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BartSMP [9]
3 years ago
11

M is the midpoint of CD. Given the coordinates of one endpoint C(10,-5) and the midpoint M(4, 0), find the coordinates of the ot

her endpoint D of CD.
Mathematics
1 answer:
mash [69]3 years ago
5 0

Answer:

D(-2, 5).

Step-by-step explanation:

We are given that M is the midpoint of CD and that C = (10, -5) and M = (4, 0).

And we want to determine the coordinates of D.

Recall that the midpoint is given by:

\displaystyle M = \left(\frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2}\right)

Let C(10, -5) be (<em>x</em>₁<em>, y</em>₁) and Point D be (<em>x</em>₂<em>, y</em>₂). The midpoint M is (4, 0). Hence:

\displaystyle (4, 0) = \left(\frac{10+x_2}{2} , \frac{-5+y_2}{2}\right)

This yields two equations:

\displaystyle \frac{x_2 + 10}{2} = 4\text{ and } \frac{y_2 - 5}{2} = 0

Solve for each:

\displaystyle \begin{aligned}x_2 + 10 &= 8 \\ x_2 &= -2 \end{aligned}

And:

\displaystyle \begin{aligned} y_2 -5 &= 0 \\ y_2 &= 5\end{aligned}

In conclusion, Point<em> </em>D = (-2, 5).

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the tickets for a benefit concert were $6 for friday night and $8 for Saturday night. the total attendence for the two nights wa
aksik [14]

Answer:

432 people on Friday and 658 on Saturday

Step-by-step explanation:

Lets use variables for each day

x=Friday and y=Saturday

now write two equations since you were given two different information (money and people)

$6 on Friday and $8 on Saturday with a total amount of $7856

the equation will be 6x+8y=7856

now the second equation will be for people

x amount of people on Friday and y amount of people on saturday for a total of 1090; the equation will be

x+y=1090

put them together

6x+8y=7856

x+y=1090

now you can cancel a variable but manipulating one of the equations. We'll use x, to cancel x you need make it zero so multiply the bottom by -6

6x+8y=7856

-6(x+y=1090)

6x+8y=7856                   now subtract downwards, with the x cancelling

-6x-6y=-6540

2y=1316                          simplify

(2y/2)=(1316/2)              

y=658

                                       insert y into x+y=1090

x+(658)=1090

    -658   -658

x=432

7 0
3 years ago
How many numbers are equal to the sum of two odd, one digit numbers
Paul [167]
Here is a list of the odd number paired

1+3, 1+5, !+7, and !+9  (there are 4 unique sums - 4, 6,8 and 10)
3+5, 3+7, 3+9  (notice I did not pair 3 with 1 and the the only new sum is 12)
5+7, 5+9  (the only new sum is 14)
7+9  (16 is a new sum)

The sums (no repeats) are 4,6,8,10,12,14 and 16 for a total of seven numbers.
5 0
3 years ago
PLS HELP PLEASE I NEED THIS!!!!! LOOK AT THE PICTURE PLS!!!!!
Solnce55 [7]
The answer is 9x^2+36x+36
You can distribute the -3 to the x and the 2 to get -3x-6 and then because it’s squared it gets multiplied by itself so (-3x-6) times(-3x-6) which gives you the answer of 9x^2+36x+36
4 0
3 years ago
Can someone PLEASE PLEASE HELP!!! I will mark brainliest!
Tcecarenko [31]
Its 2 i guess but im not sure
7 0
3 years ago
Read 2 more answers
Solve x^(2)+4x=4 for x by completing the square.
Mama L [17]

Answer:

x = 2 sqrt(2) - 2 or x = -2 - 2 sqrt(2)

Step-by-step explanation:

Solve for x:

x^2 + 4 x = 4

Add 4 to both sides:

x^2 + 4 x + 4 = 8

Write the left hand side as a square:

(x + 2)^2 = 8

Take the square root of both sides:

x + 2 = 2 sqrt(2) or x + 2 = -2 sqrt(2)

Subtract 2 from both sides:

x = 2 sqrt(2) - 2 or x + 2 = -2 sqrt(2)

Subtract 2 from both sides:

Answer: x = 2 sqrt(2) - 2 or x = -2 - 2 sqrt(2)

8 0
3 years ago
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