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3 years ago

10

The distance from Ben's home to his school is 215 miles. After covering 14 of the total distance, he stopped at a convenience st

ore.

1 answer:

kifflom [539]3 years ago

5 0

if he stops at a convenience store every 14 miles the last number would be 5

15×14+5=215

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Which number would be classified as an integer on the Venn diagram?

victus00 [196]

Integers involve with negative, so D isn't the correct answer the correct answer will be A.

7 0

4 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

A scale drawing of a school bus has a scale of 1/2 inch to 5feet. If the length of the school bus is 4 1/2 inches on the scale d

Sedaia [141]

Answer: actual length = 45 ft

Explanation:

Scale drawn:

1/2 inch = 5ft

Meaning that if the drawing scale is 0.5 inch then the actual bus would be 5ft.

If the length of the drawn school bus is 4 1/2 inches. We can write:

1/2 = 5
4 1/2 = x

=> x = (5 x 4 1/2)/1/2
Or x = (5 x 4.5)/0.5
x = 22.5/0.5
x = 45

Therefore the actual length of the bus is 45 ft

3 0

3 years ago

A chemist has a 40% alcohol solution and a 25% alcohol solution. How much of each should he mix together to get 50 liters of a 3

ludmilkaskok [199]

Answer:

33 1/3 L of the 40% solution, 16 2/3 L of the 25% solution

Step-by-step explanation:

Set up two equations...

Let x represent the number of Liters of the 40% solution

Let y represent the number of Liters of the 25% solution

We need 50 liters total, so

x + y = 50

and we need the 50 L to be 35% solution, so

0.4x = 0.25y = 0.35(50)

Solve the first equation for one variable...

x = 50 - y (subtract y from both sides in equation 1)

Now substitute that value into the second equation...

0.4(50 - y) + 0.25y = 17.5 (x becomes 50 - y, 0.35(50) = 17.5)

Now solve for y...

20 - 0.4y + 0.25y = 17.5

-0.15y = -2.5

y = 16.66666667

y = 16 2/3 L

So we need to plug that into the first equation to find 'x'

x + 16 2/3 = 50

x = 50 - 16 2/3

x = 33 1/3

3 0

3 years ago

Read 2 more answers

The gross weight of a package and its contents is 11 pounds 5 ounces. If the packaging weighs 1 pound 15 ounces, what's the net

dsp73

Answer A
For ease convert both into ounces.

Gross = (11x16) + 5 = 181 ounces
Packaging = (1x16) + 15 = 31 oz.

Now subtract Packaging from Gross

181 - 31 = 150 oz.

Divide by 16 to get pounds

150/16 = 9.375 - hence 9 lb.

and multiply 16 by .375 for ounces

0.375 x 16 = 6 oz.

Thus A : 9lb 6 oz

5 0

4 years ago

Read 2 more answers