A city planner designs a park that is a quadrilateral with vertices at J(-3, 1), K(1, 3), L(5,-1), and M(-1,-3). There is an entrance to the park at the midpoint of each side of the park. A straight path connects each entrance to the entrance on the opposite side. Assuming each unit of the coordinate plane represents 10 m, what is the total length of the path to the nearest meter?
Answers
Our first solution is to find the midpoint of each sides. This is done by taking the average of each coordinate. The equation would be:
x,midpoint = (x₁+x₂)/2
y,midpoint = (y₁+y₂)/2
So, applying the equation:
midpoint jk = (-3+1/2, 1+3/2) = (-1,2)
midpoint kl = (1+5/2, 3+⁻1/2) = (3,1)
midpoint ml = (5+⁻1/2, ⁻1+⁻3/2) = (2,-2)
midpoint jm = (⁻3+⁻1/2, 1+⁻3/2) = (-2,-1)
Next, we find the lengths of the paths by using the distance formula:
d = √(x₂ - x₁)² + (y₂ - y₁)²
Distance between jk and ml = √(⁻1-2)² + (2 - ⁻2)² = 5
Distance between jm and kl = √(3-⁻2)² + (1-⁻1)² = √29
Total distance = 5 + √29 = 10.385 units
Since the scale is 1 unit = 10 meters, the actual total length of paths is equal to:
Actual Total Distance = 10.385*10
Actual Total Distance = 103.85 meters
Related Questions
A bag has 6 yellow marbles and 6 brown marbles. Half of the brown marbles are made of glass. A marble is selected at random from the bag. What is the probability that it is a brown, glass marble?
Write your answer as a fraction in simplest form.
Answers
6 brown marbles but half of the brown marbles are made of glass
so brown and made of glass = 3
probability that it is a brown, glass marble = 3/12 = 1/4
answer
1/4
A car company tested a sports car on a road with different inclines. The test driver tested the car by driving a distance of x miles on a flat road, (x2 + 3) miles downhill, and (x − 7) miles uphill. Which simplified expression is equivalent to the total distance, in miles, for which the car was tested?
Answers
kasabihan sa bibliya
Answers
Umaasa ako na makakatulong ito!
Triangle XYZ is reflected across the line y=x and X'= (2, -15). What are the coordinates of X,?
Answers
Answer: (-15,2)
Answer:
the answer to this is A
Step-by-step explanation:
1/2x =20
Pls help
I need answer in like a minute
Answers
multiply both sides by 2/1 to get x=40
if ya meant like [tex]\frac{1}{2x}=20[/tex]
multiply both sides by x and divide both sides by 20 to get [tex]x=\frac{1}{40}[/tex]
depends which one it is
Sales of a new tablet grow by 10% every month. Sales for this month are at 5 thousand. Write an equation to represent this situation and then approximate the sales 6 months from now.
Answers
The equation is:
f ( t ) = 5,000 * ( 1.1 )^t
where t it the time in months.
f ( 6 ) = 5,000 * ( 1.1 )^6 =
= 5,000 * 1.77156 = $8,857.80
Answer: The sale 6 months from now will be $8,857.80.
45.5 meters in 13 seconds
Answers
to get you 3.5
i hope i helped
jenny borrowed $500 for 5 years at 4% interest compounded annually. what is the total amount she will have paid when she pays off the loan?
Answers
[tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
Where P is the starting amount (500$), r is the rate of interest (0.04), n is the number of times the interest is compounded per unit (1 per year), and t is the amount of time it is compounded (5 years).
Now, plug it into the formula:
[tex]A=500(1+ \frac{0.04}{1})^{5}[/tex]
Do the math, and your answer is she must pay 608.32$ when she pays her debts.
Plz help me with this math problem
Answers
Sam bought 86 pounds of flour for his bakery. Every day he used the same amount of flour to make bakery items. After 10 days, Sam was left with 25.2 pounds of flour. On average, how many pounds of flour did Sam use each day?
Answers
86-25.2 = 60.8 pounds of flour used
60.8/10 = 6.08 pounds used per day
Answer:
6.08
Step-by-step explanation:
first, i subtracted 86 from 25.2 to get what he used in the 10 days, which was 60.8, then i would divide it by 10 bc of 10 days to get 6.08. Hope this helps!
A spherical fish bowl is half-filled with water. The center of the bowl is C, and the length of segment AB is 20 inches, as shown below. Use for pi. Which of the following can be used to calculate the volume of water inside the fish bowl?
Answers
AB is the diameter of the sphere.
So the radius is 20in / 2 = 10 in
And the volume of water is half the volume of the sphere.
=> V of water = (1/2)* (4/3) π (r^3)
Also, this problems asks to use 22/7 as approximation of π.
=> V of water = (1/2) (4/3) (22/7) (10in)^3 = 2,095 in^3
Answer: (1/2)(4/3)(22/7)(10in)^3 = 2,095 in^3
At the movie theatre, you pay a different price depending on your age. Children 5 and under get in for free. Children ages 6 to 18 pay $5. Everyone else pays $8. Write a piecewise function for this situation
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{ 0 x ≤ 5
f(x) = { 5 6 ≤ x < 18
{ 8 x ≥ 18
The brackets should be one big bracket.
