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].
Need help for this problem
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?
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
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
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
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
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?
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)
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
Which equation is equivalent to 9x=5x-10
•5x = -x +3
•x - 16=18
•3x + 9 = -6
•4x = -10
write the quadratic equation in standard form going through the points (-1,-5) (0,-4) (2,10)
45 divided by 6x45(9-7)=?
Answer:
337.5
Step-by-step explanation:
What is the factor expression for 45c + 10d
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
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.
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%
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
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
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?
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
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?
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
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
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
Evaluate x/y if f x = 14 and y=-2
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.
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?
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
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List the set or sets to which each number belongs
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?
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.
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!
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.