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2 years ago

1092 is what percent of 1140

Mathematics

1 answer:

REY [17]2 years ago

7 0

95.97

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What are the coordinates of the centroid of a triangle with vertices A(−3, 1) , B(1, 6) , and C(5, 2) ? Enter your answer in the

kirza4 [7]

<u>ANSWER</u>: The centroid is (1,3)

<u>Explanation:</u>

The centroid is the intersection of the medians of the triangle.

So we need to find the equation of any two of the medians and solve simultaneously.

Since the median is the straight line from one vertex to the midpoint of the opposite side, we find the midpoint of any two sides.

We find the midpoint of AC using the formula;

$N=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

$N=(\frac{-3+5}{2}, \frac{1+2}{2})$

$N=(\frac{2}{2}, \frac{3}{2})$

$N=(1, \frac{3}{2})$

The equation of the median passes through $B(1,6)$ and $N=(1, \frac{3}{2})$ .

This line is parallel to the y-axis hence has equation

$x=1$ -------first median.

We also find the midpoint M of BC.

$M=(\frac{1+5}{2}, \frac{6+2}{2})$

$M=(\frac{6}{2}, \frac{8}{2})$

$M=(3, 4)$

The slope of the median, AM is

$Slope_{AM}=\frac{4-1}{3--3}$

$Slope_{AM}=\frac{3}{6}$

$Slope_{AM}=\frac{1}{2}$

The equation of the median AM is given by;

$y-y_1=m(x-x_1)$

We use the point M and the slope of AM.

$y-4=\frac{1}{2}(x-3)$

$2y-8=(x-3)$

$2y-x=-3+8$

$2y-x=5$ -------Second median

We now solve the equation of the two medians simultaneously by putting $x=1$ in to the equation of the second median.

$2y-1=5$

$2y=5+1$

$2y=6$

$y=3$

Hence the centroid has coordinates $(1,3)$

7 0

3 years ago

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Plzzzz help like just plzzzzz In Alana's math class, there are 12 boys and 13 girls. What is the ratio of boys to girls?

irakobra [83]

Answer:

12:13 is the ratio of boys:girls.

7 0

3 years ago

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Can you please help? Thank you...

solmaris [256]

The answer to the question

4 0

3 years ago

If 10 man can work 6hours.How many more men are needed towork in 4 hours

Lerok [7]

Answer:

5 more men

Step-by-step explanation:

10 men do a job in 6 hours.

To do the job in 2 hours, 1/3 of the time, you need 3 times as many men.

30 men do a job in 2 hours.

To do the job in twice the time, 4 hours, you need half the men.

15 men do a job in 4 hours.

15 men - 10 men = 5 men

You need 5 more men.

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2 years ago

Margot has started a construction and has this drawn on her paper. What is she constructing?

baherus [9]

For a better understanding of the explanation provided here, please find the diagrams in the two files that have been attached.

As can be clearly seen from the diagram, PR and QS are the diameters of the circle and they intersect each other at the centre, O of the circle.

The angle these diameters make at the point of intersection O is 90 degrees.

If Margot joins the points P,Q,R and S which are on the circumference of the circle, then we will get a square with sides PQ, QR, RS and SP as shown in the second diagram.

Thus, the correct option is Option A.

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4 years ago

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