The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 12 feet, represented by a vertex of (8,12)​ , and lands 16 feet from the water jet, represented by (16,0)​ . Write a function in vertex form that models the path of the stream

Answers

Answer 1

Answer:

y=-3/16(x-8)^2+12

Step-by-step explanation:

Refer to the vertex form equation for a parabola:

y=a(x-h)^2+k where (h,k) is the vertex.

Therefore, we have y=a(x-8)^2+12 as our equation so far. If we plug in (16,0) we can find a:

0=a(16-8)^2+12

0=64a+12

-12=64a

-12/64=a

-3/16=a

Therefore, your final equation is y=-3/16(x-8)^2+12

Answer 2

Answer:

y = (-5.33)(x - 8)^2 + 12

Step-by-step explanation:

The graph is a parabola which opens down and has its vertex at (8, 12).  We can immediately write y = a(x - 8)^2 + 12, knowing that if x = 8, y = 12.  To find the coefficient '1', substitute 16 for x and 0 for y:

0 = a(16 - 8)^2 + 12, or

-64a = 12, or a = -64/12 = 5.33

Then the desired function is:

y = (-5.33)(x - 8)^2 + 12


Related Questions

Translate 2 units up and 7 units right.

Answers

Answer:

R: 5,3

P: 2, -1

Q: 4, -1

Step-by-step explanation:

Hope this helped

Answer:

See pictures.

Step-by-step explanation:

Move the triangle 2 up, then 7 to the right.


Express 330 as a product of prime
factors

Answers

Answer:

All Factors of 330: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165 and 330 Prime Factors of 330: 2, 3, 5, 11

Please mark as brainliest if answer is right

Have a great day, be safe and healthy  

Thank u  

XD

Describe the sequence of transformations that maps the congruent figures.

Answers

Answer: The types of transformations that preserve congruency includes: Rotation (Turn) Turns a figure around a fixed point. Reflection (Flip) Flip of figure over a line where a mirror image is created. Translation (Slide or glide) Sliding a shape to a new place without changing the figure.

The sequence of transformations that maps the congruent figures are

Rotation, Reflection and Translation.

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

The types of transformations that preserve congruency includes: Rotation Turns a figure around a fixed point.

Since Reflection Flip of figure over a line where a mirror image is created.

And Translation Sliding a shape to a new place without changing the figure.

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Subtract 6 2/5 - 1 1/4. Simplify the answer and write as a mixed number.

Answers

Answer:5 3/20

Step-by-step explanation:

6 8/20 0- 1 5/20= 5 3/20

Help me with these questions (picture) Plsss I will reward brainliest and points

Answers

Answer:

1/4 2/3 and 1/12 sfgjikjhskskshrmsl

Answer:

1) Fill in the Blanks

The First Blank is 1/2 because 1/2 + 1/2 = 1

The Second Blank is 3/4 because 3/4 + 1/4 = 1

The Third Blank is 1/3 because 1/3 + 2/3 = 1

2) Find the LCD

The Least Common Denominator (also known as LCD) is 60

To find this, find the number that each of the denominators can multiply to and have the same one together.

3) Find the length of the final scarf

A full scarf has a length of 150cm

We must use the fragment that is 1/2 this size

150 ÷ 2 = 75

We must use the second fragment which is 3/4 150cm

Divide the scarf into 4 pieces

150 ÷ 4 = 37.5

We need 3 1/4 fragments to = 3/4

37.5 x 3 = 112.5

The final fragment is 1/3 the length of the full scarf

We must divide the scarf into 3 sections

150 ÷ 3 = 50

The three lengths we just found were 75cm, 112.5cm, and 50cm

Add all of the lengths up to find the final length of the last scarf

75 + 112.5 + 50 = 237.5cm

The Final scarf length is 237.5cm

GIVING BRAINLIEST!!!!!

The first sequence rule is multiply by 2 starting from 7. The second sequence rule is add 2 starting from 8. What is the first number that appears in both sequences?

10
14
18
28

Answers

14

7x2=14
8+2=10+2=12+2=14

Answer:

so what is the best country prospered for a reason you can't be able and also how many school system failed to get away from me to go back and forth and the other psychologist who is right to be able and to understand what a conversation has to do it again and also be a American is a great honor for a woman and the woman who are kind and also to the original artist of a president is the one that is a woman of a person and also an acid free woman who has a motherfu cking personality in her court that you can be hard pressed to be with a glock and you don't want it to get her out on a computer and also

Need help!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Take a look at the picture below

Have a good day :)

247 is the correct answee

Fifty shares of Mega Stock cost $212.50. How many shares can you buy with $850?

