Which is the equation of a parabola with Vertex (0, 0) and directrix y = 4?
Answers
Vertex (0, 0) and directrix y = 4
is a vertical parabola------> open down (directrix above the vertex)
the equation is of the form
(y-k)=4p(x-h)²--------> y=4p*x²-------> vertex (0,0)
y=4
y=h-p-----> y=-p
p=-4
the equation of the parabola is
y=-16x²
the answer is
y=-16x²
see the attached figure
Answer:
D. x^2 = -16y
Step-by-step explanation:
got it right on edge
Related Questions
G technical mathematics with calculus volume 10 find the derivative of the function y = sqrt(x^2+1) using limits definition
Answers
[tex]\displaystyle\frac{\mathrm dy}{\mathrm dx}=\lim_{h\to0}\frac{y(x+h)-y(x)}h[/tex]
[tex]\displaystyle\frac{\mathrm dy}{\mathrm dx}=\lim_{h\to0}\frac{\sqrt{(x+h)^2+1}-\sqrt{x^2+1}}h=\lim_{h\to0}\frac{\sqrt{x^2+2xh+h^2+1}-\sqrt{x^2+1}}h[/tex]
Multiply the numerator and denominator by the conjugate of the numerator:
[tex]\dfrac{\sqrt{x^2+2xh+h^2+1}-\sqrt{x^2+1}}h\cdot\dfrac{\sqrt{x^2+2xh+h^2+1}+\sqrt{x^2+1}}{\sqrt{x^2+2xh+h^2+1}+\sqrt{x^2+1}}=\dfrac{(x^2+2xh+h^2+1)-(x^2+1)}{h\left(\sqrt{x^2+2xh+h^2+1}+\sqrt{x^2+1}\right)}[/tex]
Now
[tex]\displaystyle\frac{\mathrm dy}{\mathrm dx}=\lim_{h\to0}\frac{(x^2+2xh+h^2+1)-(x^2+1)}{h\left(\sqrt{x^2+2xh+h^2+1}+\sqrt{x^2+1}\right)}[/tex]
[tex]=\displaystyle\lim_{h\to0}\frac{2xh+h^2}{h\left(\sqrt{x^2+2xh+h^2+1}+\sqrt{x^2+1}\right)}[/tex]
[tex]=\displaystyle\lim_{h\to0}\frac{2x+h}{\sqrt{x^2+2xh+h^2+1}+\sqrt{x^2+1}}[/tex]
As [tex]h\to0[/tex], in the numerator we have [tex]2x+h\to2x[/tex]; in the denominator we have [tex]\sqrt{x^2+2xh+h^2+1}\to\sqrt{x^2+1}[/tex]. So the limit is
[tex]\dfrac{2x}{2\sqrt{x^2+1}}=\dfrac x{\sqrt{x^2+1}}[/tex]
the largest doll is 12 inches tall. The height of each of the other dolls is 7/10 the height of the next larger doll. Write an expression for the height of the smallest doll. What is the height of the smallest doll?
Answers
Final answer:
The height of the smallest doll in a sequence is 4.116 inches found using the formula based on geometric progression, with each smaller doll having a height of 7/10 the height of the next larger one, starting from the largest at 12 inches.
Explanation:
To find the height of the smallest doll, we use a geometric sequence formula height of smallest doll = height of largest doll × (7/10)^n, with 'n' being the number of dolls smaller than the largest one.
To solve for a specific number of dolls, we'd need the value of 'n'. However, without knowing the total number of dolls in the sequence, we use the given formula to understand the pattern of the dolls' heights.
For illustrative purposes, if there were 3 dolls smaller than the largest, the height of the smallest doll would be 12 × (7/10)^3 = 12 × 0.343 = 4.116 inches. The exact height for the smallest doll would vary based on the total number of dolls in the set.
