A parabola can be drawn given a focus of
(8,-1) and a directrix of y = 3. What can be
said about the parabola?
Answers
Answer:
If you sketch the directrix and the focus, the vertex is halfway between them. It would be (-8,-1)
The p value is the distance from the focus to the vertex and the distance between the vertex and the directrix (they are the same) p=3.
The direction of the focus from the vertex will show which way it opens. The one opens down.
Step-by-step explanation:
hehe
Answer:
vertex: (8, 1)p-value: -2opens downwardStep-by-step explanation:
The vertex of a parabola is halfway between the focus and the directrix. The p-value of the equation is half the distance from the focus to the directrix. The parabola opens around the focus, away from the directrix.
__
vertexThat is, the vertex will lie on the same vertical line, but have a y-coordinate that is the average of the y-values of the focus and directrix. Here, that means the y-value of the vertex is ...
(directrix +focus)/2 = (3 +(-2))/2 = 1
The focus is on the vertical line x=8. The coordinates of the vertex are (8, 1).
__
p-valueThe parameter "p" is part of the leading coefficient of the quadratic defining the parabola. It fits into the vertex-form equation as shown here:
\(y=\dfrac{1}{4\mathbf{p}}(x-h)^2+k\qquad\text{vertex at $(h,k)$}\)
The value of p is the distance from the focus to the vertex. When the focus is below the vertex, as here, the value of p will be negative.
p = (focus y-value) - (vertex y-value) = (-1) -1
p = -2
__
openingThe focus lies "inside" the parabola, and the directrix lies "outside." The parabola "wraps around" the focus, away from the directrix. When the focus is below the directrix, the parabola opens downward. (The leading coefficient of the equation is negative, telling you the same thing.
_____
Additional comment
The parabola is the set of points equidistant from the focus and directrix. Thus it should come as no surprise that the vertex is equidistant from the focus and directrix. They lie on the same vertical line when the directrix is horizontal.
The latus rectum is the line segment parallel to the directrix, through the focus, with end points on the parabola. Its end points always lie on a line with slope ±1/2 through the vertex. This can help you find (or verify) the focus graphically.
Related Questions
Pls help ASAP!! Find the missing side using the rules for 45-45-90 and 30-60-90 right triangles
Answers
Answer:
oops this isn't the answer but hey L homie lol swaggy anyways lemme try and help
What is the area of the shaded region?
Answers
Answer:
208
Step-by-step explanation:
4*30 = 120
(15-4) * 8 = 88
88 + 120 = 208
Answer:
208 cm
Step-by-step explanation:
Solving right side first. 8*15=120
Take out 8cm from 30. 30 - 8 = 22
22*4= 88
88 + 120 = 208
Check work I found the total area and the white rectangle.
15*30=450 which in total area
15-4=11 11 is the left/right side of the white rectangle
30-8=22 22 is the top/bottom side of the white rectangle.
22*11= 242
208+242=450
ulsi and Gary are competing in a basketball free throw competition. Tulsi’s ratio of free throws made to free throws missed is 3 to 5. Gary’s ratio of free throws made to free throws missed is 10 to 15. Who has the better ratio for making free throws?
Answers
Answer:
Gary because 10 to 15 rounds down to 2/3 which is greater than 3 to 5
Step-by-step explanation:
Answer:
Garyyy!! super late but yea
Step-by-step explanation:
:)
need help in math class
Answers
Use the marginal tax rate chart to answer the question. Tax Bracket Marginal Tax Rate $0–$10,275 10% $10,276–$41,175 12% $41,176–$89,075 22% $89,076–$170,050 24% $170,051–$215,950 32% $215,951–$539,900 35% > $539,901 37% Determine the effective tax rate for a taxable income of $180,900. Round the final answer to the nearest hundredth.
19.50%
20.00%
21.11%
32.00%
Answers
For a taxable income of $1,80,900, the effective tax rate is 21.11%.
what is meant by marginal tax?Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.
Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.
To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.
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Any has 10 pieces of fruit. 7 are apples and the rest are oranges.
She chooses a piece of fruit at random eats it then chooses a second piece of fruit at random
Please draw this
Answers
The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.
