The line segments connecting the points (x1, y1), (x2, y1), and (x2, y2) form a triangle. Is the triangle a right triangle?

Answers

Answer 1

Answer:

Indeed, the given triangle is a right triangle.

Step-by-step explanation:

A triangle is formed by the following three points: [tex]A(x,y) = (x_{1}, y_{1})[/tex], [tex]B(x,y) = (x_{2}, y_{1})[/tex] and [tex]C(x,y) = (x_{2}, y_{2})[/tex]. Then, we construct the following vectors:

[tex]\overrightarrow {BA} = (x_{2}-x_{1}, y_{1}-y_{1})[/tex]

[tex]\overrightarrow{BA} = (x_{2}-x_{1}, 0)[/tex] (1)

[tex]\overrightarrow{BC} = (x_{2}-x_{2}, y_{2} - y_{1})[/tex]

[tex]\overrightarrow{BC} = (0, y_{2}-y_{1})[/tex] (2)

If triangle ABC is a right triangle, then [tex]\overrightarrow{BA}\,\bullet\,\overrightarrow{BC} = 0[/tex]. By (1) and (2) we have this expression:

[tex](x_{2} - x_{1})\cdot (0) + (0)\cdot (y_{2} - y_{1}) = 0[/tex]

Therefore, the given triangle is a right triangle.


Related Questions

The equation y = 450x represents the number of miles alrplane traveled y ot x hours. The graph below shows the number miles a 5hour flight , after 2 hours which airplane had traveled the farther and by how much ? I need help

Answers

Answer:

y = 200x.....the airplane travels 8000 miles in 40 hrs

Step-by-step explanation:

Answer:

Airplane W by 100 miles

Step-by-step explanation:

Airplane Z

y = 450x

Distance travelled after 2 hours

y = 450(2)

y = 900 miles

------------------------

Airplane W

Distance travelled after 2 hours

Reading from the graph

1000 miles

----------------------

after 2 hours which airplane had traveled the farther

Airplane W

and by how much

1000 - 900 = 100

Sixty percent of the people surveyed use sunscreen. A random number generator was used to simulate the results of asking the next three people. The numbers 0–5 represent people who use sunscreen, and the numbers 6–9 represent people who do not use sunscreen. What is the probability that two of the next three respondents use sunscreen?

Answers

Answer:

[tex]Pr = 0.50[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

Probability that 2 of 3 use sunscreen

From the attached data, we have:

[tex]S = \{275, 738, 419, 582, 987, 436, 578, 472, 178, 839\}[/tex]

[tex]n(S) = 10[/tex]

Events where 2 of the 3 uses sunscreen is:

[tex]x = \{275, 419, 582, 436, 472\}[/tex] --- i.e. where 0 -5 represents sunscreen

[tex]n(x) = 5[/tex]

So, the required probability is:

[tex]Pr = \frac{n(x)}{n(S)}[/tex]

[tex]Pr = \frac{5}{10}[/tex]

[tex]Pr = 0.50[/tex]

URGET PLEASE HELP
Let f(x) = 5x4 – 2x2 – 8x + 3 and g(x) =
-7x4 + 6x3 + 10x²
x + 4. What is f(x) + g(x)?

Answers

Answer:

f(x)+ g(x) = [tex]-2x^{4} + 6x^{3} +8x^{2} -8x+3[/tex]

Step-by-step explanation:

You just have to add the like terms separately,

5-7 in [tex]x^{4}[/tex]

only 6 in [tex]x^{3}[/tex]

10-2 in[tex]x^{2}[/tex]

-8 in x

and 3 as the constant

Jane wants to pick out an outfit for the school dance . She can choose from 3 pairs of pants 5 shirts and 2 pairs of shoes . How many different outfits dose Jane have to choose from?

Answers

Answer:

30

Step-by-step explanation:

we multiply each number. There are 3 pairs of pants 5 shirts and 2 pairs of shoes, so we multiply 3x5x2 to get 30

She should pick out this outfit...

You have have a bag of marbles (3 purple, 5 green, and 4
yellow)
Write your probability in fraction form-no need to reduce
1a) What is the Plyellow marble)=
1b) What is the P(purple marble)=
1c) What is the Plyellow marble "and" purple marble)
1a) 4/12, 1b) 3/12, 1c) 12/12
1a) 4/100, 1b) 3/100, 1c) 12/100
1a) 4/12, 1b) 3/12, 1c) 12/144
1a) 4, 1b) 3, 1c) 12

Answers

Answer:

4/12 = yellow

3/12 = purple

12/144 = yellow and purple

Step-by-step explanation:

the first two are pretty self explanitory. The last one requires you to multiply the answers of the first two together. Make sure you multiply both the top and the bottom (don't use common denominator here)

Answer:

The answer to this is the 3rd choice which is 1a) 4/12, 1b) 3/12, 1c) 12/144.