3 times as much as the sum of 3/4 and 2/6
Answers
The result of 3 times as much as the sum of 3/4 and 2/6 is; 13/4
Fraction and ArithmeticsFirst, we must evaluate the sum of 3/4 and 2/6; we have;
3/4 + 2/6Using the lowest common multiple; 12
We have; (9 +4)/12 = 13/12.
Therefore, 3 times 13/12 = 39/12 = 13/4
Read more on fraction addition;
https://brainly.com/question/11562149
somebody please help so I can pass, please
Rewrite the following equation in the form y = a(x - h)2 + k. Then, determine the x-coordinate of the minimum.
y=2x^2 - 32x + 56
The rewritten equation is y = ____ (x - _____ )2 + ____ .
The x-coordinate of the minimum is _____
Answers
We now from our quadratic that [tex]a=2[/tex] and [tex]b=-32[/tex], so lets use our formula:
[tex]h= \frac{-b}{2a} [/tex]
[tex]h= \frac{-(-32)}{2(2)} [/tex]
[tex]h= \frac{32}{4} [/tex]
[tex]h=8[/tex]
Now we can evaluate our quadratic at 8 to find [tex]k[/tex]:
[tex]k=2(8)^2-32(8)+56[/tex]
[tex]k=2(64)-256+56[/tex]
[tex]k=128-200[/tex]
[tex]k=-72[/tex]
So the vertex of our function is (8,-72)
Next, we are going to use the vertex to rewrite our quadratic equation:
[tex]y=a(x-h)^2+k[/tex]
[tex]y=2(x-8)^2+(-72)[/tex]
[tex]y=2(x-8)^2-72[/tex]
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.
We can conclude that:
The rewritten equation is [tex]y=2(x-8)^2-72[/tex]
The x-coordinate of the minimum is 8
Answer:
y = 2 (x - 8 )2 + (-72)) .
The x-coordinate of the minimum is 8.
Step-by-step explanation:
I just took this test on plato and I got it correct.
Please help me with this
Answers
The explanation is shown below:
1. By definition, a geometric sequence is a sequence of numbers each number, after the first one, is the result of multiply the previous number by a common ratio.
2. The Option B has the following common ratio:
(2/3) / (4/9)=1.5
1/(2/3)=1.5
r=1.5
3. The Option E has the following common ratio:
-15/3=-5
75/-15=-5
r=-5
hey can you please help me posted picture of question
Answers
Vertical translation is obtained by adding or subtracting a number from the function. Addition of a number brings about upward translation and subtraction of a number brings downward translation.
So, the answer to this question is option A
What is the median of the data set: 50, 54,62,48,49,52
Answers
First, sort the data from least to greatest:
48, 49, 50, 52, 54, 62
The median lies between the number 50 and 52
The median is 51
Explain how you would use equivalent fractions to solve 0.5 + 0.10
Answers
1/2+1/10 which would be 3/5 which that in decimal form is .6
PLZ HELP NOOWWWWWWW!!!
The diameter of a certain planet is approximately 3x10^7 meters (aka 30000000 meters). The length of a certain city is approximately 5x10^4 meters (aka 50000 meters).
How many times greater is the diameter of the planet compared to the length of the city?
Answers
You divide the diameter of the planet by the length of the city
30000000 / 50000 = 600
The diameter is 600 times greater than the length of the city
The answer is 600
Hope this helps!
solve for x 19-24. find the measure of the angle indicated in bold for 25-28.