Answers

Answer:

25

Step-by-step explanation:

what is the slope and y intercept of y=8x+1

Answers

Answer:

the slope is 8 and the y-int is 1

Step-by-step explanation:

Slope Intercept Form---> y=mx+b

m= slope

b= y-int

Answer:

y=1 hope this help

Step-by-step explanation:

David can run at a consistent rate of 8.2 miles per hour. If he has 3 and a half hours to
run, how far will he run if he runs at that rate?

Answers

Answer:

David can run 28.7 miles in 3.5 hours.

Step-by-step explanation:

8.2mph × 3.5hours = 28.7miles

good luck, i hope this helps :)

What value of x makes the 2 triangles congruent by SAS? Find the length of FE

Answers

Answer:

x = 4

FE = 8

Step-by-step explanation:

Congruent means equal. Notice how both F and C equal 30 degrees while line AC and line DF are both equal to 9 inches. This means we can equal line CB to line FE to find the value of x:

2x = x + 4

Isolate variable x by subtracting both sides by x:

2x - x = x - x + 4

x = 4

Check your work:

2(4) = 4 + 4

8 = 8

Correct

b. 48
C. 36
5. (x+4), (x+12), (x-1) and (x+5) are in proportion. Find the value of x.
b. 12
a. 15
c. 16
d., 20

Answers

Answer:

c

Step-by-step explanation:

Expressing the proportion in fractional form , that is

[tex]\frac{x+4}{x+12}[/tex] = [tex]\frac{x-1}{x+5}[/tex] ( cross- multiply )

(x + 4)(x + 5) = (x + 12)(x - 1) ← expand both sides using FOIL

x² + 9x + 20 = x² + 11x - 12 ← subtract x² + 9x from both sides

20 = 2x - 12 ( add 12 to both sides )

32 = 2x ( divide both sides by 2 )

16 = x → c

When your doing online and your bestie tells you to not text them because they don't want to get in trouble but then they be texting their online friends all the time and also posting stuff on Twitter.......

Answers

Answer:

Oh..Im so sorry that happened, Thats what you call fake friends

Step-by-step explanation:

Solve and graph.
P-3>-8

Answers

Answer:

thw answer is in the photo!

Step-by-step explanation:

hoped I helped!

The value of the inequality is P > -5.

Therefore the correct option is c.

Given is an inequality P - 3 > -8, we need to solve and graph it,

To solve the inequality P - 3 > -8, you can isolate the variable P by adding 3 to both sides of the inequality:

P - 3 + 3 > -8 + 3

Simplifying further:

P > -5

The solution to the inequality is P > -5, which means that P can take any value greater than -5.

To graph this solution on a number line, you can represent all values greater than -5 with an open circle on -5, and shade the region to the right of -5 to indicate the values that satisfy the inequality. Since the inequality does not include -5 itself (due to the strict inequality P > -5), the circle representing -5 should be left open.

Here's a visual representation of the graph (attached)

The shaded portion on the number line represents the values of P that satisfy the inequality P > -5.

Hence the value of the inequality is P > -5.

Learn more about inequality click;

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Orlando's sports-card collection features players from four teams, as shown in the table below

Answers

Answer:D

Step-by-step explanation:

Sorry Ik it’s to late lol

1. JACKSON WALKS 6 BLOCKS IN 4 MINUTES. HOW FAST IS
HE WALKING?

Answers

Answer:

Jackson is walking an average of 1.5 blocks per minute.

Step-by-step explanation:

6 divided by 4 is 1.5

The speed at Jackson for walking 6 blocks in 4 minutes will be equal to 1.5 blocks per minute.

What is an arithmetic operation?

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the instructions provided in the question,

The distance (d) traveled by Jackson = 6 blocks

The time (t) taken to travel 6 blocks by Jackson = 4 minutes

[tex]Speed(s)=\frac{Distance(d)}{Time(t)}[/tex]

Put values in the above equation,

s = 6/4

s = 1.5 blocks per minute.

