A hammock that hangs between two trees makes a parabola shape that has the equation y = 0.4(x- 3)² +1, where x is the distance from one end and y is the height above the ground, measured in meters.
A. What is the lowest point of the hammock?
B. If the hammock is attached to both trees at the same height, how far away are the trees from one another?​

Answers

Answer 1

Answer:

A. The lowest point of the hammock is at the point 1 meters above the ground and 3 meters from one end of the hammock

B. The two trees are 6 meters away from one another

Step-by-step explanation:

The given equation of the parabola representing the hammock is as follows;

y = 0.4·(x - 3)² + 1

The general equation of a parabola is a·(x - h)² + k;

Where the coordinates of the vertex point of the parabola, which is the lowest (or highest, furthest) point on the vertex is (h, k) = (3, 1)

Therefore, we have;

A, The coordinates of the lowest point on the hammock is (3, 1)

Therefore, the lowest point of the hammock is at 1 meters above the ground and 3 meters from one end of the hammock

B.  Given that the distance from one end is "x", we have;

The height at which the hammock is attached is given as the point where x = 0 as follows;

Given that the vertex of the parabola represents the axis of symmetry of the parabola, we have that the horizontal distance from one end of the hammock to the vertex point of the parabola that the hammock forms is (3 - 0) meters = 3 meters

Therefore, by the definition of symmetry, the distance from the vertex point to the other end of the parabola that the hammock forms is also 3 meters

From which we have, the distance the two trees are from one another is 3 meters + 3 meters = 6 meters.


Related Questions

Bill owns four cars each car is a different colour each day he drives to work in one of his cars the table shows the probability that bill chooses a car of a particular colour

Car/probability
Red 0.4
Blue 0.17
Yellow 0.05
White ...?
Work out the probability that bill chooses the white car.

Answers

Answer:

1 - 0.4 - 0.17 - 0.05 = 0.38

white = 0.38

Answer:

?yzuzuzuizz72i222

Step-by-step explanation:

nznznnznzjzixi

Frank Catton, the general manager of Billybob's floating raft hotel and Casino in Tunica Mississippi, has installed the "The Wheel of Doughnuts" at the check in desk. When you check in, you spin the wheel and a plate containing that many hot

doughnuts is delivered to your room the next moming for free. If your spinlands on an orange slot you get free hot chocolate too

(Give a fraction or round to 1 decimal place)

A. What is the probability that you get 7 doughnuts and hot chocolate? I

8. What is the probability that you get 7 doughnuts or hot chocolate?

Answers

Answer:

P( 7 doughnuts or hot chocolate)=0.40

Step-by-step explanation:

From the question we are told that

Total number of plates [tex]n=10[/tex]

1)Generally the probability that you get 7 doughnuts and hot chocolate is mathematically given as

7 doughnuts and hot chocolate= 1 slot

Therefore

P( 7 doughnuts and hot chocolate)= 1/10

P( 7 doughnuts and hot chocolate)= 0.10

2)Generally the probability that you get 7 doughnuts or hot chocolate is mathematically given as

P( 7 doughnuts or hot chocolate)=P(7 doughnuts)+P(hot chocolate)-P( 7 doughnuts and hot chocolate)

1 plates contains 7 doughnuts

P(7 doughnuts)=1/10

P(7 doughnuts)=0.10

4 plates contain hot chocolate

P(hot chocolate)=4/10

P(hot chocolate)=0.4

7 doughnuts and hot chocolate= 1 slot

P( 7 doughnuts and hot chocolate)= 1/10

P( 7 doughnuts and hot chocolate)= 0.10

Therefore

P( 7 doughnuts or hot chocolate)=0.10+0.4-0.10

Therefore

P( 7 doughnuts or hot chocolate)=0.40

The probability of getting 7 doughnuts or hot chocolate is 0.4

evaluate the following expressions: if X= -3 then X squared -10x=​

Answers

Answer:

39

Step-by-step explanation:

[tex] {x}^{2} - 10x \\ \\ = {( - 3)}^{2} - 10( - 3) \\ (plug \: x = - 3) \\ \\ = 9 + 30 \\ \\ \therefore({x}^{2} - 10x)_{ \{x = - 3 \}} = 39[/tex]

y=[tex]4x^{2}[/tex]+3x+4
y=5x+4

Answers

Answer:

(0, 4 ) and ( [tex]\frac{1}{2}[/tex], [tex]\frac{13}{2}[/tex] )

Step-by-step explanation:

Given the2 equations

y = 4x² + 3x + 4 → (1)

y = 5x + 4 → (2)

Substitute y = 4x² + 3x + 4 into (2)

4x² + 3x + 4 = 5x + 4 ( subtract 5x + 4 from both sides )

4x² - 2x = 0 ← factor out 2x from each term

2x(2x - 1) = 0

Equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

Substitute these values into (2) for corresponding values of y

x = 0 : y = 5(0) + 4 = 0 + 4 = 4 ⇒ (0, 4 )

x = [tex]\frac{1}{2}[/tex] : y = [tex]\frac{5}{2}[/tex] + 4 = [tex]\frac{13}{2}[/tex] ⇒ ([tex]\frac{1}{2}[/tex], [tex]\frac{13}{2}[/tex] )

the hamster walked x feet. the guinea pig walked 1/4 more than that.

