The shape of an underground pool follows a parabola with the function LaTeX: f\left(x\right)=x^2+8xf ( x ) = x 2 + 8 x. What point represents the bottom of the pool? Group of answer choices

Answers

Answer 1

Answer:

The point that represents the bottom of the pool is [tex](x,y) = (-4, -16)[/tex].

Step-by-step explanation:

Given that the shape of the underground pool is a parabola, that is, a second order polynomial. Then, the point that represents the bottom of the pool is the vertex, which is contained in the standard form of the parabola. That is:

[tex]y-k = C\cdot (x-h)^{2}[/tex] (1)

Where:

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, dimensionless.

[tex]C[/tex] - Constant, dimensionless.

The parabola is represented by [tex]f(x) = x^{2}+8\cdot x[/tex] and we proceed to transform into the desired form:

1) [tex]f(x) = x^{2}+8\cdot x[/tex] Given.

2) [tex]f(x) = (x^{2}+8\cdot x + 16)-16[/tex] Modulative property/Existence of the additive inverse.

3) [tex]f(x) +16 = (x+4)^{2}[/tex] Compatibility with the addition/Modulative property/Existence of the additive inverse/Perfect square trinomial.

4) [tex]y + 16 = (x+4)^{2}[/tex] Notation/Result.

Hence, the point that represents the bottom of the pool is [tex](x,y) = (-4, -16)[/tex].

The Shape Of An Underground Pool Follows A Parabola With The Function LaTeX: F\left(x\right)=x^2+8xf

Related Questions

Need help for this problem

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Answer:

161 degrees

Step-by-step explanation:

corresponding angles theorem

Answer:

161

Step-by-step explanation:

if g and h are parallel, angle 4 and 161 are the same

How should I explain how I got my answer?

Answers

Answer:

What is meant by "Explain your answer?"

   On tests & problem sets students are often asked to explain the reasoning behind their answers. They are often frustrated and/or confused by “explain.” What & why are they supposed to explain? Here is one answer:

   It isn't enough to get the right answer -- you have to be able to explain how you got it. To be sure you get enough practice at explaining yourself, it pays to discuss the questions with your fellow students and/or to write out explanations of your reasoning. You need to both

           (1) Include the right facts, principles, etc., AND

           (2) Explain the logic that you used to solve the problem. How did you get from the facts to the answer?

   It is not sufficient to pile up unselected facts (even if they are correct), OR just to state the facts (even if they are the right ones), without explaining how they relate to the problem at hand, OR to just explain the logical train of thought (even if it is correct), without any specifics.

   That's what you shouldn't do. What should you aim for??

   Try to explain as if you were talking to a fellow student in the class who is generally intelligent, prepared, etc., but can't figure out this particular question.  In other words, explain your reasoning step by step.  Don't just repeat all the related facts in the book or notes--try to pick out the important, relevant points, put them in logical order, and explain (or diagram) how one leads to the next. (In other words, pretend you are writing a simple* answer key.)

*Note: The keys provided after each exam or problem set are usually quite complex and go beyond what we expect from an individual student. The posted keys tend to be so long and involved because they include not only correct answers (& explanations) but also explanations of common student misconceptions.

How to Get the Most out of Explaining

   When you explain things to yourself, or to others, try not to use pronouns. Use nouns instead. This may sound silly, but it really helps you to be sure that you understand what you are saying. If you use pronouns or vague terms you can fool yourself into thinking you understand when you really don't. An example: Suppose you say "The gene is transcribed and it goes to the cytoplasm and is translated, which uses tRNA and mRNA." What do you mean by it and/or which?  Is it the gene or the mRNA? Does which refer to translation or transcription? Sometimes you know, and you are just using shorthand. But sometimes you don't know, and you don't even realize it until you are forced to pick the right terms to replace "it" and "which."  So try to be as specific as possible instead of as vague and as general as possible. Being specific has multiple advantages. It helps you to learn, it helps listeners understand what you are saying, and it helps graders on exams know that you really understand what you are talking about.

What is X? 3x - 24 = 81

Answers

Answer:

35 would be your answer

Step-by-step explanation:

3x-24=81

So first off, add 24 to 24 and 81

You would get 3=105

Now divide 3/3 and 105/3 which will get you 35!

