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3 years ago

The midpoint of a line segment with end points as (-10, y1) and (-6, 7) is (-8, 6). What is the value of y1?

1 answer:

soldier1979 [14.2K]3 years ago

8 0

The formulae for the midpoint are correct:

M ( (x₂-x₁)/2 , (y₂-y₁)/2 )

You need to invert these to get x₁ and y₁:
x₁ =2xm - x₂
y₁ =2ym - y₂

Try with the x to prove the formulae are correct:
x₁ =2·(-8) - (-6) = -16 + 6 = -10 which is what we have!

Then, use the other formula for y:
y₁ =2 ·(6) - (7) = 12 - 7 = 5

Therefore y₁ = 5

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An image is the result of an isometric transformation of its pre-image because

FrozenT [24]

the two triangles are congruent

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2 years ago

Find a number which decreased by 12 equals 3 times it’s opposite

-BARSIC- [3]

Answer:

The number is 3.

Step-by-step explanation:

To find : A number which decreased by 12 equals 3 times it’s opposite ?

Solution :

Let the number be 'x'.

It's opposite is '-x'.

A number which decreased by 12 equals 3 times it’s opposite

i.e. $x - 12 = 3(-x)$

Solving the equation,

$x-12=-3x$

$x+3x=12$

$4x=12$

$x=\frac{12}{4}$

$x=3$

Therefore, the number is 3.

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3 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.

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3 years ago

Px+35=-6x+Q

julia-pushkina [17]

The answer to this question is C

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3 years ago

After school, Emily had a science club meeting for 40 minutes, followed by a choir rehearsal

aniked [119]

Answer:

3:15 pm

Step-by-step explanation:

(1:25 + 40 min) = 2:05 + 75 min= 3:15

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3 years ago