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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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Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive. Troy
kari74 [83]

Answer:

Notebook is $4

Thumb drive is $23

Step-by-step explanation:

Let notebooks be x and thumb drives be y

6x+7y=$185

14x+12y=$332

These two are simultaneous equation. Multiplying the first equation by 7 and second by 3 we obtain

42x+49y=$1295

42x+36y=$996

Subtracting the third equation from the fourth

996-1295=-$299

(36-49)y=-23y

-23y=-$299

y=$299/13=$23

To get the value of x, we substitute the value of y into the first equation

6x+(7*23)=$185

6x=$185-$161

6x=$24

x=$4

Therefore, price of notebook is $4, price of thumb drive is $23

4 0
3 years ago
A die is loaded so that the number 6 comes up three times as often as any other number. what is the probability of rolling a 1 o
Mila [183]

Answer:

1/2.

Step-by-step explanation:

Probability totals must add up to 1.

P = probability.

If P(any number other than 6) = x,  then P(6) = 3x, so

3x + 5x = 1

x = 1/8

P(6) = 3/8 and P(not 6) = 1/8

Therefore P(6 or 1) = 3/8 + 1/8 = 1/2 (answer).


4 0
3 years ago
(9, 8) is the midpoint of mc136-1.jpg. The coordinates of S are (10, 10). What are the coordinates of R?
kolbaska11 [484]
I cant see the image...but I take it that the midpoint is (9,8) and the endpoint S is (10,10) and ur looking for the other endpoint R.

midpoint formula : (x1 + x2) / 2, (y1 + y2) / 2
(10,10)....x1 = 10 and y1 = 10
(x,y)....x2 = x and y2 = y
so we sub
(10 + x) / 2, (10 + y) / 2 = 9/8

(10 + x) / 2 = 9
10 + x = 9 * 2
10 + x = 18
x = 18 - 10
x = 8

(10 + y) / 2 = 8
10 + y = 8 * 2
10 + y = 16
y = 16 - 10
y = 6

so endpoint R has coordinates of (8,6) <===
7 0
3 years ago
In another baseball division, one team had a winning percentage of 0.444 repeating What fraction of their games did this team wi
UkoKoshka [18]

Answer:

x = \frac{4}{9}

Step-by-step explanation:

Given

Winning Percentage = 0.444 repeating

Required

Represent as a fraction

Represent the percentage with x

x = 0.444

Convert to fraction

x = \frac{444}{1000}

Next step, is to convert to fraction repeating

To do this, we simply subtract 1 from the denominator

x = \frac{444}{1000 - 1}

x = \frac{444}{999}

Simplify to the lowest term: Divide numerator and denominator by 37

x = \frac{444/37}{999/37}

x = \frac{12}{27}

Simplify to the lowest term: Divide numerator and denominator by 3

x = \frac{12/3}{27/3}

x = \frac{4}{9}

Hence;

There winning fraction is \frac{4}{9}

8 0
2 years ago
Add: (-3p6 + 5) + 9p6
timama [110]

Answer:

6p^6+ 5

Step-by-step explanation:

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((0 -  (3 • (p6))) +  5) +  32p6

Step  2  :

Equation at the end of step  2  :

 ((0 -  3p6) +  5) +  32p6

Step  3  :

Trying to factor as a Sum of Cubes :

3.1      Factoring:  6p6+5

4 0
3 years ago
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