Answers
angle (21x+6) is equal angle 90°-----> by alternate exterior angles
so
21x+6=90--------> 21x=84----------> x=4°
the answer N 19) is 4 degrees
N 20)
angle 75 is equal angle 11x-2-----> by corresponding angles
so
11x-2=75-----> 11x=77--------> x=7°
the answer N 20) is x=7 degrees
N 21)
angle 60 is equal angle (8x-4)------> by alternate interior angles
so
8x-4=60-----> 8x=64--------> x=64/8-----> x=8°
the answer N 21) is x=8 degrees
N 22)
angle (x+139) is equal to angle 132-----> by alternate interior angles
so
x+139=132-------> x=132-139--------> x=-7 °
the answer N 22) is x=-7 degrees
N 23)
angle (-1+14x) is equal to angle (12x+17)----> by alternate exterior angles
so
-1+14x=12x+17------> 14x-12x=17+1----> 2x=18----> x=9
the answer N 23) is x=9 degrees
N 24)
angle (23x-5) is equal to angle (21x+5)----> by corresponding angles
so
23x-5=21x+5-----> 23x-21x=5+5-----> 2x=10-----> x=5
the answer N 24) is x=5 degrees
N 25)
angle (x+96) and angle (x+96)-------> are supplementary angles
so
x+96+x+96=180--------->2x+192=180------> x=-6°
the angle indicated in bold is (-6+96)=90°
N 26)
angle (20x+5) and angle (24x-1)-------> are supplementary angles
so
20x+5+24x-1=180------> 44x=176-----> x=4°
the angle indicated in bold is (20*4+5)=85°
N 27)
angle (6x) is equal to angle (5x+10)--------> by corresponding angles
so
6x=5x+10------> 6x-5x=10------> x=10
the angle indicated in bold is (6*10)=60°
N 28)
angle (x+109) and angle (x+89) are supplementary angles
so
x+109+x+89=180----> 2x=-18-------> x=-9
the angle indicated in bold is (x+89)----> -9+89=80°
To solve for x in 19-24, x = -5. For the angle measurement in question for 25-28, more information is needed.
Explanation:To solve for x in 19-24, we subtract 24 from 19, which gives us x = -5.
Regarding the measurement of the angle indicated in bold for 25-28, the provided options (a, b, c) seem to be unrelated to this question. Could you please provide more information or clarify your query?
What equation results from completing the square and then factoring? x^2-8x=39
Answers
x²-8x=39
Group terms that contain the same variable
(x²-8x)=39
Complete
the square. Remember to balance the equation by adding the same constants
to each side
(x²-8x+16)=39+16
Rewrite as perfect squares
(x-4)²=55-------> (x-4)²-55=0(+/-)]x-4]=√55
(+)]x-4]=√55--------> x=4+√55
(-)]x-4]=√55-------> x=4-√55
the answer is
(x-4)²-55=0
Answer: (x-4)²=55
Step-by-step explanation:
This is apex answer
Kelly ask Tyrese to help her use the vertical line test to determine whether or not the curve that she was given it is a function Tyrese informed Kelly that an order for the given curve to be designated as a function of a vertical line drawn through any x value must intersect the Curve___ time(s)
Answers
General Idea:
Vertical line test is a test used to determine if a relation is a function. As per vertical line test, a relation is a function if there are no vertical lines that intersect the graph at more than one point.
Applying the concept:
Kelly ask Tyrese to help her use the vertical line test to determine whether or not the curve that she was given it is a function Tyrese informed Kelly that an order for the given curve to be designated as a function of a vertical line drawn through any x value must intersect the Curve [tex] ONE [/tex] time.
A six-sided die in which each side is equally likely to appear is repeatedly rolled until the total of all rolls exceed 400
Answers
Approximately 0.2266, or 22.66%, is the probability that rolling the die more than 140 times is needed to exceed a total of 400.
To approximate the probability that rolling the die more than 140 times is needed to exceed a total of 400, we can use a normal approximation to the binomial distribution since the number of rolls is large.
