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vekshin1
3 years ago
10

M is the centroid (center of gravity) of △ABC, line k goes thru M and intersects AB and AC . The distances of the vertices B and

C from line k are 17 and 13 respectively. Find the distance of the vertex A from line k.
Mathematics
1 answer:
lana [24]3 years ago
5 0

Answer:

  30

Step-by-step explanation:

The midpoint of BC will be a distance from line k that is the average of the distances of B and C: (17+13)/2 = 15. Call that midpoint P. We know distance MP is half of distance MA. This same relationship will hold with respect to the distances from P and A to any line through M. That is, the distance from line k (through M) is twice the distance from P to line k: 30 units.

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Triangle ABC with vertices A (-1, 4), B( -4, 1), and C(-1, 1) is reflected across the y-axis and then translated 4 units to the
Anna71 [15]

Given:

Triangle ABC with vertices A (-1, 4), B( -4, 1), and C(-1, 1) is reflected across the y-axis and then translated 4 units to the left to form triangle A’B’C’.

To find:

The coordinates of the vertices of triangle A’B’C’.

Solution:

If triangle ABC reflected across y-axis, then

(x,y)\to (-x,y)

A(-1,4)\to A_1(1,4)

B(-4,1)\to B_1(4,1)

C(-1,1)\to C_1(1,1)

Coordinates of image after reflection across y-axis are A_1(1,4),B_1(4,1),C_1(1,1).

Then triangle translated 4 units to the left to form triangle A’B’C’.

(x,y)\to (x-4,y)

A_1(1,4)\to A'(-3,4)

B_1(4,1)\to B'(0,1)

C_1(1,1)\to C'(-3,1)

Therefore, the vertices of triangle A’B’C’ are A’ (-3, 4), B’ (0, 1), C’ (-3, 1).

Hence, the correct option is B.

6 0
3 years ago
The abc company has a net income of $56.000, ASSETS AT BEGINNING OF YEAR ARE $263.000 AND ASSETS AT END OF YEAR ARE $313.000. wH
Doss [256]
Assets are 19.4% total amount
7 0
3 years ago
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One half of your CDs are scratched. One fifth will not play properly. You have 40 CDs. How many will not work play properly
kvasek [131]
1/2 of 40= 20

40/5=8

20+8=28

28 of your CDs will not work properly.

I hope this helps!
6 0
3 years ago
Read 2 more answers
Hey can someone help me
enyata [817]

Answer:

602.88in²

Step-by-step explanation:

Formula for finding the volume of oblique triangle is expressed as

A = πr²h

Given

radius r = 4in

height h = 12in

Substitute

A = π*4²*12

A = 3.14*16*12

A = 3.14 * 192

A = 602.88in²

Hence the area of the cylinder is 602.88in²

5 0
3 years ago
Can someone tell me if im right? PLEASE DONT JUST SAY YES if you don’t know
tia_tia [17]

Answer: You are incorrect, the slope is correct, but the actual y-intercept is 205 ft.

Then the equation is:

y = (-15 ft/min)*x + 205 ft

Step-by-step explanation:

Ok, let's solve this.

We know that water is drained from a reservoir, let's assume that we can model this situation with a linear relation:

y = a*x + b

Where x is time, y is the height of the water in the reservoir, a is the slope (in this case represents how much changes the height of the water in the reservoir in one unit of time) and b is the initial height of the water in the reservoir.

We know that for a line that passes through the points (x₁, y₁) and (x₂, y₂) the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

For this particular case we know that after 2 minutes the height of the water is 175 ft, then we have the point (2 min, 175 ft)

and after 5 minutes (so 7 minutes in total), the height of the water is 100ft, then: (7 ft, 100ft)

Then the slope of this:

a = (100 ft - 175 ft)/(7 min - 2 min) = (-75ft/5min) = - 15 ft/min

Then our line is something like:

y = (-15ft/min)*x + b

To find the value of b, we can use the fact that when x = 2 min, y = 175 ft

So if we replace these two values in the equation we get:

175ft = (-15 ft/min)*2 min + b

175 ft = -30 ft + b

175 ft + 30 ft = b                  

(here is your problem, it seems like you subtracted instead of adding in this part)

205 ft = b

Then the equation is:

y = (-15 ft/min)*x + 205 ft

So you are incorrect (but only for a little bit), you computed wrong the y-intercept.

3 0
3 years ago
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