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
ddd [48]
3 years ago
15

I need help with this question please

Mathematics
1 answer:
german3 years ago
8 0

Answer:

C.

Step-by-step explanation:

Given

A =(x_1,y_1)

B =(x_2,y_2)

C =(x_3,y_3)

D =(x_4,y_4)

Required:

Which condition proves that AB is perpendicular to CD

First, calculate the slopes of both.

<u>For AB</u>

m_1 = \frac{y_2 -y_1}{x_2 - x_1}

<u>For CD</u>

m_2 = \frac{y_4 -y_3}{x_4 - x_2}

The condition of perpendicularity is:

m_1 * m_2 = -1

Substitute values for m1 and m2

\frac{y_2 -y_1}{x_2 - x_1} * \frac{y_4 -y_3}{x_4 - x_2} = -1

Option (c) is correct

You might be interested in
Based on a study of population projections for 2000 to​ 2050, the projected population of a group of people​ (in millions) can b
Olegator [25]

Answer:

(a) 0.107 million per year

(b) 0.114 million per year

Step-by-step explanation:

A(t) = 11.19(1.009)^t

(a) The average rate of change between 2000 and 2014 is determined by dividing the difference in the populations in the two years by the number of years. In the year 2000, t=0 and in 2014, t=14. Mathematically,

\text{Rate}=\dfrac{A(2014) - A(2000)}{2014-2000}=\dfrac{11.19(1.009)^14-11.19(1.009)^0} {14}

A(0)=\dfrac{12.69-11.19}{14}=\dfrac{1.5}{14}=0.107

(b) The instantaneous rate of change is determined by finding the differential derivative at that year.

The result of differentiating functions of the firm y=a^x (where a is a constant) is \dfrac{dy}{dx}=a^x\ln a. Let's use in this in finding the derivative of A(t).

A\prime(t) = \dfrac{A}{t}=11.19\cdot1.009^t\ln1.009

In the year 2014, t=14.

A\prime(14) =11.19\cdot1.009^14\ln1.009=0.114

6 0
3 years ago
Follow the process of completing the square to solve 2x2 + 8x - 12 = 0. After adding B2 to both sides of the equation in step 4,
Katena32 [7]
2x^2 + 8x - 12 = 0..divide by 2
x^2 + 4x - 6 = 0
x^2 + 4x = 6...add 4 to both sides of the equation
x^2 + 4x + 4 = 6 + 4
(x + 2)^2 = 10....<== ur constant is 10
x + 2 = (+-)sqrt 10
x = -2 (+ - ) sqrt 10

x = -2 + sqrt 10
x = -2 - sqrt 10

3 0
3 years ago
Read 2 more answers
Find the slope of the line.
lukranit [14]

Answer:

0

Step-by-step explanation:

slope = dy/dx

= 0/x

= 0

7 0
2 years ago
I really need help i don’t get this at ALL. :(
bonufazy [111]

Step-by-step explanation:

You have to go to Y axis first then to X. For example : (4,5) go up 4 and go to x axis and when u get to 5 you put a dot. The same thing if is (-4,-5) go down 4 and to the left 5 and mark a dot. When you mark the dot put (_,_).

Hope you understand. Let me know if you don't.

6 0
3 years ago
Bartholemew will draw with replacement 160 tickets at random from a box with five tickets [0, 0, 0, 1, 2]. Estimate the chance t
cupoosta [38]

Answer:

0.0786

Step-by-step explanation:

It is given that Bartholemew had drawn the replacement of 160 tickets.

There are five tickets = [0, 0, 0, 1, 2]

Now we need to find the estimate of the ticket that has 1 on it and it turns up on the 32 draws exactly.

Since the probability of the drawing 1 out of 5 tickets is given by,   $\frac{1}{5} = 0.2$

So the binomial with the parameter of n = 160 and p = 0.2, we get

P (it turns up on exactly 32 draws) = P(X = 32)

Therefore,

$C(160, 32)\times (0.2)^{32}\times (0.8)^{160-32}$

= 0.0786

4 0
2 years ago
Other questions:
  • 200 days from March 3 is
    5·2 answers
  • Burj al Arab hotel another one of the world's tallest buildings Built in 1973, it is 1,136 feet high and has 80 stories. If each
    5·1 answer
  • Maria has 4 gallons of water. Ryan has 14 quarts of water. How many more cups of water does Maria have than Ryan​?
    5·2 answers
  • the flag pole in front of the school casts a shadow 40 feet long when the measurement of the angle of elevation to the sun is 31
    11·1 answer
  • A line on a graph shows a proportional relationship between the hours worked, x, and the total pay y. Two points on the graph ar
    7·2 answers
  • Solve the equation in the image. <br> 10 points!!
    11·1 answer
  • The difference between five times a number and twice that number
    5·1 answer
  • Martin jogged around the lake in an hour. Esperanza jogged around the lake in an hour. How much1 1 /4 5/6 longer did Martin take
    9·1 answer
  • Heeelpppppppppppppppppppppppppppppppp
    5·2 answers
  • 5/9 power -2 * 3/5 power -3 * 3/5 power 0
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!