Factor the polynomial completely: 16t*2-24t+9

You order office supplies for your company every quarter. The invoices for the first three quarters are $615, $791, and $803. Wh

guapka [62]

Answer:

$2209

Step-by-step explanation:

Add all three numbers together

4 0

3 years ago

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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

How many times does 50 go into 4000

iVinArrow [24]

Well, if you just divide 4000 by 50, you can see that the answer will come out as:
80
~TO check: 80 multiplied by 50 would come out to the answer of 4,000.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hope this helped! :D

8 0

3 years ago

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if trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A’lie

maria [59]

Answer:

Answer: (second option) (-4,1)

Step-by-step explanation:

Transformations of Points and Shapes

The image shows a trapezoid ABCD where point A has coordinates (-4,1).

The following transformations are performed:

Reflection over the y-axis: If a point (x,y) is reflected over the y-axis, it becomes (-x,y). Thus point A becomes A'=(4,1)

Reflection over the x-axis: If a point (x,y) is reflected over the x-axis, it becomes (x,-y). Thus point A' becomes A''=(4,-1)

Rotation 180°: If a point (x,y) is rotated 180°, it becomes (-x,-y). Thus point A'' becomes A'''=(-4,1)

Answer: (second option) (-4,1)

5 0

3 years ago

On a typical day, flights at a local airport arrive at a rate of 10 every 15 minutes. At this rate, how many flights would you e

Hunter-Best [27]

40 because 15×4 is 60 and there is 60 minutes in an hour

3 0

3 years ago