What fraction should go into the boxes?Total number of fruits Amy has = 10
Number of Apples = 7
Number of Oranges = 3
First random pieces of fruits chosen:
Probability of choosing Apples = 6/9
Probability of choosing Oranges = 3/9
Second random pieces of fruits chosen:
Probability of choosing Apples = 6/8
= 3/4
Probability of choosing Oranges = 2/8
= 1/4
Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.
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Karen has a square rug that covers 76.5 ft^2 of her living room floor. Which measurement is closest to the side length of this rug in feet?
A. 8 ft
B. 9 ft
C. 19 ft
D. 20 ft
E. 38 ft
F. None of the above
Answers
The length of a side of a cube is 7. 5 cm. Find the volume of the new cube if the length of each side of the cube is doubled
Answers
Answer:
3375cm³
Step-by-step explanation:
volume of old cube = 7.5³ = 421.875 cm³
volume of new cube = (2 X 7.5)³ = 15³ = 3375cm³
After drinking, the body eliminates 37% of the alcohol present in the body per hour.
a) The amount of alcohol in grams in the body on an hourly basis is described by a discrete time dynamical system (DTDS) of the form xn+1=f(xn), where xn is the number of grams of alcohol in the body after n hours. Give the updating function f (as a function of the variable x).
b) Peter had three alcoholic drinks that brought the alcohol content in his body to 41 grams, and then he stopped drinking. Give the initial condition (in grams) for the DTDS in (a).
c) Find the solution of the DTDS in (a) with the initial condition given in (b). (Your answer will be a function of the variable n, which represents time in hours.)
Answers
The solution of the DTDS is xn = (0.63)^n * 41 grams, where n represents time in hours.
a) The updating function f(x) for the discrete time dynamical system (DTDS) can be derived from the given information that the body eliminates 37% of the alcohol present in the body per hour.
Since 37% of the alcohol is eliminated, the amount remaining after one hour can be calculated by subtracting 37% of the current amount from the current amount. This can be expressed as:
f(x) = x - 0.37x
Simplifying the equation:
f(x) = 0.63x
b) The initial condition for the DTDS is given as Peter having 41 grams of alcohol in his body after consuming three alcoholic drinks. Therefore, the initial condition is:
x0 = 41 grams
c) To find the solution of the DTDS with the given initial condition, we can use the updating function f(x) and iterate it over time.
For n hours, the solution is given by:
xn = f^n(x0)
Applying the updating function f(x) repeatedly for n times:
xn = f(f(f(...f(x0))))
In this case, since the function f(x) is f(x) = 0.63x, the solution can be written as:
xn = (0.63)^n * x0
Substituting the initial condition x0 = 41 grams, the solution becomes:
xn = (0.63)^n * 41 grams
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can you answer 20 x 3/4
Answers
Answer:15
Step-by-step explanation:
Answer15
Step-by-step explanation:
5 points
14. A Bakery made 140 buns. A Restaurant bought 80 of the buns. The
remaining buns were put in to 4 buns each. How many bags of buns are
there. *
60
55
35
15
Answers
Answer: 15
Step-by-step explanation: we have 140 buns if a bakery bought 80 that means we don't have the 80 buns so we remove 80 from 140 so 140-80= 60. and so The remaining buns were put into 4 buns each. so we divide cause they are in 4 and so 60 divided by 4 is 15.
HOPE THIS HELPS!
The polynomial f(x)=b 0
+b 1
⋅x+b 2
⋅x 2
+b 3
⋅x 3
+b 4
⋅x 4
, passes through five (x,y) points: (−3,6.8),(−1.5,15.2),(0.5,14.5),(2,−21.2), and (5,10). You will write a script to solve for the unknown parameters b 0
,b 1
,…, bs using \ the backslash operator First, create a vector x vec of
of the x data values x 1
,x 2
,..,x 5
and a vector y vec of the y data values y 1
,y 2
,..,y 5
. Note the first element of x vec is x1=−3 and the first element of y vec is y1=6.8, etc. Make xvec and yvec column vectors. Scatter plot the data: plot (xvec, yvec, 'or') o red o symbol Second, create a coefficient matrix A corresponding to the system of equations y
=A b
, where yA involves the x-values. The first column of A is all 1's. Use elementwise exponentiation of xvec to create the remaining columns. A= ⎝
⎛
1
⋮
1
x 1
⋮
x 5
x 1
2
⋮
x 5
2
x 1
3
⋮
x 5
3
x 1
4
⋮
x 5
4
⎠
⎞
Third, use \ to use Gaussian elimination to solve for the unknown bvec. Finally, use bvec in the following code to create an anonymous function for the model and to overlay a plot of the data and the model fit. poly_fit =rho(x)[1,x,x ∧
2,x ∧
3,x ∧
4]∗ bvec # dot product plot (xvec, yvec, 'or') hold on; o hold current figure window for next plot fplot(poly_fit, [−3,5],100) \& plot anon function legend("data", "model fit") \& add legend hold off; % remove hold so new plots in new figure
Answers
The given MATLAB script solves for the unknown parameters of a polynomial using the backslash operator and creates a scatter plot of the data points along with the model fit of the polynomial.
