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2 years ago

Usevthe distribute property to express24(3f+6q).

Mathematics

1 answer:

Reika [66]2 years ago

4 0

Answer:

FACTOR: 8f 3 (3f 6 −2f 4 −4f 3 −4)

Step-by-step explanation:

EVALUATE: 24f 9 −16f 7 −32f 6−32f 3

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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

PLEASE HELP ILL GIVE BRAINLIEST<br> WHATS THE PERCENT CHANGE SHOW WORK

mote1985 [20]

Answer:

34.55556%

Step-by-step explanation:

3 0

2 years ago

Hello! Please help.

valina [46]

1 -

3 cups left.

David biked a total of 158 miles (option C)

Why?

- First exercise:

To solve the problem we need to consider that for each 1/2 cup of cornmeal, we will have 6 corn muffins.

So, calculating we have:

$TotalMuffins=24=4*6\\\\UsedCups=\frac{1}{2}*4=2Cups$

We can see that, if each 1/2 cups can give us 6 corn muffins, 2 cups can give us 24 corn muffins.

$CupsLeft=5cups-2cups=3cups$

Hence, there are 3 cups left.

- Second exercise:

We can solve the problem by multiplying or adding the fractions according to the number of dots assigned to each one.

So, calculating we have:

$FirstDay=10miles*2=20miles\\SecondDay=10\frac{1}{2}miles=10.5miles\\ThirdDay=11miles*3=33miles\\FourthDay=11\frac{1}{2}miles*4=11.5miles*4=46miles\\FifthDay=12miles*3=36miles\\SixthDay=12\frac{1}{2}miles=12.5miles$

$Total=20miles+10.5miles+33miles+46miles+36miles+12.5miles\\Total=158miles$

Hence, we have that David covered a total 158 miles. (Option C)

Have a nice day!

5 0

3 years ago

Read 2 more answers

The SAT mathematics scores in the state of Florida are approximately normally distributed with a mean of 500 and a standard devi

Yanka [14]

The interval $(300,700)$ corresponds to the part of the distribution lying within 2 standard deviations of the mean (since 500-2*100=300 and 500+2*100=700). The empirical rule states that approximately 95% of the distribution is expected to fall in this range.