First, let's calculate the mean (μ) and standard deviation (σ) of the number of rolls needed to exceed 400:
[tex]\[ \text{Mean (μ)} = \frac{\text{Total target}}{\text{Expected value per roll}} = \frac{400}{\frac{7}{2}} \][/tex]
[tex]\[ \text{Standard deviation (σ)} = \sqrt{\frac{\text{Total target} \times (\text{Sides}^2 - 1)}{12}} = \sqrt{\frac{400 \times (6^2 - 1)}{12}} \][/tex]
Now, we'll use the normal approximation and the z-score formula to find the probability:
[tex]\[ z = \frac{\text{X} - \text{μ}}{\text{σ}} \][/tex]
[tex]\[ z = \frac{140 - \text{μ}}{\text{σ}} \][/tex]
Then, we look up the z-score in a standard normal distribution table or use a calculator to find the probability associated with that z-score.
Let's calculate these values.
First, let's calculate the mean (μ) and standard deviation (σ):
[tex]\[ \text{Mean (μ)} = \frac{400}{\frac{7}{2}} = \frac{800}{7} \approx 114.29 \][/tex]
[tex]\[ \text{Standard deviation (σ)} = \sqrt{\frac{400 \times (6^2 - 1)}{12}} = \sqrt{\frac{400 \times 35}{12}} \approx \sqrt{\frac{14000}{12}} \approx \sqrt{1166.67} \approx 34.16 \][/tex]
Now, let's find the z-score for rolling the die more than 140 times:
[tex]\[ z = \frac{140 - \text{μ}}{\text{σ}} = \frac{140 - 114.29}{34.16} \approx \frac{25.71}{34.16} \approx 0.75 \][/tex]
Using a standard normal distribution table or calculator, we find the probability associated with a z-score of 0.75, which represents the probability that rolling the die more than 140 times is needed to exceed a total of 400.
The Correct Question is :
A six-sided die, in which each side is equally likely to appear, is repeatedly rolled until the total of all rolls exceeds 400. Approximate the probability that this will require more than 140 rolls.
The approximate probability that it will require more than 140 rolls for the total to exceed 400 is 0.005.
To find the approximate probability that it will require more than 140 rolls for the total to exceed 400, we can relate it to the probability that the sum of the first 140 rolls is less than 400.
Let X be the random variable representing the sum of the rolls. We want to find P(X > 400), which is the probability that it will require more than 140 rolls.
We can calculate this by finding the complement of the event that the sum of the first 140 rolls is less than 400.
Let A be the event that the sum of the first 140 rolls is less than 400. Then, P(A) is the probability that we're interested in.
Now, we calculate P(A):
Since each side of the die is equally likely, the expected value of the roll is [tex]\( \frac{1+6}{2} = 3.5 \)[/tex].
The expected value of the sum of the first 140 rolls is [tex]\( 140 \times 3.5 = 490 \)[/tex].
Therefore, P(A) can be approximated using the normal distribution, since the sum of the rolls follows approximately a normal distribution due to the Central Limit Theorem.
Using the properties of the normal distribution, we can standardize the value:
[tex]\[ Z = \frac{400 - 490}{\sqrt{140 \times \left(\frac{1}{12}\right)}} \][/tex]
Here, [tex]\( \frac{1}{12} \)[/tex] is the variance of a single roll of the die.
Now, we find P(A) using the standardized value of Z:
P(A) = P(X < 400) = P(Z > z)
We can then find the probability from a standard normal distribution table or calculator.
[tex]\[ P(A) \approx P(Z > -2.589) \][/tex]
From a standard normal distribution table, we find that [tex]\( P(Z > -2.589) \approx 0.995 \)[/tex].
So, the approximate probability that it will require more than 140 rolls for the total to exceed 400 is 1 - 0.995 = 0.005.
The probable question may be:
A six-sided die, in which each side is equally likely to appear, is repeatedly rolled until the total of all rolls exceeds 400. What is the approximate probability that this will require more than 140 rolls? (Hint: Relate this to the probability that the sum of the first 140 rolls is less than 400.)
What is the cube root of 216x^9y^8
Answers
Please, see the attached file.
Thanks.