Hopefully this helps!

Answer: 35

Step-by-step explanation:

you add 24 to the other side of the equal sign and you get 105. then you’re left with 3x=105 and you divide 105 by 3 and get 35=x

A ladder is leaning against a building so that the top of the ladder is touching the roof line. The bottom of the ladder is 8 feet from the building and the ladder is 17 feet long. How far is the roof line from the ground? 15 ft 9 ft 18.8 ft 25 ft

Answers

Answer: 15 ft

Step-by-step explanation:

I took the test :)

Answer:

its 15 but can yall do step by step

Step-by-step explanation:

Help fast it’s due soon

Answers

Answer:

slope is 0

Step-by-step explanation:

the line is flat

The slope is 0, it doesn't curve or anything, the line is straight

A jar is filled with pennies, nickels, and dimes. The probability of picking a
penny is 1/4, and the probability of picking a dime is 1/3. What is the
probability of picking a nickel?
1/5
1/3
5/12
7/12

Answers

Answer:

5/12

Step-by-step explanation:

Make 1/4 and 1/3, 3/12 and 4/12, add them up to equal 7/12 then subract 7 from twelve and you have 5. 5/12

Use algebraic strategies to solve sqrt(2x + 3) = x . How many solutions did you find? Which strategies did you use?

Answers

Answer:

itsx= -3

Step-by-step explanation:

Solve. State the Inverse operation you used. 1. k X 4 = 96 | 2. b = 12 = 12 | 3. 9X n = 5.4 | 4. y X 16 = 48 | 6. 3.9 x m= 19.5 | 5. 25 = t4 8. 2+5 = 1 |7. 40 = x= 2 |10. 330 =rX 3 |9. 7.1 x t= 21.3 |11. 1-0.5 = 2 |12. 11 xg= 55
(Theres a total of 12 equations when there's a | its onto the text question)​

Answers

Answer:

hmu on sn*p and I got u kevinscoolrevi7

What are the max/min values of the following equation?
y = 2x3 – 2x² – 18x + 18



Someone please help me out

Answers

What I think is t.....

Which equation is equivalent to 9x=5x-10
•5x = -x +3
•x - 16=18
•3x + 9 = -6
•4x = -10

Answers

9x=5x-10
-5x -5x
4x=-10

write the quadratic equation in standard form going through the points (-1,-5) (0,-4) (2,10)

Answers

Dismal high dash app nah hell shall facho call hi Chuck coco go scanners cop

45 divided by 6x45(9-7)=?

Answers

12





....................

Answer:

337.5

Step-by-step explanation:

What is the factor expression for 45c + 10d

Answers

Answer:

9c + 2d

Step-by-step explanation:

45c + 10d (divide by 5)

9c + 2d

Not 100% if this is how you do factor expression, but if it is then it is right

Hope this helps ya! Keep smiling!

Answer:

9c + 2d

Step-by-step explanation:

ASAP 25 POINTS WILL MARK BRAINLIEST MULTIPLE CHOICE
Determine whether the sequence of mapping rules will lead to the image being congruent to the pre-image (x,y)→(x−2, y)
Question 1 options:

No, the preimage will be smaller

Yes, this is a translation which doesn't change the pre-image size

No, this is a translation which will change the pre-image size

Yes, this is a reflection which doesn't change the pre-image size

Answers

Answer:

Yes, this is a translation which doesn't change the pre-image size

Step-by-step explanation:

Find the measure of the missing angles.

Answers

Answer:

d= 99   e= 81   f= 99

Step-by-step explanation:

Answer:

d = 90

e = 81

f = 99

Step-by-step explanation:

First, find e because you can figure it out by vertical angles. 81 and e are vertical so e is 81. To find f, you subtract 180 by 81 because it's a straight line which is 99. So f is 99. To find d, you can use the right angle next to it. 180-90 is 90. So d is 90.

what is the answer if the wholesale price is $68 and the markup is 85%

Answers

Answer:  57.8

Step-by-step explanation: you can eithere do 68 % 85 or other way which i forgot

HELP ME FAST PLZZ!!!! I REALLY NEED HELP!!! 20 POINTS PLZ HELP

Answers

Answer:

you didnt add the options of what the drop downs were for

Step-by-step explanation:

What is the square root of 75 using imaginary numbers

Answers

Answer:

8.660254038

Step-by-step explanation:

or 5✓3

hope this helps

32. The length of a rectangle measures six more than the width. The perimeter of the rectangle is 38.
What are the dimensions of the rectangle?