Here's a script in MATLAB that solves for the unknown parameters of the polynomial using the backslash operator and creates a plot of the data and the model fit:
```matlab
% Data points
xvec = [-3; -1.5; 0.5; 2; 5];
yvec = [6.8; 15.2; 14.5; -21.2; 10];
% Scatter plot of the data
scatter(xvec, yvec, 'or');
hold on;
% Coefficient matrix A
A = [ones(size(xvec)), xvec, xvec.², xvec.³, xvec.⁴];
% Solve for the unknown parameters
bvec = A \ yvec;
% Model function
poly_fit = ®(x) polyval(flip(bvec), x);
% Plot the model fit
fplot(poly_fit, [-3, 5], 'b');
hold off;
% Add legend to the plot
legend("Data", "Model Fit");
```
This script first defines the x and y vectors for the data points. It then creates a scatter plot of the data using the `scatter` function. The coefficient matrix A is formed using the x values, and the backslash operator `\` is used to solve for the unknown parameters bvec.
Next, an anonymous function `poly_fit` is created to represent the model using the obtained parameters. The `fplot` function is used to plot the model fit over the range [-3, 5].
Finally, the legend is added to the plot to distinguish the data and the model fit.
Note: This script assumes that you have MATLAB installed and the Curve Fitting Toolbox is available.
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Complete Question:
A 7-ounce jar of instant coffee costs $11.78. Find the cost per ounce. Round to the nearest cent.
Answers
Answer:
1.68 per ounce
Step-by-step explanation:
11.78÷7=1.68285714286
1.68285714286 rounded to the nearest cent =1.68
what is the probability that a 2-card hand (drawn from a standard deck of 52) has two queens, two kings, or one of each?
Answers
2/221 is the probability that a 2-card hand has two queens, two kings, or one of each.
What is probability?Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or the probability that a statement is true.Probability varies between zero and 1, wherein zero approaches are not possible and 1 approach is certain.Now, calculate the probability as follows:
There are 4 kings and 4 queens in a deck of cards.Then, it can be either KK or QQ.
Select 2 kings from 4 king cards that can be done in 4c₂=6 ways.Select 2 queens from 4 queen cards that can be done in c₂ = 6 ways.Total ways = 52c₂ = 1326So required probability = 2king or 2 queen
= 6/1326 + 6/1326= 12/1326= 2/221Therefore, the probability that a 2-card hand (drawn from a standard deck of 52) has two queens, two kings, or one of each is 2/221.
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área, perímetro y ecuación general de la trayectoria de una avioneta que se mantiene sobrevolando a una
distancia constante de 4 km de la torre del aeropuerto, esperando instrucciones para su aterrizaje.
Answers
Sketch the region bounded by the given curves, then find the centroid of its area. 1. y = 12 – 3x², y = 4 – x² 2. y = 2x– x², y = 2x² - 4x
Answers
The centroid of the area bounded by the curves y = 12 - 3x² and y = 4 - x² can be found by sketching the region, finding intersecting points, and calculating the centroid coordinates using integration formulas.
To find the centroid of the area bounded by the curves y = 12 - 3x² and y = 4 - x², first sketch the region and then calculate the centroid coordinates (X-bar, Y-bar).
1. Sketch the region:
Plot the given functions on a coordinate plane. The region bounded by the curves is where y = 12 - 3x² is above y = 4 - x².