(216x^9y^8)^(1/3)
216^(1/3) = 6
9/3 = 3
8/3 = 2 2/3
(216x^9y^8)^(1/3) = 6 x^3 y^2 y^(2/3)
what is the median for the set of data shown? 26,34,38,49,65,75,81
Answers
Answer: 49
Step-by-step explanation:
We need to remember that the median of a set of data is the middle value in the set.
To find the median of a set of data the first step is to arrange the data in order from least to greatest, but, in this case, the set of data given is already arranged from least to greatest:
26,34,38,49,65,75,81
Therefore, you can oberve that the middle value in the set is the following:
26,34,38,49,65,75,81
Then, the median for this set of data is: 49
The answer is provided in the image attached.
Suppose that a sample of size 44 is drawn from a population with mean 36 and standard deviation 47, find the standard deviation of the distribution of sample means
Answers
Answer:
Standard deviation of the distribution of sample means = 7.0855
Step-by-step explanation:
We are given that a sample of size 44 is drawn from a population with mean 36 and standard deviation 47.
Using Central Limit Theorem, it is stated that;
Standard deviation of the distribution of sample means = [tex]\frac{Population S.D.}{\sqrt{n} }[/tex]
= [tex]\frac{\sigma}{\sqrt{n} }[/tex] = [tex]\frac{47}{\sqrt{44} }[/tex] = 7.0855
On a bulletin board, the principal, Ms.Gomez, put 115 photos of the fourth grade students in her school. She put the photo in 5 esqueleto rows. How many photos did she put in each row?
Answers
23 photos per row. Got it? Good.
When s is the open hemisphere x 2 + y 2 + z 2 = 1, z ≤ 0 , oriented by the inward normal pointing to the origin, then the boundary orientation on ∂s is clockwise. true or false?
Answers
Therefore, the answer above False
304 students went on a field trip. seven buses were filled and 17 students traveled in cars. how many students were in each bus?
Answers
-
304: total students
17: riding in car
7: number of buses
-
304 - 17 = 287
287 divided by 7 = 41
An analogy makes a comparison between objects based on their similar qualities. Cassidy wanted to create an analogy for the motion of atoms in solids, liquids, and gases, so she compared them to marbles in a tray. Which best compares the phases of matter to marbles in a tray? A solid is like the tray being shaken and the marbles moving around it, and a liquid is like the tray being shaken slowly and all the marbles moving in their positions. A solid is like the tray being shaken slowly and all the marbles moving in their positions, a liquid is like the tray being shaken and the marbles moving around it, and a gas is like the tray being shaken hard and the marbles moving vigorously around it. A gas is like the tray being shaken slowly and all the marbles moving in their positions, and a solid is like the tray being shaken hard and the marbles moving vigorously around it. A liquid is like the tray being shaken hard and the marbles moving vigorously around it, and a gas is like the tray being shaken slowly and all the marbles moving in their positions.
Answers
Answer:
B
Step-by-step explanation:
given f(x)=x^2 +3 find h(x) h(x)=f(5x)-f(-2)
Answers
Answer:
h(x) = 25x^2 -4
Step-by-step explanation:
Fill in the given arguments and evaluate:
h(x) = f(5x) -f(-2)
= ((5x)^2 +3) - ((-2)^2 +3)
h(x) = 25x^2 -4
what is the quotient of 1 over (1 plus the square root of 3)?
Answers
[tex]\dfrac{1}{1+\sqrt{3}}=\dfrac{1}{1+\sqrt{3}}\cdot \dfrac{1-\sqrt{3}}{1-\sqrt{3}}\\\\=\dfrac{1-\sqrt{3}}{1^{2}-(\sqrt{3})^{2}}=\dfrac{1-\sqrt{3}}{1-3}\\\\=\dfrac{\sqrt{3}-1}{2}[/tex]
This eqvaluates to approximately 0.3660254037844386.
