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Angelina_Jolie [31]
2 years ago
13

If A= (6,11), B= (1,5), and C= (7,0), show by means of slopes that ABC is a right triangle. Name the hypotenuse.

Mathematics
1 answer:
nexus9112 [7]2 years ago
6 0

Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse

<h3>Right angled triangle</h3>

A right angles triangle is a triangle that has 3 sides and angles with one of its angles to be 90 degrees.

For the given coordinates to be a right angled triangle, one of the line must be perpendicular to the other and for two lines to be perpendicular, the product of its slope must be -1.

Find the slopes of AB, BC and AC

Slope of AB = 5-11/1-6
Slope of AB = -6/-5 = 6/5

Slope of BC = 0-5/7-1
Slope of BC = -5/6

Slope of AC = 0-11/7-6
Slope of AC = -11/1. = -11

Take the product of AB and BC
AB * BC = 6/5 * -5/6
AB * BC = -1

Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse

Learn more on right angle triangle here: brainly.com/question/22790996

#SPJ1

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Grandma gives 180 marbles to her ten grandchildren. No two children get the same amount of marbles. Betsy gets the most. What is
SOVA2 [1]

Answer:

23 marbles

Step-by-step explanation:

Number of children = 10

Number of marbles = 180

Since Betsy gets the most and no 2 children gets the same number of marbles

The least number of marbles Betsy could get will be x ; with the other 9 children receiving 1 less each

That is :

Betsy = x

9th child = x - 1

8th child = x - 2,... 1st child = x - 9

Hence,

(x + x - 1 + x - 2 + x - 3 + x - 4 + x - 5 + x - 6 + x - 7 + x - 8 + x - 9) = 180

10x - 45 = 180

10x = 180 + 45

x = 225 / 10

x = 22.5

x = 23

Hence, the least Betsy could get is 23 marbles

5 0
3 years ago
Jackson borrows $400 with an interest rate of 1.5%.How much interest will he pay after 4 years?
mafiozo [28]

Answer:

24 interest after 4 years

Step-by-step explanation:

I just took 400 and multiplied it to 1.5%(.015) to get 6 and then multiplied that to 4 to get 24 and you could it if you want. Ask if you have a question.

6 0
4 years ago
ANSWER IF YOU KNOW!!!!! THANKS
Ad libitum [116K]

Answer:

The third graph.

Step-by-step explanation:

The equations for the lines will be

P(x) = 2x-4

l(x) = -2x-4

When x = 0 both of these functions equal -4. The only graph where this happens is the third one.

You can check this by looking at the slopes and plugging in points.

6 0
3 years ago
Read 2 more answers
Help me PLEASEEEEEEEEEEEEE
Andrej [43]

The correct answer is 2.5 cm

Explanation:

In any polygon, the area refers to the total space occupied by the polygon. In the case of triangles, the area can be calculated by multiplying the base and height and then dividing the by 2. This means b x h / 2 = area of a triangle. According to this, the area of the triangle presented is 15

5 cm (base) x  6 cm (height) = 30 cm

30 cm / 2 =  15 cm (total area)

This also means the area of the rectangle is 15 considering both figures have the same area. Additionally, the area in rectangles is calculated by multiplying the length base by the width. This implies in the case presented 6 cm x w cm = 15 cm (total area), and you can determine the value of w by using a simple equation as

6 x w = 15

w = 15 / 6

w =  2.5

Also, you can know this is the correct value because 6 cm (length) x 2.5 (width) = 15 cm which is the correct area

4 0
4 years ago
dog brought a new jet ski for $299 down in 14 monthly payments are $57 how much did Doug pay for the jet ski total
Effectus [21]

If he paid $57 monthly for 14 months, the total amount paid is:

57\times14=798

He paid $798 in total

8 0
1 year ago
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