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Need help with 20y + 60 = 100

Answers

Answer:

2

Step-by-step explanation:

puting right terms together to find value of y

Answer:y = 2

Step-by-step explanation:

IF we are solving for y...

20y + 60 = 100

Subtract 60 from both sides to get y by itself...

20y = 40

divide by 20 to get y...

y = 2

14788962389598
where is the 5

Answers

Answer:

The third number from the end :3

Step-by-step explanation:

Hope this helps ^^

3.
In which situation below would you want to use the Explicit Formula instead of the Recursive Formula
a.Find the 4th term when the first term is 7 and the common difference is -2.
b.Find the 7th term when the first term is -1 and the common difference is 10.
c.Find the 7th term when the first term is -1 and the common difference is 10.
d.Find the 11th term when the first term is -3 and the common difference is 4.

Answers

Answer:

b

Step-by-step explanation:

An explicit formula for a sequence allows you to find the value of any term in the sequence. ... A recursive formula for a sequence allows you to find the value of the nth term in the sequence if you know the value of the (n-1)th term in the sequence.

The explicit formula will be best used in finding the 7th term when the first term is -1 and the common difference is 10, the correct option is B.

What is a Recursive formula?

A recursive formula is used to determine the nth term when (n-1) th term is given in the series.

The Explicit formula is when any term of the sequence has to be determined on the basis of the first term and the common difference.

The recursive formula just requires one operation, while the explicit formula requires multiple operations,

The recursive formula is limited to determining the consecutive terms while the explicit formula can be used to determine any term of the sequence.

The explicit formula will be best used in finding the 7th term when the first term is -1 and the common difference is 10.

To know more about Recursive Formula

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Can 12:18 be simplified

Answers

Answer:

Yes, 12:18 is simplified to 2:3

Step-by-step explanation:

Answer:2/3 is the simplest form of 12/18.

Step-by-step explanation:

yes, 12/18 can simplified

PLS HELP NO ONE IS HELPING ME!!! D: i need a answer and to explain in 10 mins!! my teacher is gonna YELL AT ME AHHHHHHHHHHHHHHHHHHHHHHHHHHHH

Answers

Answer:

for question 1:  raynie can ride her skateboard 2 miles in 10 minutes how many miles can she ride her skate board in 1.5 hours (answer) - 18 miles.

question 2: Andrew's sandwich consists of 20 gram piece of cheese a 60 gram piece turkey and two 30 gram slices of bread. (answer) - 30%

plz help solve due tonight

Answers

Answer is 39.55 I’m pretty sure

Please answer thanks you (:

Answers

Answer:

B

Step-by-step explanation:

I believe it is B because it is the only one that doesnt have x values that repeat and give different answers.

Ex. For a, the x value in the first and third coords gives both 1 and 3 as answers.

Every x has to have a unique y value, so

(2,10) (3,12) is ok, but (2,10) (2,12) is not.

Sorry if this doesnt make sense haha

solve this question.

Answers

Answer:

The answer is 9. Hope it helps :)

Step-by-step explanation:

12+4÷2^3-7×0.5

= 12+4÷8-7×0.5

= 12+0.5-7×0.5

= 12+0.5-3.5

= 12.5-3.5

= 9

The function ggg models the number of mosquitoes (in millions of mosquitoes) in a certain area as a function of rainfall (in centimeters) in that area. Which of these statements are true? Choose all answers that apply: Choose all answers that apply: (Choice A) A More rainfall relates to more mosquitoes as long as rainfall is less than 2\text{ cm}2 cm2, start text, space, c, m, end text. (Choice B) B More rainfall relates to more mosquitoes as long as rainfall is more than 2\text{ cm}2 cm2, start text, space, c, m, end text. (Choice C) C When there is no rainfall, there are about 111 million mosquitoes. (Choice D) D When there is no rainfall, there are about 222 million mosquitoes.

