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viktelen [127]
3 years ago
10

Vanessa draws one side of equilateral ΔABC on the coordinate plane at points A(–2, 1) and B(4,1). What are the possible coordina

tes of vertex C? Select all that apply.
Mathematics
1 answer:
grandymaker [24]3 years ago
4 0

Important question. No menu of choices given so we'll just have to figure it out.

It's not possible in two dimensions for all three vertices of an equilateral triangle to be lattice points, i.e. points with integer coordinates.  

Since A(-2,1) and B(4,1) have integer coordinates, our other point won't. There will be a √3 involved, the algebraic tell that there's a 30/60/90 triangle lurking somewhere in the problem.

Here the given side is parallel to the x axis which makes things easier.  

|AB| = 4 - -2 = 6

The x coordinate of the third vertex will be the same as that of the midpoint of AB, let's call it M,

M = ( (-2 + 4) / 2, (1 + 1)/2 ) = (1, 1)

We're making some progress.  Whatever our height h is our two candidates for the third vertex C are (1, 1 ± h).

Since |AB|=6, we get |AB|=|BC|=|AC|=6 because it's an equilateral triangle.

The altitude CM bisects the triangle into 2 30/60/90 triangles.  Let's take one of them, AMC.  Angle AMC is a right angle, so we have a right triangle with legs |AM|=3 and |CM|=h, and hypotenuse |AC|=6. The Pythagorean Theorem tells us:

3² + h² = 6²

9 + h² = 36

h² = 27

h = 3√3

Answer: C is (1, 1 + 3√3) or (1, 1 - 3√3)

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A town in east Texas received 10 inches of rain in 2 weeks. If it kept raining at this rate for a 31- day month, how much rain d
umka21 [38]

2 weeks = 14 days

10 / 14 = 0.71428571428

0.71428571428 * 31 = 22.1428571429

The town received about 22 inches of rain.

If you include the 2 weeks, then it would be 32 inches of rain.


Hope this helps!

7 0
3 years ago
4x + y = 3 -2x + 3y = -19 what's the solution plz help
Rainbow [258]

The solution to given system of equations is x = 2 and y = -5

<em><u>Solution:</u></em>

<em><u>Given the system of equations are:</u></em>

4x + y = 3 ---------- eqn 1

-2x + 3y = -19 ---------- eqn 2

We have to find the solution to above system of equations

<em><u>We can solve the system by substitution method</u></em>

From eqn 1,

4x + y = 3

Isolate y to one side

y = 3 - 4x ----------- eqn 3

<em><u>Substitute eqn 3 in eqn 2</u></em>

-2x + 3(3 - 4x) = -19

-2x + 9 - 12x = -19

Combine the like terms

-14x = -19 - 9

-14x = -28

Divide both sides of equation by -14

<h3>x = 2</h3>

<em><u>Substitute x = 2 in eqn 3</u></em>

y = 3 - 4(2)

y = 3 - 8

<h3>y = -5</h3>

Thus the solution is x = 2 and y = -5

5 0
3 years ago
PLEASEEEEE HELPPPPPP ASAPPPPPPPP
natta225 [31]

9514 1404 393

Answer:

  64r -48r -144

Step-by-step explanation:

The January cost expression is ...

  62p -48p -144 -432 = profit

The cost is identified as having 3 components, so the profit will have 4 components:

  (selling price)×p - ((cost per unit)×p +(fixed monthly cost)) -(first month startup cost) = profit

Comparing this to the given equation, we identify the components as ...

  selling price = 62

  cost per unit = 48

  fixed monthly cost = 144

  first month startup cost = 432

We note that 432 = 3×144, so is consistent with the description of startup costs.

Increasing the selling price by $2 will raise it from 62 to 64. In February, the initial month startup cost disappears, so the profit equation becomes ...

  (selling price)×r - ((cost per unit)×r +(fixed monthly cost)) = profit

  64r -48r -144 = profit

5 0
3 years ago
ANSWERS QUICKLY PLEASE
marshall27 [118]
It’s an irrational number (can’t be expressed as a fraction with two integers).
7 0
3 years ago
Simplify the following expression.<br><br> 6 - (-19)
NISA [10]

Answer:

The answer is 25 but I'm not sure you can simplify a whole number

3 0
3 years ago
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