What happened to the snowman during the heat wave?

Two airplanes are flying to the same airport. Their positions are shown in the graph. Write a system of linear equations that re

Liono4ka [1.6K]

To write the system we need the slope of each line and at least one point on the line. The two lines to consider will be the lines connecting the location of each plane to the airport they are flying to. It is also worth noting that the coordinates of the airport represent the point of intersection of the two lines and thus the solution to the system.

1. slope of the line connecting airplane one and the airport: m = 2 you can see this clearly if you graph the two points. From airplane 1 location we rise 8 units and move to the right 4 units to get to the airport. Slope is defined as rise over run: so 8 divided by 4 = 2(the slope) Now substitute the slope and the point (2,4) into point-slope form of a line:

y - 4 = 2(x -4) the standard form of this equation is 2x - y = 0

2. slope of the line connecting airplane 2 and the airport: m = - $\frac{1}{3}$ To find this slope, simply observe the vertical change of down 3 and a horizontal shift of right 9 from the airport to airplane 2. Now substitute this slope and and the point (15,9) into point-slope form of a line:

y - 9 = $- \frac{1}{3}$ (x - 15) the standard form of this equation is:
x + 3y = 42

Let's write the system:
2x - y = 0
x + 3y = 42
Multiply the first equation by 3 to get the new system
6x - 3y = 0
x + 3y = 42 add these two equations to get an equation in terms of x

7x = 42 thus x = 6 and substituting this value into 2x - y = 0 we see y = 12
In other words, we have proven that the location of the airport is in fact the solution to our system.

PS: You just have to do a little algebra to get from point-slope form of the two equations to standard form. I did not show this process, but if you need it just let me know... thanks

6 0

2 years ago

What is the approximate perimeter of the figure?

exis [7]

<span>This is a perimeter of 1/4 of a circle. We know that the radius of the circle: r = 5 in. Also the perimeter of the circle is : 2 * r * Pi = 2 * 5 * 3.14 = 31.4 in. For the quarter of a circle it its 31.4 : 4 = 7.85 in. After that we can add the 2 lengths of the radius: P = 5 + 5 + 7.85 = 17.85 in ( approx. 17.9 in ). Answer: C ) 17.9 in. </span>

7 0

2 years ago

Quadrilateral ABCD is translated 7 units down and 2 units to the right. The length of side AB of the original quadrilateral is u

Phoenix [80]

Answer

AB would be the same as the original because the size never changes.

Step-by-step explanation:

5 0

2 years ago

Hariette would like to review the income and expenses that were actually paid last month so she can determine how much to set as

Brrunno [24]

Answer:

Hybrid basis

Step-by-step explanation:

There are different methods of accounting used by businesses depending on their peculiar needs. Below are the type of accounting methods:

- Cash basis is when revenues and expenses are recognised when cash is recieved or paid out.

-Accrual basis is when revenue and expenses are recognised when they are earned. For example if services are rendered to a client that will pay in a week's time, since service has already been given it is considered that the future payment has been earned.

- Modified basis combines elements of cash and accrual basis. For example considering short term assets like accounts receivable and accounts payable as cash items. Long term assets are recorded on accrual basis.

- Hybrid basis is used when cash and accrual methods are used for various expenses and tax. Mostly it is used for internal accounting purposes.

In this scenario Hariette would like to review the income and expenses that were actually paid last month. This requires a cash basis that shows actual amount recieved and paid last month. Account receivable and payable are not considered.

In setting aside money for tax she will employ accrual basis accounting. It is an expense that is estimated for future use.

So the hybrid basis is the method that will be most suitable.

5 0

2 years ago

Today, the Great Pyramid at Giza near Cairo, Egypt stands 137 meters tall, coming to a point.Its base is a square with each side

Vlad1618 [11]

Hope you can see the picture and understand the drawings.

It can seem complex at first but you just have to think it through.

I use pythagoras' theorem to find the diagonal of the base square and then use that information along with the height with the aid of that ever so handy pythagoras' theorem to find the length of the slope.

8 0

2 years ago