Which equation has a focus at (–6, 12) and directrix of x = –12?
1. ) ( y - 12)^2 = 1/12 ( x + 9 )
2. ) ( y - 12 )^2 = -1/12 ( x + 9 )
3. ) ( y - 12)^2 = 12 ( x+9 )
4. ) ( y - 12)62 = -12 (x + 9 )
Answer: C
Answers
None of the given options have a focus at (-6, 12) and directrix of x = -12,so none of the option is correct.
To find the equation with a focus at (-6, 12) and directrix of x = -12, we can use the general equation for a parabola with a vertical axis of symmetry:
(y - k)^2 = 4p(x - h)
where (h, k) is the focus and x = h - p is the directrix.
Given the focus (-6, 12) and directrix x = -12, we can determine the value of p:
p = h - (-12) = -6 - (-12) = 6
Now, we can plug in the values of h, k, and p into the equation:
(y - 12)^2 = 4(6)(x + 6)
Simplify the equation:
(y - 12)^2 = 24(x + 6)
Now, let's compare this equation to the given options:
1. (y - 12)^2 = 1/12 (x + 9)
2. (y - 12)^2 = -1/12 (x + 9)
3. (y - 12)^2 = 12 (x + 9)
4. (y - 12)^2 = -12 (x + 9)
None of the given options match the equation we found. Therefore, none of the given options have a focus at (-6, 12) and directrix of x = -12
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Related Questions
The worker was paid a day rate of $50 plus $3 for each box he filled with the apples that he
picked.
32 + 50
0.13z + 30
Answers
Answer:
A y=mx+b y=3x+50
because $3 is the rate and $50 is what you get started off with
At the end of may, janet told sam that she has read 10 books this year and reads 2 books each month. Sam wants to catch up to janet. He tracks his book reading with a table on his door. Using his table below, what month will sam have read the same amount of books as janet?.
Answers
The month in which Sam will have read the same number of books as Janet is June.
To determine in which month Sam will have read the same number of books as Janet, let's analyze the table of Sam's book reading progress. Without the specific table provided, I will illustrate the steps to find the desired month.
Let's assume the table represents the number of books Sam has read each month:
Month Number of Books Read
Jan 0
Feb 2
Mar 4
Apr 6
May 8
Janet mentioned that she has read 10 books this year, with a consistent rate of 2 books per month. Given that information, we can see that Janet has read 2 books per month for every month of the year, including May.
To find the month where Sam will have read the same number of books as Janet, we need to determine when Sam's cumulative number of books matches or surpasses Janet's total.
By looking at the table, we can see that Sam will reach or surpass 10 books in the month of June. In June, Sam will have read a total of 10 books, the same number as Janet.
Therefore, the month in which Sam will have read the same number of books as Janet is June.
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Solve for the roots in simplest form using the quadratic formula:
4x^2-36x = -93
Answers
Answer:
x=9+/-2i√3/2
Step-by-step explanation:
5x + 13 = 7
Solve for x
Answers
Answer: x=−6/5
Step-by-step explanation: Hope this help :D
Answer:
-1.2
Step-by-step explanation:
5x+13=7
5x= -6
x=-6/5 or -1.2
math question need help with it
Answers
Answer:
c- 4 x 10^7
Step-by-step explanation:
for scientific notation, the first number can not be greater than 9
so you have to split your number into a decimal
37,250,000
3.7250000
so the first part of your equation is 4 because the 7 rounds up the 3
then, there are 7 digits after the decimal, so that is your exponent
it is also positive.
so your final answer is
4 x 10^7 :)
Solve the initial value problem using Laplace transform method y ′′ −4y ′+4y=t 2e 2t,y(0)=0,y ′(0)=0
Answers
The solution to the initial value problem is \(y(t) = (1/24)t^4 e^(2t)\) .
To solve the initial value problem using Laplace transform, we first take the Laplace transform of both sides of the differential equation.
