1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ratelena [41]
3 years ago
6

Use the distance formula, show that the points (4,0), (2,1), and (-1,-5) form the vertices of a right triangle

Mathematics
1 answer:
mario62 [17]3 years ago
6 0

Step-by-step explanation:

The distance formula between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Substitute the coordinates of the points.

A(4,\ 0),\ B(2,\ 1),\ C(-1,\ -5)\\\\AB=\sqrt{(2-4)^2+(1-0)^2}=\sqrt{(-2)^2+1^2}=\sqrt{4+1}=\sqrt5\\\\AC=\sqrt{(-1-4)^2+(-5-0)^2}=\sqrt{(-5)^2+(-5)^2}=\sqrt{25+25}=\sqrt{50}\\\\BC=\sqrt{(-1-2)^2+(-5-1)^2}=\sqrt{(-3)^2+(-6)^2}=\sqrt{9+36}=\sqrt{45}

If a ≤ b < c are the sides of the right triangle, then

a² + b² = c²

\sqrt5

used (\sqrt{a})^2=a for a ≥ 0.

AB^2+BC^2=AC^2 therefore ΔABC is a right triangle.

You might be interested in
2 which of the following is a perfect cube<br> a) 400 -<br> D. 3375–<br> C 8000 -
allochka39001 [22]

Answer:

8000 is a perfect cube but 3375 can be also but i m a little sure that 8000 is a perfect cube

8 0
3 years ago
If a dress costs $27,000 when it is on sale for 10% off, what is its original cost?
Ede4ka [16]

Answer:

30,000

Step-by-step explanation:

10% of 30,000 is 3,000

30,000 - 3,000 = 27,000

4 0
2 years ago
You have 24 months left until you graduate and you plan on buying yourself a new $20,000 car on graduation day. If you invest $3
shusha [124]

Answer: No, the money won't be enough to buy the car

Step-by-step explanation:

you plan on buying yourself a new $20,000 car on graduation day and graduation day is 24 months time. If you invest $300 a month for the next 24 months.

The principal amount, p = 300

He is earning 4% a month, it means that it was compounded once in four months. This also means that it was compounded quarterly. So

n = 4

The rate at which the principal was compounded is 4%. So

r = 4/100 = 0.04

It was compounded for a total of 24 months. This is equivalent to 2 years. So

n = 2

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount that would be compounded at the end of n years.

A = 300(1 + (0.04/4)/4)^4×2

A = 300(1 + 0.01)^8

A = 300(1.01)^8

A = $324.857

The total amount at the end of 24 months is below the cost of the car which is $20000. So he won't have enough money to buy the car

3 0
3 years ago
Simplify the expression.
Nimfa-mama [501]
The answer is C.15c+72
5 0
2 years ago
I beg of you to please some-one help..I can't figure this out and it's driving me nuts- I will give Brainlist!
lyudmila [28]

Answer:

<em>A = 70</em>

Step-by-step explanation:

<em>CB </em>is equal to <em>EZ </em>and <em>E </em>equals 35, and <em>E </em>and <em>C </em>are the same, therefore, both <em>E </em>equals 35. Since there's 180 degrees in a triangle, and <em>ABY </em>equals 105, you have to subtract 180 - 105 to get the other angle. When you do that, you get that <em>B </em>equals 75. You have to add <em>E </em>and <em>B</em> (35 + 75), since that's in the same triangle as <em>A. </em>When you do that, you get 110. Subtract 180 - 110 to get <em>A, </em>which is 70.

3 0
3 years ago
Other questions:
  • David is the president of his student council.When the leadership team met for the first time, he asked each person to shake eac
    7·1 answer
  • What is the definition of the quadratic formula?
    12·1 answer
  • The local animal shelter accepts abandoned cats and dogs. They usually receive twice as many cats as dogs. They estimate that 80
    10·1 answer
  • Write your own word problem and share it with the group. Then translate your problem into its resulting math equation. What step
    6·1 answer
  • Find the angle of arc BC
    7·1 answer
  • Kelly is 8 years younger than her sister. The sum of her age is 44 years. How old is jelly and how old is her sister?
    6·1 answer
  • What is 3w=6<br> W=<br> Pls help
    5·1 answer
  • Find the value of the variable 7x + 19 11x -89 60°​
    14·1 answer
  • You have 9 ½ pounds of flour. Each cookie takes ¾ pounds to make. How many cookies can I make?
    11·1 answer
  • 3) T'challa makes $55 an hour and works 30 hours a week. He loses 20% of his paycheck to
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!