A certain number is multiplied by 3, and then 5 is added to the result. The final answer is 41. What is the number
Answers
Each pack of hot dogs contains 10 hot dogs (no buns), but each pack of hot dog buns contains 8 buns. Phil buys a number of these packs for a barbecue. After the barbecue, Phil finds that he has 4 hot dogs left over. What is the SECOND smallest number of packs of hot dogs he could have bought?
Answers
we might need to find greatest common denomenator?
or we could just do trial and error
hmm
wait a minute
lets do this
d=number of hot dog packs
b=number of hot dog bbuns
the number of hot dogs is 4 more than the number of buns
10d=4+8b
divide both sides by 2 to make it easier
5d=2+4b
one way is to do trial and error
try values of d and find what values work for b (remember, all whole values)
if d=1, no value works for b
if d=2, b=2
that is the smallest value
keep going up
if d=3, no value works for b
if d=4, no value works for b
if d=5, no value works for b
if d=6, b=7
so 6 packs is the answer
The second smallest number of packs of hot dogs that Phil could have bought is three. This gives him 30 hot dogs, and after eating some, he would be left with 4. The number 30 ends with a 0 and when 4 is subtracted from it, it does result in a number ending in 4 (26 in this case).
Explanation:To solve this problem, we need to understand that Phil must have bought a number of hot dog packs where the total number of hot dogs (10 per pack) ends with a 4. This is because after eating some, he had 4 hot dogs leftover. If he bought 1 pack of hot dogs, he'd have 10. This does not work because it doesn't end with 4. However, if Phil bought 2 packs, this would give him 20 hot dogs, which does end with 0.
We need to continue on this pattern, using multiples of 10, until we find the second smallest number that, when 4 is subtracted from it, leaves a number ending in 4. That number is 30, which gives 30 hot dogs. After eating some, he would be left over with 4 dogs, hence he has eaten 26 dogs (30-4=26). This means, the second smallest number of hot dog packs Phil could have bought is three.
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The next three terms in the pattern 1, 10, 19, 28, 37 are
Answers
To find the next three terms, we need to find the patterns in this sequence. In this case, we see that the first number add 9 to get the second number, the second number add 9 to get the third number, and so on. Now, we can create the formula for this which is n+9 where n is the number before the next number. Here we go:
1
1+9=10
10+9=19
19+9=28
28+9=37
37+9=46
46+9=55
55+9=64. As a result, the next three terms in the pattern 1, 10, 19, 28, 37 are 46,55,64. Hope it help!
Janet's Junk Shop is having its annual sale. Matt wants to buy a mixer that originally sold for $28.62 and is now on sale for off. Matt also has a coupon for an additional 15% off the discounted price.
How much will Matt pay for the mixer?
Answers
[tex]FinalPrice =[/tex]
[tex](Original Price \times(\frac{100\% - Discount}{100\%}))\times(\frac{100\% - Discount_2}{100\%}) =[/tex]
[tex]\big(\$28.62\times(\frac{100\% - 25\%}{100\%})\big) \times(\frac{100\% - 15\%}{100\%}) = [/tex]
[tex]\big(\$28.62\times(\frac{3}{4})\big) \times(\frac{17}{20}) \approx \$18.25[/tex]
Matt will pay [tex]\$18.25[/tex] for the mixer
The scores of several classmates on a language arts test are shown below: 86 points 87 points 87 points 94 points 95 points 82 points 78 points 89 points 80 points 84 points What is the median score for these students?
Answers
86+87/2 = 86.5
Answer:
78,80,82,84,86,87,87,89,94,95
86+87/2 = 86.5
Step-by-step explanation:
Gavin agrees to buy a 6-month package deal of monthly gym passes and in turn receives a 15% discount. Write an algebraic expression to represent the total cost of the monthly passes with the discount, if x represents the cost of each monthly pass.
Answers
15%*y=Z
that is the equations
Why would experimental probability differ from theoretical probability?
Answers
A gift box is a rectangular prism14inches long,5inches wide,and 4inches high.If the box is to be covered in fabric ,how much fabric is needed if there is no overlap?
Answers
when he length=L
width=W
and height=H
SA=2(LW+WH+LH)
so
L=14
W=5
H=4
subsitute
SA=2((14)(5)+(5)(4)+(14)(4))
SA=2(70+20+56)
SA=2(146)
SA=292
you need 292 square inches of fabric
The total fabric needed would be 292 square inches.
To calculate how much fabric is needed to cover the gift box without overlap, we must find the surface area of the rectangular prism representing the box. The formula to find the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l represents the length, w represents the width, and h represents the height.
Given the dimensions of the box are 14 inches (length), 5 inches (width), and 4 inches (height), we calculate the surface area as follows:
2 (14 × 5) = 2 × 70 = 140 square inches (for the top and bottom)2 (14 × 4) = 2 × 56 = 112 square inches (for the front and back)2 (5 × 4) = 2 × 20 = 40 square inches (for the left and right sides)The total surface area is 140 + 112 + 40 = 292 square inches of fabric needed to cover the entire box.