Answers

Answer: 12.5

You start with the equations "2x +2y=38" and "6+x=y". By adding and subtracting in the second equation, you get "2x +2y=38" and "x-y=-6". When you multiply the second equation by 2, you get "2x-2y=-12."

subtracting the equations "2x +2y=38" and "2x-2y=-12" gets you to "4y=50", where you have to divide two sides by 4 and get "y=12.5"

how to i find the missing 2 angles

Answers

Answer:

therefore, x is 71 degrees

Step-by-step explanation:

we know that the exterior angle is 142 degrees.

we also know that we have to find x, which is labeled two times as an interior triangle (in the same triangle), so they must be the same degree.

there are different ways to solve this but the easiest way is this:

exterior angle = opposite interior angle 1 + opposite interior angle 2

142 degrees = x + x

142 degrees = 2x

142/2 = x

x = 71

therefore, x is 71 degrees

The area in square feet of a rectangular field is x^2-100x+2400. The width, in feet is x-40. What is the length, in feet?

Answers

Answer:

x-60

Step-by-step explanation:

You have to factor out the quadratic.

You know that one of the factors is x-40.

To factor:

Find a number that when added to -40, gives you -100, and also when multiplied, gives you 2400.

That such number is -60.

Add an x before it, and you get (x-60)

The function h(0) = -16t2 + vt + 10 gives the height of a platform diver above the water, in feet, t seconds after

Answers

Complete Question:

The height of a diver jumping from a diving platform is about [tex]h(t)= 16t^2 +11t+10[/tex], where h is the height of the diver in feet above the water and t is the time measured in seconds, when diving from a platform about 34.3 feet above the water with an upward initial velocity of 11 ft/sec..  After how many seconds is the diver's height above the water 15 feet?

Answer:

0.3125 seconds

Step-by-step explanation:

Given

[tex]h(t)= 16t^2 +11t+10[/tex]

Required

Time when the diver is above 15ft

This implies that h(t) = 15

So, we have:

[tex]15= 16t^2 +11t+10[/tex]

Collect Like Terms

[tex]0= 16t^2 +11t+10 - 15[/tex]

[tex]0= 16t^2 +11t-5[/tex]

[tex]16t^2 +11t-5=0[/tex]

Expand:

[tex]16t^2 + 16t - 5t - 5 = 0[/tex]

Factorize:

[tex]16t(t + 1) - 5(t + 1) = 0[/tex]

[tex](16t - 5)(t + 1)=0[/tex]

Split

[tex]16t - 5 = 0[/tex] or [tex]t + 1 = 0[/tex]

[tex]16t = 5[/tex] or [tex]t + 1 = 0[/tex]

Solve for t

[tex]t = 5/16[/tex] or [tex]t = -1[/tex]

[tex]t = 0.3125[/tex] or [tex]t = -1[/tex]

But time can't be negative. So:

[tex]t = 0.3125[/tex]

Hence, it will take the diver 0.3125 seconds to be at a height above 15 feet

It will take t = 0.3125 seconds is the diver's height above the water 15 feet.

Given ,

The height of a diver jumping from a diving platform is h

 h(t) = [tex]-16t^{2} + vt + 10[/tex]

The diver's height above the water 15 feet

Velocity = v = 11 ft per second

We have to find, t seconds is the diver's height above the water 15 feet.

According to the question,

[tex]h(t) = -16t^{2} +vt+10[/tex]

Where v = 11, h(t) = 15

15 = -16[tex]t^{2}[/tex] + 11t + 10  

15 - 10 = [tex]-16t^{2} + 11t[/tex]

5 = [tex]-16t^{2} +11t[/tex]

[tex]16t^{2} -11t +5= 0[/tex]

[tex]16t^{2} -16t - 5t + 5 = 0[/tex]

16t ( t - 1 ) - 5 ( t + 1 ) = 0

(16t - 5 ) ( t + 1 ) = 0

16t - 5 = 0

16t = 5

t = [tex]\frac{5}{16}[/tex]

t = 0.3125

And t + 1 = 0

t = -1

Time can not be negative so we can't take t = -1 .