Answers

Answer:

2x+[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

hamster=x

guinea pig = x+ 1/4

x+x=2x

then just add the 1/4

Jason needs to find the volume of the sphere shown below. Which formula should be used ?

Answers

Answer:

dont see sphere

Step-by-step explanation:

need a quick answer please

Answers

Answer:

x= 3

Step-by-step explanation:

12x-12x= 2x 1+5=6

2x=6

x=3

Answer: x=3

Step-by-step explanation:

(10x+1)=(12x-5) (you make them equal because they are vertical)

-2x+1=-5

-2x=-6

x=3

I'm not really sure but I tried, sorry.

Isabelle, Joel, and Bryan sat on their grandmother's porch shelling peas for dinner. There were 2 big bowls of peas, and each person shelled an equal amount. How many bowls of peas did each person shell?

Answers

Answer:

2/3 bowls of peas

Step-by-step explanation:

Given that there were 2 big bowls of peas, and each person shelled an equal amount. Since there are three persons, the ratio of the number of bowls of peas available to the number of persons will give the number of  bowls of peas did each person shell.

Hence each person must have shell

= 2/3 bowls of peas


Name two examples of quadrilaterals,

Answers

Answer:

square and rectangle

Step-by-step explanation:

Answer:

Squares, Trapezoids, Rhombuses, Kites, Parellelograms, or Rectangles

Step-by-step explanation:

"Quad" means that there is 4 sides on something, and all of these shapes have 4 sides, so obviously, that means they are quadrilaterals.

I need help what is 15 times 238

Answers

Answer:

hello.....................

Step-by-step explanation:

Answer:

3,570

Step-by-step explanation:

why did you not look it up on the internet lol

Juan and Ari went to the farmers market to buy fruit. Juan's bag of apples that he bought weighed StartFraction 31 over 7 EndFraction pounds. Ari's bag of oranges that he bought weighed StartFraction 19 over 3 EndFraction pounds. Using compatible fractions, estimate how much heavier Ari's bag is compared to Juan's bag. 1 and one-half pounds 2 pounds 6 pounds 10 and one-half pounds

Answers

Juan and Ari went to the farmers market to buy fruit. Juan’s bag of apples that he bought weighed 31/7 pounds. Ari’s bag of oranges that she bought weighed 19/3 pounds. Using compatible fractions, estimate how much heavier Ari's bag is compared to Juan's bag.

A) 1 and one-half pounds

B) 2 pounds

C) 6 pounds

D) 10 and one-half pounds

Answer:

B: approximately 2 pounds

Step-by-step explanation:

Juan’s bag weighed 31/7 pounds

Ari's bag weighed 19/3 pounds.

We are told to use compatible fractions to determine the difference. Thus we have to make sure the denominator is the same;

For Juan, let's multiply both numerator and denominator by 3 to get; 93/21 pounds

For Ari, let's multiply both numerator and denominator by 7 to get; 133/21

Thus, difference is;

(133/21) - (93/21) = 40/21

This gives;

1.9 pounds heavier

This is approximately 2 pounds

Answer:

B. 2 pounds

Step-by-step explanation:

24 yd = ___ ft
SHOW WORK PLEASE I WANNA KNOW HOW TO DO IT ILL BE SO HAPPY BC IM KINDA CONFUSED

Answers

Answer:

72

Step-by-step explanation:

1 Yard is 3 Feet

Since we know this we Multiply 3 by 24.

Hope this helps   ▼・ᴥ・▼

Answer:

72ft

Step-by-step explanation:

1 yd = 3ft

so you would do 24 times 3 to get 72

Magic The Gathering (MTG) booster packs cost 4 for $12. At this rate, how much will 9 booster packs cost?

Answers

Answer

$27

Step-by-step explanation:

12/4=3

3x9=27

$12/4 = $3 for 1
$3 * 9 = $27
The answer is $27

Is -8 = 8

A. One solution
B. Two solutions
C. Infinitely many solutions
D. No solution

Answers

No solution

The answer is D

The histogram shows how many pairs of sneakers are on sale at the local shoe store. How
many pairs of sneakers smaller than size 8 are on sale?
Sneaker Sale
Number of Palrs
20
18
16
14
12
10
8
6
4
2
0
2-4
5-7
8-10
11-13
Sneaker Size
14
22
37
49

Answers

Answer: 22

Step-by-step explanation:

9-2x ≤-5


show work please i need this for hw thankss

Answers

answer is x={7,8,9...}

note= (-5 when u take to other side it will become positive)

Please help me ASAP!! Thank you!

