A student is setting up a relay race around the perimeter of a

Triangle TRE has vertices T(3,6), R(-3,10), and E(-9,4). Find the coordinates of point M if line TM is a median of triangle TRE

Sergeeva-Olga [200]

Answer:

The coordinate of point M = (-6,7)

Explanation:

The Median of a triangle is a line segment from a vertex to the midpoint of the opposite side of a triangle.

Given: $\triangle TRE$ has vertices T(3,6) , R(-3,10) and E(-9,4).

Here, line TM is a median of triangle TRE where M is the midpoint of RE.

The midpoint of M of the line segment from R(-3,10) to E(-9,4) is;

M = $(\frac{-3+(-9)}{2}, \frac{10+4}{2}) = ( \frac{-12}{2}, \frac{14}{2} )=(-6,7)$

Therefore, the coordinate of point M is, (-6,7).

7 0

2 years ago

Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- an

slega [8]

Answer:

1) There were 33 $4,000 investors and 27 $8,000 investors.

2) The solution in x = 4, y = 9.

3) There were 24 nickels and 56 dimes.

Step-by-step explanation:

1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $4,000 or $8,000. If the partnership raised $348,000, then how many investors contributed $4,000 and how many contributed $8,000?

I am going to say that:

x is the number of investors that contributed 4,000.

y is the number of investors that contributed 8,000.

Building the system:

There are 60 investors. So:

$x + y = 60$

In all, the partnership raised $348,000. So:

$4000x + 8000y = 348000$

I am going to simplify by 4000. So:

$x + 2y = 87$

Solving the system:

The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:

$1)x + y = 60$

$2)x + 2y = 87$

I am going to multiply 1) by -1. So we have

$1)-x - y = -60$

$2)x + 2y = 87$

By addition, the x are going to cancel each other

$-x + x - y + 2y = -60 + 87$

$y = 27$

For x:

$x + y = 60$

$x = 60-y = 60-27 = 33$

There were 33 $4,000 investors and 27 $8,000 investors.

2) Solve the system by row-reducing the corresponding augmented matrix.

$2x + y = 17$

$x + y = 13$

This system has the following augmented matrix:

$\left[\begin{array}{ccc}2&1&17\\1&1&13\end{array}\right]$

To help the row reducing, i am going to swap the first with the second line:

$L1 L2$

So we have:

$\left[\begin{array}{ccc}1&1&13\\2&1&17\end{array}\right]$

Now, reducing the first column.

$L2 = L2 - 2L1$

So we have:

$\left[\begin{array}{ccc}1&1&13\\0&-1&-9\end{array}\right]$

Now we do:

$L2 = -L2$

And the matrix is:

$\left[\begin{array}{ccc}1&1&13\\0&1&9\end{array}\right]$

Now to reduce the second column, we do:

$L1 = L1 - L2$

$\left[\begin{array}{ccc}1&0&4\\0&1&9\end{array}\right]$ .

So the solution is:

x = 4, y = 9.

3) A jar contains 80 nickels and dimes worth $6.80. How many of each kind of coin are in the jar?

I am going to say that x is the number of nickels and y is the number of dimes.

Each nickel is worth 5 cents and each dime is worth 10 cents.

Building the system:

There are 80 coins in all:

$x + y = 80$

They are worth $6.80. So:

$0.05x + 0.10y = 6.80$

Solving the system:

$1)x + y = 80$

$2)0.05x + 0.10y = 6.80$

I am going to divide 1) by -10, so we can cancel y. So:

$1)-0.10x - 0.10y = -8$

$2)0.05x + 0.10y = 6.80$

Adding:

$-0.10x + 0.05x - 0.10y + 0.10y = -8 + 6.80$

$-0.05x = -1.2$ *(-100)

$5x = 120$

$x = \frac{120}{5}$

$x = 24$

Also

$x + y = 80$

$y = 80-x = 80-24 = 56$

There were 24 nickels and 56 dimes.

8 0

3 years ago

The cost of renting a boat is $51 for 5 hours. Which of the following is not an equivalent rate? Give the letter of your answer

alexgriva [62]

B. Obviously all the numbers have to do with one and it’s 30. If it’s wrong let me know !

4 0

2 years ago

Please help pic attatched i will give brainliest

Alchen [17]

Answer:

N'(x)=90 In(43)*43^x-90 In(50)*43^x /50^x

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Please help!!!!!!!!!!!!!!

Doss [256]

The equation would be (100-10) ÷30 your answer would be 3

3 0

2 years ago

Read 2 more answers