the right angle is located. Here, that is vertex A.

The orthocenter is (2, 0).

__

The orthocenter is the point where the altitudes intersect.

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Answer:

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Step-by-step explanation:

f(x) = 4x^2 + 8x − 5

To find the x intercepts set y = 0

0 =4x^2 + 8x − 5

Factor

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Using the zero product property

2x-1 =0     2x+5 =0

2x=1            2x = -5

x = 1/2           x = -5/2

The x intercepts are ( 1/2 ,0)   and ( -5/2,0)

Rewriting in vertex form by completing the square

4 ( x^2 + 2x) -5

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Given: Line A R bisects ∠BAC; AB = AC
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The ΔABR ≅ ΔACR are congruent by SAS theorem

Option D is the correct answer.

The missing diagram is attched with the answer.

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In both the triangle we have a common side , AR

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The radius of a circle is the separation between any two points on its circumference. R or r is typically used to indicate it.

The diameter of a circle cuts through the centre whereas the radius extends from the centre to the edges of the circle. The diameter of a circle effectively divides the shape in two.

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Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different
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Answer:

(a)  As time increases, the amount of water in the pool increases.

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(b)  65 gallons

Step-by-step explanation:

From inspection of the table, we can see that <u>as time increases, the amount of water in the pool increases</u>.

We are told that Ann adds water at a constant rate.  Therefore, this can be modeled as a linear function.  

The rate at which the water is increasing is the <em>rate of change</em> (which is also the <em>slope </em>of a linear function).

Choose 2 ordered pairs from the table:

\textsf{let}\:(x_1,y_1)=(8, 153)

\textsf{let}\:(x_2,y_2)=(12,197)

Input these into the slope formula:

\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11

Therefore, the rate at which the water in the pool is increasing is:

<u>11 gallons per minute</u>

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

y-y_1=m(x-x_1)

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\implies y=11x-88+153

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When Ann had added no water, x = 0.  Therefore,

y=11(0)+65

y=65

So there was <u>65 gallons</u> of water in the pool before Ann starting adding water.

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2 years ago
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