For the data set below, calculate the variance to the nearest hundredth decimal place. 27 38 47 42 33 56 37 57 38 52
Answers
Var=Σ(x-μ)²/(n-1)
mean=(27+38+47+42+33+56+37+57+38+52)/10=42.7
Σ(x-μ)²=(27-42.7)²+(38-42.7)²+(47-42.7)²+(42-42.7)²+(33-42.7)²+(56-42.7)²+(37-42.7)²+(57-42.7)²+(38-42.7)²+(52-42.7)²
=904.1
Thus variance will be:
904.1/(10-1)
=100.45555556
~100.5
Can anyone help ME? PLEASE HELP IF I DONT TURN THIS IN BY TOMMOROW I DONT GET TO GO TO NEW YORK AND THAT IS MY DREAM
Answers
∠b = 180 = 25 -25 = 130 (Angles in a triangle)
∠c = 180 - 130 = 50 (Adjacent angles on a straight line)
∠d = ∠b = 130 (Vertically opposite angles)
∠e = ∠c = 50 (Vertically opposite angles)
∠f = 180 - 90 - 50 = 40 (Angles in a triangle)
∠g = 180 - 65 - 50 = 65 (Angles in a triangle)
∠h = 90 - 65 = 25 (Complementary angles)
*Enjoy your trip to New York!
Determine whether the given equation has one solution, no solution, or infinitely many solutions. x+4/4=x+3/3
A. one solution
B. no solution
C. infinitely many solutions
D. cannot be determined
Please explain what you did to get the answer (it'll help me learn better)
Answers
Check the attachment.
Hope it helps you :)
Answer:
There can be only one solution
Step-by-step explanation:
The only soution is zero, because anything else is unequal.
PLEASE HELP ***What is the length of AC??? Please help me understand how to find this
Answers
AC and CE have the same ratio as BA and DE. So you can get the answer by getting their proportions.
84 = 7
156-x x
Cross multiply, transpose, and simplify to get the variable x.
84x = 1092-7x
84x + 7x = 1092
91x = 1092
x = 12
To get AC, substitute.
AC = 156 - x
AC = 156 - 12
AC = 144
The Fergusons reported making the following payments during the year:
State income taxes of $4,400. Federal tax withholding of $4,000.
Alimony payments to John’s former wife of $10,000.
Child support payments for John’s child with his former wife of $4,100.
$3,200 of real property taxes.
Sandy was reimbursed $600 for employee business expenses she incurred. She was required to provide documentation for her expenses to her employer.
In addition to the $750 of Web design expenses, John attended a conference to improve his skills associated with his Web design work. His trip was for three days and he incurred the following expenses: airfare $370, total taxi fares for trip $180, meals $80, and conference fee of $200.
$3,600 to Kid Care day care center for Samantha’s care while John and Sandy worked.
$14,000 interest on their home mortgage.
$3,000 interest on a $40,000 home-equity loan. They used the loan to pay for a family vacation and new car.
$6,000 cash charitable contributions to qualified charities.
Donation of used furniture to Goodwill. The furniture had a fair market value of $400 and cost $2,000.
a. What is the Fergusons’ 2017 federal income taxes payable or refund, including any self-employment tax and AMT, if applicable? (Use the 2017 AMT exemptions.) (Round your answer to 2 decimal places.)
Answers
Answer:163.46
Step-by-step explanation:
exponential function for 2,6,18,54
Answers
y = A * (b) ^ x
Where,
A: initial amount
b: growth rate
x: domain of the function.
We have then that the function is:
y = 2 * (3) ^ x
For example,
for x = 0:
y = 2 * (3) ^ 0
y = 2
for x = 1:
y = 2 * (3) ^ 1
y = 6
for x = 2:
y = 2 * (3) ^ 2
y = 18
for x = 3:
y = 2 * (3) ^ 3
y = 54
Answer:
y = 2 * (3) ^ x
Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a two or a three. what are the expected winnings?
Answers
whats 70/100 as a decimal
Answers
percentage:70%