Answers

Answer:

(Choice A) A More rainfall relates to more mosquitoes, as long as rainfall is less than 2 cm²

Step-by-step explanation:

The given function for the number of mosquitoes, (by analysis of the options) is, g(x) = 4·x - x²

Where;

x = The amount of rainfall

g(x) = The number of mosquitoes in millions

The given function can be expressed as follows;

g(x) = 4·x - x² + 0

The maximum point is given by g'(x) = d(4·x - x²)/dx = 4 - 2·x = 0

At the maximum (turning point), we have;

4 - 2·x = 0

4 = 2·x

x = 4/2 = 2

The level of rainfall that gives the maximum number of mosquitoes is, x = 2 cm²

The number of mosquitoes increases from zero rainfall up to the maximum number of 4 million mosquitoes at 2 cm² rainfall and then decreases to zero as the rainfall increases further more than 2 cm², as shown in the attached  graph of the function g(x) that models the number of mosquitoes created with MS Excel

Therefore, the true statement is (Choice A) more rainfall relates to more mosquitoes, as long as (the level of) rainfall is less than (the maximum) 2 cm².

In the figure, AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. Prove that △AEB ≅ △DEC by matching each mathematical statement with its reason.

*(select) = A, B, C, D, E, F, G, H, I, J

A. XY is perpendicular to AB.
B. XY ⊥ CD
C. m∠AXE = 90°, m∠DYE = 90°.
D. ∠AXE ≅ ∠DYE.
E. XE ≅ YE
F. ∠A ≅ ∠D
G. △AEX ≅ △DEY
H. AE ≅ DE
I. ∠AEB ≅ ∠DEC
J. △AEB ≅ △DEC

Statements:
(select) Definition of a perpendicular bisector
(select) ASA Triangle Congruence
(select) Definition of a midpoint
(select) In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
(select) Vertical Angles Theorem
(select) Definition of perpendicular lines
(select) Right angles are congruent.
(select) AAS Triangle Congruence
(select) Alternate Interior Angles Theorem
(select) Corresponding parts of congruent triangles are congruent.

Answers

Answer:

From top to bottom:

A, J, E, B, I, C, D, G, F, H

See below for more clarification.

Step-by-step explanation:

We are given that AB is parallel to CD, XY is the perpendicular bisector of AB, and E is the midpoint of XY. And we want to prove that ΔAEB ≅ ΔDEC.

Statements:

1) XY is perpendicular to AB.

Definition of perpendicular bisector.

2) XY ⊥ CD.

In a plane, if a transveral is perpendicular to one of the two parallel lines, then it is perpendicular to the other.

3) m∠AXE = 90°, m∠DYE = 90°.

Definition of perpendicular lines.

4) ∠AXE ≅ ∠DYE.

Right angles are congruent.

5) XE ≅ YE

Definition of a midpoint.

6) ∠A ≅ ∠D.

Alternate Interior Angles Theorem

7) ΔAEX ≅ ΔDEY

AAS Triangle Congruence*

(*∠A ≅ ∠D, ∠AXE ≅ ∠DYE, and XE ≅ YE)

8) AE ≅ DE

Corresponding parts of congruent triangles are congruent (CPCTC).

9) ∠AEB ≅ ∠DEC

Vertical Angles Theorem

10) ΔAEB ≅ ΔDEC

ASA Triangle Congruence**

(**∠A ≅ ∠D, AE ≅ DE, and ∠AEB ≅ ∠DEC)

One of the legs of a right triangle measures 9 cm and its hypotenuse measures 13 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answers

Answer:

9.4

Step-by-step explanation:

Hopefully this explains it well enough, I can go deeper if needed :)

Cal has a collection of 186 toy farm animals which she no longer 2,5 She code
stee them between her 3 young cousins. How many toys do they receive each?

Answers

Answer:

62 (I guess, if I understand your text correctly)

Step-by-step explanation:

you mean she did not need her toy farm animals anymore and gives all of them evenly to her 3 younger cousins ?

then it is a very simple division : 186 / 3 = 62

do you not know how to divide ?

186 / 3

you take the number on the right and compare it to the first (most left) digit position on the left side and see, if the right side can divide this left position.

so, in our case, 1 / 3. Is that possible ? no. so, the result is 0, and we keep the leftover from the left side (still this "1").

now we attach the next digit (going from left to right) from the left side : 18

and we compare again - can we divide now this left side by the right side ? in our example 18 / 3. is that possible ? yes ! the result is 6. we attach this result to our previous result (0) and get 06 (or simply 6). and now there is nothing left in our intermediate division (18/3 creates no remainder, it is just straight 6).

so, our leftover on the left side is 0, and we attach the next digit (again, going from left to right) on the left side to the leftover : 06 (or simply 6).