2. Find centroid coordinates:
To find the centroid, first, determine the intersecting points of the curves. Then, use the formula for the centroid coordinates, which are X-bar = (1/A) * ∫x * (f(x) - g(x))dx and Y-bar = (1/2A) * ∫(f²(x) - g²(x))dx, where f(x) and g(x) are the given functions, and A is the area of the region.
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What are equivalent statements to a + 3 = 18 and 4 ∙ b = 32?
Answers
Answer:
a=18-3 and b=32÷8
Step-by-step explanation:
the first one
please explain the answer
Answers
Answer: £4.26
Step-by-step explanation:
i think it is this:
the oranges cost £1.42 per kg and you have 1.5 kg of oranges so do £1.42 x 3=£4.26
I NEED HELP NOW ITS DUE TOMORROW!
A farmer owns a total of 14 acres in land. The land is separated into 5 5/6 equally sized sections. How many acres are in each section?
Write your answer as a mixed number in simplest form.
Answers
Answer:
2 2/5
Step-by-step explanation:
14 divided by 5/6 is 2 2/5
PLEASE I BEG OF YOU TO HELP ME PLEASE
Answers
Answer:
its B
Step-by-step explanation:
i did it earlier today
Answer:
A
Step-by-step explanation:
-1x-12≤-4
-x≤8
x≥-8
what are the properties ?
Line 1: (-7x+3)+2x
Line 2: (3+(-7x))+2x
Line 3: 3+(-7x+2x)
Line 4: 3+(-5x)
Answers
Step-by-step explanation:
line number Property
Line 1: (-7x+3)+2x associative (gathering -7x and 3)
Line 2: (3+(-7x))+2x. Commutative (change the positions of 3 and -7x)
Line 3: 3+(-7x+2x). associatI’ve
Line 4: 3+(-5x)
Fathi has $1.10 in his printing account. Each sheet of paper he uses reduces his printing account balance by $0.25. Fathi wants to print out a PDF document that is 47 pages long. To save paper, he decides to print on both sides of each sheet and to print two pages on each side of the sheet.
After Fathi prints, what will be the balance in his printing account?
Answers
Answer: Faith's printing account balance will become $-1.90, or $1.90 below 0.
Step-by-step explanation:
Each sheet of paper can print 4 pages. Since it is 47 pages long, she will need 12 pages. That will cost 3 dollars, since 0.25x12=3. 1.10-3=-1.90 dollars, which means that she is $1.90 in debt.
Find the circumference and area of a circle with diameter 22 ft.
Answers
Answer:
C ≅ 69.08
a= 380.1 square inches
Step-by-step explanation:
A study on students drinking habits wants to determine the true average number of alcoholic drinks all uf greek students have in a one week period. We know from preliminary studies that the standard deviation is around 6. 3. How many students should be sampled to be within 0. 5 drink of population mean with 95% probability?.
Answers
Number of students need to be sampled = 610
A study to determine the true average number of alcoholic drinks consumed by Greek students is conducted.
Standard Deviation, σ = 6.3
Margin Error of population mean, E = 0.5
Probability = 95% = 0.95
The p-value corresponding to 0.95 probability = (1+0.95)/2 = 0.975
The z-score corresponding to this p-value = 1.96 [from the z-tables]
Now, The margin error, E = zσ/√n, where n is the sample size
⇒ n = (zσ/E)²
⇒ n = (1.96 x 6.3/0.5)²
⇒ n ≈ 610
Hence 610 students need to be sampled.
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food safety guidlines recommend that a beef rib roast should cook for 23 minutes per pound based on 325f oven setting. how many hours should it take to cook a 5.17 pound roast?
Answers
It should take approximately 1.98 hours, or around 1 hour and 59 minutes, to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.
To calculate the cooking time for a 5.17 pound roast, we can use the recommended guideline of 23 minutes per pound. First, we need to convert the weight from pounds to minutes, and then convert minutes to hours.
Cooking time in minutes = 5.17 pounds * 23 minutes/pound
Cooking time in minutes = 118.91 minutes
To convert minutes to hours, we divide the total minutes by 60:
Cooking time in hours = 118.91 minutes / 60
Cooking time in hours ≈ 1.98 hours
Therefore, it should take approximately 1.98 hours to cook a 5.17 pound beef rib roast based on the recommended guideline of 23 minutes per pound at a 325°F oven setting.
