40,897 in expanded form

Help A.S.A.P please thank you and please :D

Lina20 [59]

Answer:

Emma was right to say that both packages are close to 2 pounds.

If we round-off the weights of both to the nearest whole number we would get 2 pounds on both. We look at the the difference of both from 2 pounds we get the following:

2.36 - 2.0 = 0.36

2.09 - 2.0 = 0.09

The smaller the difference the closer it is to the base value. So we can say that the closest one is 2.0 pounds is the package that weighs 2.09 pounds.

8 0

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.

8 0

4 years ago

Find the value of x.

allsm [11]

Answer:

x=51

Step-by-step explanation:

Formula: 35+16=x

Step 1: Simplify both sides of the equation.

35+16=x

(35+16)=x(Combine Like Terms)

51=x

Step 2: Flip the equation.

x=51

Hope this helps.

8 0

3 years ago

What are the most bags Mrs. Dupree can make? Will choose brainliest and will report absurd answers

Umnica [9.8K]

Answer:

B. 4 bags

Step-by-step explanation:

The number of bags that will have the same quantities of the different gifts is the Greatest Common Divisor of the numbers of gifts.

GCD(24, 32, 44) = 4

Mrs. Dupree can make at most 4 identical bags.

___

The GCD can be found by looking at factors:

24 = 4·6
32 = 4·8
44 = 4·11

4 is the largest common factor of these numbers.

__

The GCD can also be found using Euclid's algorithm. In that algorithm, the larger number is divided by the smaller, with the remainder replacing the larger number after each step. If the remainder is zero, the smaller number is the GCD.

The GCD of several numbers can be found by finding the GCD of a pair, then of that value and the next number:

GCD(24, 32, 44) = GCD(GCD(24, 32), 44) = GCD(8, 44) = 4

_

32/24 = 1 r 8 . . . . first step in Euclid's algorithm for GCD(24, 32)

24/8 = 3 r 0 ⇒ GCD(24, 32) = 8

Then

44/8 = 5 r 4

8/4 = 2 r 0 ⇒ GCD(8, 44) = 4 = GCD(24, 32, 44)

3 0

3 years ago

Use the drawing tool(s) to form the correct answer on the provided graph.

vfiekz [6]

3x-2y= -12
y=4x+1
3x-2(4x+1)= -12
3x-8x-2= -12
-5x=-12+2
-5x=-10
x= -10/-5
x=2
y=4x+1
y=4•2+1
y=8+1
y=9

(x,y) = (2,9)

6 0

3 years ago