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.

Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is the solution set of this problem?
a. (♾,-21)
b. (♾, -21)
c. (-21,♾)
d. (21,♾)​

Topic: Integrals
Subject: Calculus

If anyone could help I’d appreciate! I will certainly award points and give brainliest answer ASAP!! I promise :)

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?

PLS ANSWER NO MESSING AROUND PLSSSSSS TWO PEOPLE ALREADY FAKED IT

How would you graph the solution to 3x ≤ -15?

A car with a mass of 500 kg is accelerating at 10 m/s². What is the force being applied the car’s engine?

Estimate the product 0.62 x 104

Can someone help me???

Give your answer in simplest form.

When Rhonda was 12, her grandmother made her a quilt. Each pattern in the quilt contained 126 quares. The
pattern was repeated 8 times to make the entire quilt. How many squares were in Rhonda's quit?

What is the slope of the line through (3,7) and (-1,4)

solve equation by factoring 8x^2-8x=0

What is the y-intercept of the line 3x – 4y = 24?

The volume of a right circular cone is 45 cubic centimeters, and the radius of
the base is 3 centimeters. What is the height of the cone in centimeters?

Is there another way to convert fractions to decimals?

which of the following terminating decimals is equivalent to -1 3\4

I’ll give the Brainliest to who answers this question with a reasonable explanation.

Find the best buy between 6.2 oz. for $2.97 or 8 oz. for $3.47.

A) Buying 8 oz for $3.47 is the better buy.

B) Buying 6.2 oz for $2.97 is the better buy.

Thank you!

V = LWH solve for the variable w

0.7,7/9,7/8 order least to greatest

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.

______ terms are also expressions. (please fill in the blank)
A. No
B. All
C. Some

which is the best estimate for this expression ?
a) 300
b) 40
c) 3
d)0.4​

22. Determine the value of c so that the line
segment with endpoints B(2, 2) and C(9,6)
BC
is parallel to the line segment with endpoints
D(c, -7) and E(5, -3).

help is appreciated !!!

Giving 100 points if someone can answer this correctly...

x³+y³+z³=42

What is x y and z multiplied by 9.08 * 10³

this question is dumb. you should be able to get it

Which of these expressions shows unlike terms?

Your answer:

2x +7x


2x+2y


2(x+1)


3x+1x

Paul drank 18.2 ounces of water per day during soccer practice for a total of 54.6 ounces of water. Ryan drank 20.4 ounces of water each day after football practice for a total of 81.6 ounces of water. How many more days of practice did Ryan have than Paul?
A.
They both had the same number of days.
B.
1 day
C.
2 days
D.
3 days

If there are 63 butterflies in 3 gardens, how many butterflies are in 2 gardens?

Find the distance between -12 and 25

Solve the following formula for
x

y=2mx+3b

PLEASEEEE HELPPP!!

Which property is illustrated by the equation
3x – 6y = 3(x - 2y)?
1. associative
2.Commutative
3.distributive
4.closure