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stepan [7]
3 years ago
9

a (1,4) b (-1,2) c (5,-2) are the vertices of triangle abc find the sum of coordinates of the point where the right bisector of

bc intersects the median through c
Mathematics
1 answer:
zmey [24]3 years ago
3 0

Answer:

3.

Step-by-step explanation:

Find the midpoint of BC:

midpoint = (-1+5)/2, (2-2)/2 = (2, 0).

The slope of BC = (2 - -2) / (-1-5) = -2/3.

Find the equation of the right bisector of BC:

The slope = -1 / -2/3 = 3/2.

y-y1 = m(x-x1)

y - 0 = 3/2(x - 2)

y = 3/2x - 3.

Now find the equation of the median through C:

The midpoint of AB = (1 - 1)/2, (4+2)/2

= (0, 3).

The equation of the median:

The slope = (-2-3) / (5-0)

= -1.

The equation is:

y - 3 = -1(x - 0)

y -3 = -x.

Now we find the point of intersection by solving the 2 equations:

y - 3 = -x

y = 3/2x - 3

y = -x + 3

So:

3/2x - 3 = -x + 3

3/2x + x = 6

5/2 x = 6

x = 12/5.

y =  -12/5 + 3

= -12/5 + 15/5

= 3/5.

The sum of the coordinates = 12/5 + 3 /5

= 15/5

= 3.

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Toko follows a budget to buy supplies to paint his room. He spends 1/2 of his budget on a roller, a tray, and tape. He spends $1
Natasha_Volkova [10]
The answer is $36.

B - budget
So the calculation is as following:
B= \frac{1}{2}B + 12.27 +  \frac{3.82}{ \frac{2}{3} } = \frac{1}{2}B + 12.27 + \frac{3.82*3}{2}=   \frac{1}{2}B + 12.27 +5.73
B= \frac{1}{2} B + 18
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3 years ago
You deposit $ 1200 in an account. The annual interest rate is 3%. How long will it take you to earn $108 in simple interest?
alukav5142 [94]
The correct answer is 3
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3 years ago
Find 4 consecutive even integers such that when three times the smallest of the intagers is added to twice the largest their sum
zhannawk [14.2K]
If x is the first of the integers then the statement is:

(x) , (x+2) , (x+4) , (x+6)

This means that the smallest is x and the largest is x + 6

so:
3(x) + 2(x+6) = 293
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5x = 281
x = 56.2
This gives us a none integer (decimal)
What now?

Wait remember how x started as the lowest? what if x was the highest instead?

x, x-2, x-4, x-6
so:

3(x-6) + 2(x) = 293
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This is as close as have gotten to the answer
Cant seem to get an integer.
Maybe error in the question or some bad math on my part.


3 0
3 years ago
I need help please! The sequence 6,18,54,162, ... shows the number of pushups Kendall did each week, starting with her first wee
Romashka-Z-Leto [24]

Answer:

a: 3

b. 6973568802

Step-by-step explanation:

a₁ = 6 , r = 3 , a₂₀ =?

Result:

a₂₀ = 6973568802

Explanation:

To find a₂₀ we use the formula

aₙ = a₁ · r ^ⁿ⁻¹

In this example we have a₁ = 6 , r = 3 , n = 20. After substituting these values to above

formula, we obtain:

aₙ = a₁ · r ^ⁿ⁻¹

a₂₀ = 6 · 3 ^²⁰⁻¹

a₂₀ = 6 · 1162261467

a₂₀ = 6973568802

3 0
3 years ago
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