Answers

Answer:

The third one

Step-by-step explanation:

June needs at least $575 to go on a vacation. She earns $10 an hour for babysitting and already has $252 saved for the trip. Which inequality can be used to find the number of hours she needs to babysit

Answers

Answer:

[tex]252 + 10h \ge 575[/tex]

Step-by-step explanation:

Given

[tex]Savings = 252[/tex]

[tex]Target=575[/tex] -- atleast

[tex]Earnings = \$10[/tex] per hour

Required

Represent as an inequality

Suppose that she babysits for h hours, her total earnings would be:

[tex]Total\ Earnings = 10h[/tex]

In inequalities:

At least means [tex]\ge[/tex]

So, when the total earnings is added to her savings, we have:

[tex]Savings + Total\ Earnings \ge Target[/tex]

Substitute values for Savings, Total Earnings and Target

[tex]252 + 10h \ge 575[/tex]

A number cube has sides numbered 1 through 6 the probability of rolla 2 is 1/6 what is the probability of not rolling a 2

Answers

Answer:

5/6

Step-by-step explanation:

It would be 5/6 because there are 5 possible answers other than 3 making it 5/6

The slope, m, of a linear equation can be found using the formula m = StartFraction y 2 minus y a Over x 2 minus x 1 EndFraction., where the x- and y-values come from two ordered pairs, and (x1, y1) and (x2, y2).

Answers

Answer:

Please check the explanation.

Step-by-step explanation:

Given the points

(x₁, y₁)(x₂, y₂)

Using the formula  to determine the slope between (x₁, y₁) and (x₂, y₂) of the linear function

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

For example, let the points be

(x₁, y₁) = (1, 2)

(x₂, y₂) = (3, 4)

Determining the slope between

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [4 - 2] / [3 - 1]

               = 2 / 2

               = 1

Thus,

The slope of the line between the points (1, 2)  and (3, 4)  will be: m = 1

please simplify -8(-3a-2)

Answers

Answer: 24a+16

Step-by-step explanation:

Answer:

=24a+16

Step-by-step explanation:

Let's first take our problem-

−8(−3a−2)

Simplify -

=(−8)(−3a+−2)

=(−8)(−3a)+(−8)(−2)

And you get your answer-

=24a+16

Five friends went to a movie. Each friend bought a ticket and a
medium-sized bag of popcorn. The total amount they spent
was $61.25. What was the price of each movie ticket?
(Medium price is $3.75

Answers

$61.25 - $3.75 i think

A stray dog ate 12 of your muffins. That was of all of them. With how many muffins did
you start? Write an equation and solve the problem.

plz help

Answers

Answer:

A stray dog ate 12 of your muffins. That was of all of them. With how many muffins did

you start? Write an equation and solve the problem.

plz help

Step-by-step explanation:

um if he ate ALL of them wouldn't it be 12?

2 1/2 divided by 2 1/3

Answers

Answer:

Exact Form: 15/2

Decimal Form: 7.5

Mixed Number Form: 7 1/2

Step-by-step explanation:

Answer:

1[tex]\frac{1}{14}[/tex]

Step-by-step explanation:

Turn the mixed fractions into improper fractions:

2 1/2 = 5/2

2 1/3 = 7/3

5/2 ÷ 7/3

Replace the division sign with a multiplication sign by reciprocating 7/3.

5/2 × 3/7

Multiply the numerators and the denominators.

= 15/14

Simplify 15/14 by turning it into a mixed fraction.

1[tex]\frac{1}{14}[/tex]

I hope this helps!

Helena makes 500$ per week, and she puts 15% of her paycheck in savings. How much money does she put in savings

Answers

Answer:

75$

Step-by-step explanation:

[tex]500(0.15) = 75[/tex]

75 is your answer!!!!!!!!!!!!!!!!!!!!

please help!:) Using the function g( x) = -4 x – 17, calculate g(-2)

Answers

Step-by-step explanation:

you'll substitute x for -2

g(-2) = -4 *(-2) - 17 = 8 - 17 = -9

hope i helped :)

Including Jose, there are eight people in his family. If order matters, how many ways can he arrange his family members into a row of five seats if Jose must sit in the first seat?

Answers

Answer:

840 ways

Step-by-step explanation:

From the above question, we are told that order matters, hence, to solve the above question, we use the Permutation formula.

P(n, r) = nPr = n!/(n -r)!

From the above question,

Since Jose is included in the 8 people and he takes the first seat

n = 8 - 1 = 7 people

r = 5 - 1 = 4 seats

This is because, once Jose takes the first seat, there are 4 seats left with 7 people waiting to be seated

Hence,

7P4 = 7!/(7 - 4)!

7P4 = 7!/3!

7P4 = 5040/6

7P4 = 840 ways

Answer:

840

Step-by-step explanation:

edg 2021

HELP IM IN A QUZZ...

Answers

What is it? Is there a picture

2(z-3)
[tex]2(z - 3) \geqslant 5[/tex]

Answers

Answer:

2z-6

Step-by-step explanation:

2(z-3)

2(z)-2(3)=2z-6

hii please help i’ll give brainliest if you give a correct answer

Answers

Answer:

i think it'll be the first one and the last one

Step-by-step explanation:

1 & 3 hope that helped haha
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