The vertices of her garden are located at the points (−1,5), (4,2) and (9,−4) on a coordinate grid. If each unit on the grid represents a foot and the material costs $8 per foot, how much will she pay for the material on the side between points (−1,5) and (4,2)?

Given:

The vertices of the garden on a coordinate grid are (−1,5), (4,2) and (9,−4).

Each unit on the grid represents a foot and the material costs $8 per foot.

To find:

The cost for the material on the side between points (−1,5) and (4,2).

Solution:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the above formula, the distance between points (−1,5) and (4,2) is

[tex]d=\sqrt{(4-(-1))^2+(2-5)^2}[/tex]

[tex]d=\sqrt{(4+1)^2+(-3)^2}[/tex]

[tex]d=\sqrt{(5)^2+(-3)^2}[/tex]

On further simplification, we get

[tex]d=\sqrt{25+9}[/tex]

[tex]d=\sqrt{34}[/tex]

[tex]d\approx 5.83[/tex]

Now,

1 unit = 1 foot and 1 foot material costs is $8.

So, 1 unit material cost is $8.

Cost of material for 5.83 units is

[tex]5.83\times 8=46.64[/tex]

Therefore, the cost for the material on the side between points (−1,5) and (4,2) is $46.64.

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Here is the other question
Part A and B are done

A. Lesson
1. Describe the formula for slope in words and with an equation.
M=y^2-y^1/x^2-x^1
1. What is the slope of all horizontal lines? What is the slope of all vertical lines?
The slope of all horizontal lines is 0. The slope of all vertical lines is undefined.


B. Lesson Content
3. Copy and paste the 3-step procedure for finding the slope using the formula.

4. Use Example 3 as your model for the following: In the 2000 census, the population was 8000; in the 2010 census, the population was 7500. Find the rate of growth for the town. Show the 3-step procedure, as well as the final answer in words.
A(200(x1), 8000(y1)) and B(2010(x2), 7500(y2))
M=(y2-y1)(x1-x2)=7500-8000/2010-2000
M=-50=50 people per year decrease



C. Write the slope-intercept (y = mx + b) form of the equation from the information given. Show your steps as done in the lesson content to earn credit.

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PLEASEEEE HELPPP!!

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PLEASE HELP ME LIKE IM GOING TO CRY ILL give you brainliest if the answer is correct and 20/40 points..............Ben participated in a race. During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours. During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. What equation could you write to solve for the number of hours Ben ran during each half of the race? Let y represent the number of miles in half the race. Write two equations, one for the first half of the race and one for the second half. How could you transform these two equations to be the same as the original equation you wrote to solve for x? What do you think this means about solving for the variables in a situation represented by two equations?

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