Step-by-step explanation:

This is pretty simple. To identify the probability of the yellow marbles, you can find the amount of yellow marbles and the total amount of marbles. You take it as a fraction which would be 4/12.

The total amount of marbles : 3 purple + 5 green + 4 yellow = 12 total marbles

The amount of yellow marbles : 4 yellow

Probability of yellow marbles : 4/12

To identify the probability of the yellow marbles, you can find the amount of purple marbles and the total amount of marbles. You take it as a fraction which would be 3/12.

The total amount of marbles : 3 purple + 5 green + 4 yellow = 12 total marbles

The amount of purple marbles : 3 purple

Probability of purple marbles : 3/12

To identify the probability of both the yellow and purple marbles, you can find the amount of yellow and purple marbles along with the total amount of marbles. Since we know this from the work above, you just need to multiply both probabilities. You take it as a fraction which would be 12/144.

The total amount of marbles : 3 purple + 5 green + 4 yellow = 12 total marbles

The amount of yellow marbles : 4 yellow

The amount of purple marbles : 3 purple

Probability of yellow marbles : 4/12

Probability of purple marbles : 3/12

Probability of both marbles : 12/144

hii! i’ll give brainliest pls help

Answers

Answer:

the answer's option 3 * landslide *

Step-by-step explanation:

-

Answer:

Option 3

Step-by-step explanation:

A landslide is the most occurring disaster for people living in hills

Hope it helps

Alonzo runs each lap in 6 minutes. He will run at most 30 minutes today. What are the possible numbers of laps he will run today?

Use n for the number of laps he will run today.
Write your answer as an inequality solved for n.

Answers

Answer:

N= 5

Step-by-step explanation:

30 ÷ 6 = n

n = 5

30 ÷ 6 = 5

Hope this helps!!

Nelson got a pack of 12 pencils. he took 3 pencils and put it in is desk at school and 2 pencils to put in is locker at school. what is the fraction of total pencils that Nelson took to school

Answers

1 1\2. so he had that fraction as all after

Mr. Bates and Mr. Z want to refinish the community center gym floor. The rectangular floor is 15.2 m wide and 25.6 long. If each gallon of polyurethane covers about 180 square meters, how many gallons should Mr. Bates and Mr. Z buy? *

Answers

Answer:

3 gallons

Step-by-step explanation:

area = 15.2 x 25.6 = 389.12 m²

389.12/180 = 2.16

Will mark brainliest!
Find the Volume of the Sphere. Use 3.14 for pi. Round your answer to the nearest whole number.

Answers

Answer:

It is 14130 mm^3

Step-by-step explanation:

So the equation for the volume of a sphere is (4/3) (3.14) r^3. So since we already have the radius, we just plug it in to get the answer:

(4/3) (3.14) r^3

(4/3) (3.14) 15^3

(4/3) (3.14) 3375

(4/3) (10597.5)

14130 mm^3

Convert 29.5 kilograms to grams.

Enter your answer in the box.

Answers

Answer:

29,500 g

Step-by-step explanation:

1 kg = 1000 g.

29500

Step-by-step explanation:

29 multiplied by 1000 is 29k grams and if we add the .5 kilos which is basically 500 grams we get 29500 grams.

Find the range. 15,18,13,17,15

Answers

The answer is 5. The biggest number - the smallest number (18-13=5)

The radius of a circle is 2 m. Find the circumference to the nearest tenth.

Answers

Answer:

25.13 or 25.1

Step-by-step explanation:

2 x pi/3.14x4

Answer:

12.6

Step-by-step explanation:

circumference=2πr

=2 x 3.142 x 2

= 12.6 to the nearest tenth

Find the value of x

Answers

Answer:

The value of [tex]x[/tex] is 2.

Step-by-step explanation:

Given that [tex]\overline{HI}[/tex] and [tex]\overline{HJ}[/tex] are secant to arcs [tex]HI[/tex] and [tex]HJ[/tex], which have the same central angles. Therefore, [tex]HI = HJ[/tex] due to symmetry:

[tex]HI = HJ[/tex] (1)

[tex]2\cdot x + 1 = 5\cdot x - 5[/tex]

[tex]3\cdot x = 6[/tex]

[tex]x = 2[/tex]

Hence, the value of [tex]x[/tex] is 2.

Which lists the fractions from least to greatest?
A.-1/3,-2/3,1/3
B.1/3,-1/3,-2/3
C.1/3,-2/3,1/3
D.-2/3,1/3,-1/3
E.-2/3,-1/3,1/3

Answers

Answer:

E

Step-by-step explanation:

Im doing an extra practice and need help with this one problem

Answers

Answer:

it might be this 8.74777778 im not sure if it is tho so if im wrong then im sorry

Step-by-step explanation:

Find the magnitude and directon of F +ū.