and we compare again - can we divide now this left side by the right side ? in our example 6 / 3. is that possible ? yes ! the result is 2. we attach this result to our previous result (06) and get 062 (or simply 62). and now there is nothing left in our intermediate division (6/3 creates no remainder, it is just straight 2).

so, our leftover on the left side is 0, and we attach the next digit (again, going from left to right) on the left side to the leftover : oh, there are no more digits. we are finished !

and we have calculated just by hand or mind without any calculator that 186/3 = 62

: A box contains 512 grams of cereal. One serving of cereal is 56 grams. How many servings of cereal does the box contain? A. 9 1/4 B. 9 1/8 C. 9 8/56 D. 9 8/512

Answers

Answer:

C. 9 8/56

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Box contain = 512 grams

One serving = 56 gram

So, we can calculate the number of serving by using following formula,

Number of serving = Box contain ÷ One serving

By putting the value, we get

Number of serving = 512 ÷ 56

= 9.14 or 9 8/56

The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
405, 397, 389,...
Find the 31st term.

Answers

Answer:

165

Step-by-step explanation:

tn = t1 + (n - 1)(d)

t31 = 405 + (31 - 1)(-8)

t31 = 405 + (30)(-8)

= 405 - 240

= 165

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Qu es el Crculo Unitario which one ? A? B? C? D? The Harlem Renaissance ended mostly because of...a. The KKKb. The Red Summerc. The Great Depressiond. World War 2 Select the correct answer. Why did Martin Luther criticize the Roman Catholic Church? A. It was in favor of sola scriptura. B. It was encouraging science. C. It was using indulgences for financial benefits. D. It condemned corruption. what is the correct mean of explicits PLEASE ANSWER ASAP WILL MARK BRAINLIEST!!!Which of the following characters is repeatedly described as "fastidious"?a.) Mr. Keetchb.) Zachariahc.) Captain Jaggeryd.) Charlotte Doyle Copybold Corporation is a start-up company that has a capital structure with a debt/assets ratio equal to 0.75. Copybold has no preferred stock. There are two possible scenarios with respect to the firm's operations : Feast or Famine. The Feast scenario has a 60 percent probability of occurring, and the forecast earnings before interest and taxes (EBIT) in this scenario is $60,000. The Famine scenario has a 40 percent chance of occurring, and the EBIT is expected to be $20,000. Further, the firm's cost of debt is 12 percent. The firm has $400,000 in total assets, and its marginal tax rate is 40 percent. The company has 10,000 shares of stock outstanding. What is the difference between the earnings per share (EPS) forecasts for the Feast scenario and the Famine scenario Help asap!!will give brainliest for best answer!! pls help PLS PLS PLS PLS 20 POINTS The graphs below have the same shape. What is the equation of the bluegraph? Help plz..And No links!! I repeat No links!! Help me and show work plz Find the area of the regular 15-gon with a 7 mm radius The density of table sugar is 1.59g/cm3 what is the volume of 7.85g of sugar? according to atticus what is optimistic about toms case Government must support the common good by establishing electric utility monopolies and regulating all trade agreements that allow goods to enter the country.Who would have disagreed with this comment and why? (1 point)Group of answer choicesKarl Marx would have disagreed with this statement. He believed government should not regulate the economy, but should control trade.John Keynes would have disagreed with this statement. He did not believe government should pass laws to regulate the economy or control trade.Adam Smith would have disagreed with this statement. He believed government should not regulate the economy or control trade.Karl Marx would have disagreed with this statement. He believed government should pass laws to regulate the economy but not trade. IY mH sa ImA student writes the sentence shown and reads it to the teacher as follows."I was at my house and saw a little mouse."The student's written sentence indicates that the student does not understand which of the followingconcepts?+ Most words contain several letter-sound combinations.Printed material is made up of letters.Letters have both uppercase and lowercase forms.Letters represent sounds. I NEED HELP ON THESE!! PLEASE1.) The decline in data entry, typing, and assembly jobs is best explained by:A.) a decrease in the national minimum wage.B.) the widespread availability of improved technology that can perform many of the same functions.C.) a lack of apprenticeship programs in the U.S.D.) None of these choices are correct. 2.) Bills are proposed by:A.) the President of the United States.B.) Congress.C.) the EPA.D.) None of these choices are correct. which example is NOT an example of a form of nonviolent protests What is constitutional, statutory, case, and common law?