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
weqwewe [10]
3 years ago
10

The endpoints of line

formula"> are C(1,-6) and D(7,5). Find the coordinates of the midpoint M.

Mathematics
2 answers:
Juli2301 [7.4K]3 years ago
8 0

\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ C(\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad D(\stackrel{x_2}{7}~,~\stackrel{y_2}{5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{7+1}{2}~~,~~\cfrac{5-6}{2} \right)\implies \left( \cfrac{8}{2}~,~\cfrac{-1}{2} \right)\implies \stackrel{M}{\left( 4~,~-\frac{1}{2} \right)}

9966 [12]3 years ago
4 0

Answer is provided in the image attached.

Hope this helped!

Have a great day!

-TheBlueFox-

You might be interested in
The typical full-time employee in a particular hotel works a 40-hour week. Last month, the hotel's 80 employees worked a total o
Mila [183]

Answer: There are 25 FTEs.

Step-by-step explanation:

Since we have given that

Number of hour week for full time employee = 40 hours

In a month we know that

Number of weeks = 4

Total number of hours in a month would be

40\times 4\\\\=160\ hours

If in last month, the hotel's 80 employees worked a total of 4000 hours,

So, Full time equivalent workers were employed by the hotel last month would be

\dfrac{4000}{160}\\\\=25

Hence, there are 25 FTEs.

7 0
3 years ago
What is 70 percent of 1872
uranmaximum [27]

Answer:

1310.4

Step-by-step explanation:

1872 x 0.7 = 1310.4

4 0
3 years ago
Read 2 more answers
Which ratio can be used to solve for y in the triangle below?
frosja888 [35]

Answer:A

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Yo please help i’ll give u a brainliest
Elodia [21]

Answer:

4

Step-by-step explanation:

1st: do 2x3=6 so if 1 6in scoop makes one pitcher of tea then you could make about 4 pitchers of tea because there are the volume of the pitcher of tea mix is 24in so 24/6=4

3 0
3 years ago
A company wishes to manufacture some boxes out of card. The boxes will have 6 sides (i.e. they covered at the top). They wish th
Serhud [2]

Answer:

The dimensions are, base b=\sqrt[3]{200}, depth d=\sqrt[3]{200} and height h=\sqrt[3]{200}.

Step-by-step explanation:

First we have to understand the problem, we have a box of unknown dimensions (base b, depth d and height h), and we want to optimize the used material in the box. We know the volume V we want, how we want to optimize the card used in the box we need to minimize the Area A of the box.

The equations are then, for Volume

V=200cm^3 = b.h.d

For Area

A=2.b.h+2.d.h+2.b.d

From the Volume equation we clear the variable b to get,

b=\frac{200}{d.h}

And we replace this value into the Area equation to get,

A=2.(\frac{200}{d.h} ).h+2.d.h+2.(\frac{200}{d.h} ).d

A=2.(\frac{200}{d} )+2.d.h+2.(\frac{200}{h} )

So, we have our function f(x,y)=A(d,h), which we have to minimize. We apply the first partial derivative and equalize to zero to know the optimum point of the function, getting

\frac{\partial A}{\partial d} =-\frac{400}{d^2}+2h=0

\frac{\partial A}{\partial h} =-\frac{400}{h^2}+2d=0

After solving the system of equations, we get that the optimum point value is d=\sqrt[3]{200} and  h=\sqrt[3]{200}, replacing this values into the equation of variable b we get b=\sqrt[3]{200}.

Now, we have to check with the hessian matrix if the value is a minimum,

The hessian matrix is defined as,

H=\left[\begin{array}{ccc}\frac{\partial^2 A}{\partial d^2} &\frac{\partial^2 A}{\partial d \partial h}\\\frac{\partial^2 A}{\partial h \partial d}&\frac{\partial^2 A}{\partial p^2}\end{array}\right]

we know that,

\frac{\partial^2 A}{\partial d^2}=\frac{\partial}{\partial d}(-\frac{400}{d^2}+2h )=\frac{800}{d^3}

\frac{\partial^2 A}{\partial h^2}=\frac{\partial}{\partial h}(-\frac{400}{h^2}+2d )=\frac{800}{h^3}

\frac{\partial^2 A}{\partial d \partial h}=\frac{\partial^2 A}{\partial h \partial d}=\frac{\partial}{\partial h}(-\frac{400}{d^2}+2h )=2

Then, our matrix is

H=\left[\begin{array}{ccc}4&2\\2&4\end{array}\right]

Now, we found the eigenvalues of the matrix as follow

det(H-\lambda I)=det(\left[\begin{array}{ccc}4-\lambda&2\\2&4-\lambda\end{array}\right] )=(4-\lambda)^2-4=0

Solving for\lambda, we get that the eigenvalues are:  \lambda_1=2 and \lambda_2=6, how both are positive the Hessian matrix is positive definite which means that the functionA(d,h) is minimum at that point.

4 0
3 years ago
Other questions:
  • What's the answer to 4n - 9 = -9
    5·2 answers
  • What's 5x - 4x to the second power + 3 in standees form?
    15·1 answer
  • Who can help me with this I’ll mark u as brainliest
    14·2 answers
  • Can someone please answer this for me.
    14·1 answer
  • Please help, 15 points + brainliest!
    9·2 answers
  • You have one type of candy that sells for $2.50/lb and another type of candy that sells for $8.20/lb. You would like to have 17.
    6·1 answer
  • 9. The Brightline train travels 204 miles in 3 hours, moving at a constant
    12·1 answer
  • What is the perimeter of the are. Please show work.​
    8·1 answer
  • Need help anyone help plz im struggling
    7·1 answer
  • Can someone find the answers of this Multiple Choice Questions for me?? Please!
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!