Answers

Answer:

Step-by-step explanation:

Pls help me fast thx

Answers

Answer:

The answer is C

Step-by-step explanation:

Workers load 5 identical large crates and 3 identical small crates onto a freight elevator. The crates have a combined weight of 1375 pounds. Later
that day, the workers load 3 more identical large crates and 6 more identical small crates onto the freight elevator. These crates have a combined
weight of 1350 pounds.

Answers

Answer: The total would be 40.53

Step-by-step explanation:

On the same day, Parker’s friend, Peggy, was charged $5 for 1 1/2 lb. of gummy candy. Explain in terms of the graph why this must be a mistake.

Answers

Answer:

After a quick online search, I've found that the complete question is:

a) Parker paid $4.50 for three pounds of gummy candy. Assuming each pound of gummy candy costs  the same amount, complete the table of values representing the cost of gummy candy in pounds.

Then we want to graph the points, and then comes our question:

c) On the same day, Parker’s friend, Peggy, was charged $5 for 1 1/2 lb. of gummy candy. Explain in terms of the graph why this must be a mistake.

So first, we know that this is a proportional relationship (each pound of candy costs the same)

And 0 pounds of candy should cost $0.

Then the relation between y (price) and x (number of lb) is:

y = k*lb

where k is the cost per lb.

Knowing that Parker paid $4.50 for three pounds of gummy candy, the relation is:

$4.50 = k*3lb

($4.50/3lb) = k = $1.50/lb

Then the linear relation is:

y = ($1.50/lb)*x

Now, in this question we can see that Parker's friend was charged $5 for ( 1 and 1/2) lb of candy.

If we replace those values in the equation, we get:

$5 = ($1.50/lb)*(1 + 1/2)lb = $2.25

This equation is false, then, in terms of the graph, the point ( (1 and 1/2)lb, $5) does not belong on the graph that you found in the previous points.

which statement does not describe a normal distribution?
A: The median is equal to the mean
B: The distribution is not symmetric
C: The number of observations trails off as you move away from the mean
D: Most of the observations are near the mean

Answers

Answer:

B.

Step-by-step explanation:

The distribution is symmetric

Answer:

B.  The distribution is not symmetric

Step-by-step explanation:

What is the equation of a line parallel to y=-3/2x+9

Answers

Answer:

y = - [tex]\frac{3}{2}[/tex]x

Step-by-step explanation:

Parallel lines are two lines that have the same plane and slope but never intersect.

3.2 ft 2 fti2 ft 4 ft ft2 plz help​

Answers

what's the question?

Answer:

Step-by-step explanation:

Cody purchased a car for $4500 that will depreciate 28% a year. Write an exponential growth/decay equation that represents the value of Cody's car overtime. How much will the car be worth in 15 years? Round to the nearest cent.

Answers

Answer:

$32.60

Step-by-step explanation:

This question has to to do with exponential decay. The formula is given as:

y = a(1 - r)^x

y = Value of the material after x years

a = Initial value of the material

x = Time in years

r = rate of depreciation or decay

Therefore,

y = 4500 × (1 - 0.28)¹⁵

y = 4500 × 0.72¹⁵

y = $32.598675906

y = Approximately = $32.60

Therefore the of the car after 15 years = $32.60

Can somebody help me out my grade are bad

Answers

Answer:

There’s only 1 horizontal line of symmetry

Step-by-step explanation:

Answer:

there is only 1 line of symmetry that is horizontal

-4 -11 = ?
x X 3 = 15
4 x 2 x 3x = 48
Answer Choices:
A) -15, 5, 2
B) 15, 4, 13
C) 11, 4, 8
PLEASE HELP!

Answers

Answer:

A) -15, 5, 2

Step-by-step explanation:

Step-by-step explanation:

-4 -11 = ?

x X 3 = 15

4 x 2 x 3x = 48

Answer Choices:

B) 15, 4, 13

Can someone help me with this pls there is the picture

Answers

The length is 70 it’s the most logical answer

The diameter of a circle is 50.267 feet. Find the circumference of the circle and use 3.14 for π. Round your answer to the nearest whole number.

The circumference is
feet.

Answers

Answer:

C=2πr=2·π·25.13≈157.9153

Step-by-step explanation:

How long will it take an investment of $400 earning 3% annual interest compounded monthly to triple in value?

Answers

Answer:

$12 is 3% of $400, triple the value is $1200, it would take 100 months, or 8 years

A.) Kokochi walks 4 and 1 twelfth miles in one day. He walks the same distance for one week. How many miles does Kokochi walk?

B.) The next week, Kokochi walks 8 and 1 fourth miles in one day for a week. How many miles does Kokochi walk?

C.) What is the distance Kokochi walked if the answers to part A and B were combined?

Answers

Answer:

A) 28 7/12, or 343/12, or 28.583

B) 57.75

C) 86.3 or 86 1/3

Step-by-step explanation:

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