Ryan, Jessica, and Mark each solved this system of equations. All of their answers are different. Find and explain the mistakes. What is the correct answer?
y = 3x + 2
6x – 2y = 10
Ryan’s answer:
I solved by adding the equations. The solution is .
y = 3x + 2 → 3x + y = 2
6x – 2y = 10 → 3x – y = 5
6x = 7
x =
6x – 2y = 10 → 6 – 2y = 10
7 – 2y = 10
–2y = –3
y = -
Jesse’s answer:
I used matrices. The solution is .
Mark’s answer:
I graphed the equations. The lines are parallel and do not intersect, so there is no solution.
Answers
-2y = -6x + 10...reduce by dividing by -2
y = 3x - 5....slope = 3 and y int = -5
y = 3x + 2 ...slope = 3, y int = 2
These lines are parallel. Parallel lines will have the same slope, but different y int's. There is no solution to this because ur lines never intersect.
Mark's answer is correct
6x - 2y = 10
-2y = -6x + 10
reduce by dividing by -2
y = 3x - 5
slope = 3 and y int = -5
y = 3x + 2
slope = 3, y int = 2
These lines are parallel. Parallel lines will have the same slope, but different y integers. There is no solution to this because the lines never intersect.
Mark's answer is correct
3(x+1)-[2(3-2x)-3(3-x)]
Answers
3x+3-2-3x+9
Combine like terms
0x+3-2+9
X=10
Solve the equation ax + 1 = bx for 'x'. Please be sure to include all steps.
Answers
ax + 1 = bx
ax - bx = -1
x(a-b) = -1
x = -1 /(a-b)
1 = bx - ax <-- Subtract ax both each side
1 = x(b - a)
1/(b - a) = x <-- Divide both sides by b - a
So, x is equal to 1/(b - a).
Does the equation represent a direct variation? If so, find the constant of variation. 2x - 4y = 0
Answers
2x-4y=0 subtract 2x from both sides
-4y=-2x divide both sides by -4
y=x/2 or to be clear:
y=(1/2)x
So there is a constant of variation k=1/2 of the form y=kx, so this equation is a direct variation.
*note, it is called a direct variation because as the independent variable increases/decreases, the independent variable increases/decreases by the same factor...
9.Jessa drew a circle with a circumference of 18.84 inches. Which of these dimensions could be the diameter, in inches Jessa used to draw her circle? Use 3.14 for pi.
A 6
B 15.7
C 3
D 9.42
Answers
The circumference can be found just by multiplying the diameter by pi.
So all you need to do is 18.84/3.14 which is 6.
Answer:
A. 6
Step-by-step explanation:
Write the formula c = 2πr. Substitute the value 18.84 feet for c. Solve the equation for c. Since the radius always measures one-half the length of the diameter, multiply the value of c by 2.
Write 0.8 repeating as a fraction
Answers
Answer: 8/9
Step-by-step explanation: I got the answer right
whats the property in equation 3(2x-6)=6x-18
Answers
Distributive property
hope it helps
modal of 9
10
11
14
19
22
27
29
21
18
11
6
Answers
How do you find the LCM???
I know that I asked how to find the LCM of 8 and 9 but I don't know what to multiply by to get it.
Answers
If you don't already know it: is 8 a factor of 9 or do they have equal factors? No.
Is 9 a factor of 8 or do they have equal factors? No.
The easy way: multiply 8 by 9 to get LCM :)
complete the point slope equation of line through (1,-1) and (5,2) use exact numbers
y-(-1)=
Answers
slope = (2 - (-1) / (5 - 1) = 3/4
there will be 2 point slope answers for this..
y - y1 = m(x - x1)
slope(m) = 3/4
(1,-1)...x1 = 1 and y1 = -1
sub
y - (-1) = 3/4(x - 1)
y + 1 = 3/4(x - 1) <=== this is one of them
y - y1 = m(x - x1)
slope(m) = 3/4
(5,2)...x1 = 5 and y1 = 2
sub
y - 2 = 3/4(x - 5) <== here is the other one
The point - slope equation of line passing through points (1, -1) and (5, 2) is (y + 1) = (3/4)(x - 1).
What is the general equation of a Straight line?
The general equation of a straight line is -
y = mx + c[m] → is slope of line.[c] → is the y - intercept.Other possible equations of lines are -
Point - slope form → (y - y₁) = m(x - x₁) Two point - slope form → (y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) Intercept form → x/a + y/b = 1 Normal form → x cos(β) + y sin(β) = LGiven is a line passing through points (1, -1) and (5, 2).
The point slope form of the line is -
(y - y₁) = m(x - x₁)
y - (- 1) = {(2 + 1)/(5 - 1)}(x - 1)
y + 1 = (3/4)(x - 1)
Therefore, the point - slope equation of line passing through points (1, -1) and (5, 2) is -
(y + 1) = (3/4)(x - 1)
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