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the sum of two rational numbers is 17/18 If one of the numbers is 5/24 find the other number
Answers
Step-by-step explanation:
x + y = 17/18
x = 5/24
5/24 + y = 17/18
to bring both fractions to the same denominator (I see it is 72, but let's do it formally correct for you to learn), we look for the LCM, the lowest common multiple of both.
for this we split both numbers into their prime factors and then build the the combination of the longest chains per prime factor :
24 = 2×2×2×3
18 = 2×3×3
the LCM (and the new denominator) is then
2×2×2×3×3 = 8×9 = 72
so,
15/72 + y = 68/72
y = 53/72
53 is a prime number, so the fraction cannot be further refined.
You can send and receive text messages on your cellphone for $0.12 a message your cellphone provider also offers a plan for an unlimited number of messages for $4 per month. How many text messages must you send and receive a month to make the unlimited plan a better buy?
Answers
Answer:
33.333
Step-by-step explanation:
Does anybody know what g(x)=3 when x ?
Answers
Answer:
9
Step-by-step explanation:
g(x) = y
So to find x when g(x) = 3, go look at the y = 3 line and find the point, in this case (9,3) the x value (9) is your answer.
Given the following LP model, which is the correct standard form? Max(Z)=2X1+X2 Restrictions / Constrains 11×1+3×2≥33
8×1+5×2≤40
7×1+10×2≤70
7×1+10×2≤70 X1,X2≥0 Use this problem's information to answer questions 19 to 21. a. Max(Z)=3×1+2X2
11×1+3×2−51≤33
8×1+5×2+52≥40
7×1+10×2+53≥70
b. Max(Z)=3×1+2×2 11×1+3×2+51=33 8×1+5×2−52=40 7×1+10×2−53=70
c. Max(Z)=3×1+2×2 11×1+3×2−51=33 8×1+5×2+52=40 7×1+10×2+53=70
d. Max(Z)=3×1+2×2 11X1+3×2+$1=33 8×1+5×2+52=40 7×1+10×2+53=70
Answers
The correct standard form for the given LP model is option C: Max(Z) = 3x1 + 2x2, subject to the constraints 11x1 + 3x2 - 5 <= 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70, with x1, x2 >= 0. This option aligns with the original objective function and constraints of the LP model.
To convert the LP model into standard form, we need to rewrite the constraints with the variables on the left-hand side and constants on the right-hand side, with inequality signs (<= or >=) consistent throughout. Additionally, we introduce slack or surplus variables to transform any non-standard constraints.
In option C, the constraints are correctly transformed as 11x1 + 3x2 - 5 = 33, 8x1 + 5x2 + 5 >= 40, and 7x1 + 10x2 + 5 >= 70. These constraints are consistent with the original model. The objective function remains the same, Max(Z) = 3x1 + 2x2.
Option A has incorrect signs in the transformed constraints, and option B introduces surplus variables (+5) instead of slack variables (-5), resulting in an incorrect standard form. Option D includes a non-standard term with a dollar sign, which is inconsistent with linear programming conventions.
Therefore, option C is the correct standard form, adhering to the original LP model's objective function and constraints.
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a friend rolls two dice and tells you that there is at least one 6. what is the probability the sum of two rolls is 9?
Answers
The probability that the sum of two rolls is 9 given that there is at least one 6 rolled is 1/11 or approximately 0.09. To see why, we can use conditional probability. Let A be the event that there is at least one 6 rolled, and let B be the event that the sum of two rolls is 9. We want to find P(B|A), the probability of B given A.
First, let's find P(A), the probability of rolling at least one 6. The only way to not roll a 6 is to roll two non-6 numbers, which has a probability of (5/6)*(5/6) = 25/36. So the probability of rolling at least one 6 is 1 - 25/36 = 11/36.
Next, let's find P(B and A), the probability of rolling a 9 and at least one 6. There are four ways to roll a 9: (3,6), (4,5), (5,4), and (6,3). In each case, one of the dice is a 6, so the probability of rolling a 9 and at least one 6 is 4/36.
Finally, we can use the formula
\(P(B|A) = P(B and A) / P(A)\)
to find the desired probability:
\(P(B|A) = P(B and A) / P(A)\) = (4/36) / (11/36) = 4/11
So the probability that the sum of two rolls is 9 given that there is at least one 6 rolled is 4/11 or approximately 0.09.
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