So, The required value of time is t = 0.3125

Hence, it will take t= 0.3125 seconds is the diver's height above the water 15 feet.

For the more information about Equation of motion click the link given below.

https://brainly.com/question/13514745

is the relation a function? explain ​

Answers

Answer:

Yes the input x is only used once all the first numbers are different

Step-by-step explanation:

11,7

22,7

15,8

Yes because each input only has one output

Each x has only one y

Evaluate x/y if f x = 14 and y=-2

Answers

Answer:

-7

Step-by-step explanation:

First, we need to substitute x in as 14 since that is what x is equal to.

1.  x / y  =>  14 / y

Next, we need to substitute y in as -2 since that is what y is equal to.

2.  14 / y  =>  14 / -2

Now to solve it;

3.  14 / -2  =>  -7

So now we now that x / y equals -7 when x = 14 and y = -2.

Feel free to give brainliest.

Have an awesome day! Happy Thanksgiving!

Gordon types 2,184 words in 28 minutes. Find the unit rate. Gordon types ________ words per minute.

Answers

Answer:

78

Step-by-step explanation:

[tex]\frac{2184 words}{28 minutes} = \frac{78 words}{1 minute}[/tex]

Answer:

It’s 78 words per minute

Step-by-step explanation:

To solve this problem do 2,184 divided by 28 this will equal 78

Square PINT has vertices N(4, 2) and T(3, 8). What is the area of square PINT?

Answers

Answer: the answer is 37

Step-by-step explanation: someone said it was incorrect but it’s correct trust me my teacher gave us the answer

The area of the square PINT will be 37 square units.

What is an area of a square?

The space occupied by any two-dimensional figure in a plane is called the area. Here we have three shapes a triangle, a rectangle, and a parallelogram.

Given that Square PINT has vertices N(4, 2) and T(3, 8). The area of the square will be calculated by finding the distance between two points N(4, 2) and T(3, 8), and squaring it.

The length of the line segment bridging two points on a plane is known as the distance between the points.

Area = Distance² = ( x₂ - x₁ )² + ( y₂ - y₁ )²

Area = Distance² = ( 4 - 3 )² + ( 8 - 2 )²

Area = Distance² = (1 )² + ( 6 )²

Area = Distance² = (1 )² + ( 6 )² = 37 square units

Therefore, the area of the square PINT will be 37 square units.

To know more about an area follow

https://brainly.com/question/24487155

#SPJ6

List the set or sets to which each number belongs

Answers

Ummmmm.......you didn’t post a pic my guy

she uses 2/3 cup of sugar to make 1/4 sheet cake.how much sugar would she need to make a full sheet cake?​

Answers

Answer:

Answer: B 2 2/3 mark em brainliest plz

Step-by-step explanation:

2/3 + 2/3+2/3+2/3= 2.66 also 2 2/3 2/3 times 4= 2 2/3

Jose is trying to decide how many friends he can invite to his roller skating party. Skate rentals cost $2.50 per person, including Jose, and he knows that 3 adult chaperones plan to skate.

How many friends can Jose invite if he wants to spend only $50.00 total on skate rentals?Jose can invite _______ friends.

Answers

Answer:

Step-by-step explanation:

himself and three chaperones=4

4*2.50= 10.00

50.-10.= 40 left

40/2.50 rental= 16

So he has enough for 16 friends, 3 chaperones and himself.

check:

20 people *2.50= 50.00

What is y?
And please show work!

Answers

Answer: 97 degrees

Step-by-step explanation:

I drew some letters on your attachment to make it easier for you to understand.

To find angle y you need to find angle x first, you do that by doing (180=A+B+C) and you solve for A which is x degrees (A=180-B-C)

When you use angle C you must combine the 26 degrees and 55 degrees because if you use only 55 let's say, that would be the angle for triangle CDB, and we need C for triangle ABC.

So: A=180-42-81 -> A=57 degrees

Now you know Angle A (57 degrees) and Angle ACD (26 degrees)

All you have to do to find Y is to do: y=180-x-26

So y would be: 97 degrees

Keep in mind this is one of two solution methods I can see, if you want me to show you the other one as well just tell me in the comments, you are welcome.

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