Applying the Laplace transform to the given equation, we have:
\(s^2Y(s) - sy(0) - y'(0) - 4(sY(s) - y(0)) + 4Y(s) = L[t^2e^(2t)]\)
Using the initial conditions y(0) = 0 and y'(0) = 0, the equation simplifies to:
\(s^2Y(s) - 4sY(s) + 4Y(s) = L[t^2e^(2t)]\)
Combining like terms, we have:
\((s^2 - 4s + 4)Y(s) = L[t^2e^(2t)]\)
Factorizing the quadratic term, we get:
\((s - 2)^2Y(s) = L[t^2e^(2t)]\)
Dividing both sides by (s - 2)^2, we have:
\(Y(s) = L[t^2e^(2t)] / (s - 2)^2\)
To find the Laplace transform of \(t^2e^(2t)\) , we use the property:
\(L[t^n e^(at)] = n!(s - a)^(-n-1)\)
Applying this property, we have:
\(L[t^2e^(2t)] = 2!(s - 2)^(-2-1) = 2/(s - 2)^3\)
Substituting this back into the equation, we get:
\(Y(s) = 2/(s - 2)^3 / (s - 2)^2\)
Simplifying further, we have:
\(Y(s) = 2/(s - 2)^5\)
Now, we need to find the inverse Laplace transform of Y(s) to obtain the solution y(t). Using the property:
\(L^(-1)[(s - a)^(-n-1)] = (1/n!)t^n e^(at)\)
Applying this property, we have:
\(y(t) = (1/4!)t^4 e^(2t)\)
Therefore, the solution to the initial value problem is \(y(t) = (1/24)t^4 e^(2t)\).
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told..................
Answers
Answer:
B
Step-by-step explanation:
You can solve the system of equations by elimination, since 3y and -3y will cancel out.
After combining the two equations, you will get 19x = -152.
Divide each side by 19:
x = -8, so the answer is B
What is 1/3 of 12 i need the answer
Answers
Answer:
4
Step-by-step explanation:
it takes 3 to make a full so do 12 divide by 3 and thats 4
LAST QUESTION!!!!!! WILL GIVE BRANLIEST!!!!! PLS JUST TAKE A LOOK!!!!!! SHARE YO SMARTNESS!!!!!!!!
In which of the following situations would it be more appropriate to use the distance formula instead of the midpoint formula?
A) To determine where to take a break midway through your road-trip. B) To calculate where to center your TV on your wall.
C) To determine a fair meeting point between you and your friend's house.
D) To find the length of the first base line on a baseball field.
Answers
Answer:
D
Step-by-step explanation:
D is more appropriate for distance formula because you are looking for the whole length between two points rather than the point in between the the two points such as in the other answers.
This exercise involves the use of an unrealistically small population to provide a concrete ilustration for the exact distribution of a sample proportion. A population consists of one man and four women. The first name of the man is Noah, the first names of the women are Emma, Rose, Abigail, and Becca. Suppose that the specified attribute is "male. Complete parts (a) through (e) below a. Determine the population proportion, p (Type an integer or a decimal. Do not round)
Answers
The population proportion of males is 0.2, or 20%. This means that in the population of one man and four women, 20% of the individuals are male.
The population is defined as the entire group of individuals that we are interested in studying. In this exercise, the population consists of one man and four women, for a total of five individuals.
The attribute of interest is "male", which means we are looking to determine the proportion of individuals in the population who are male. In this case, there is only one male in the population (Noah) and a total of five individuals, so the proportion of males in the population can be calculated as:
p = number of males / total population size
In this case, the number of males is 1, and the total population size is 5, so the proportion of males in the population is:
p = 1/5
p = 0.2
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find the value of 2/5 - 3
Answers
\(\boxed{\large{\bold{\blue{ANSWER~:) }}}}\)
\(\sf{\dfrac{2}{5}-3 }\) \(\sf{\dfrac{2-10}{5} }\) \(\sf{\dfrac{-8}{5} }\)\(\sf{ }\)
I have the equation I just don't know how to solve it
Answers
the answer to your question is a.
A shipping company uses a formula to determine the cost for shipping a package: c = 2.79 + 0.38p, where c is the cost of shipping and p is the number of pounds. What is the cost of shipping a package that weighs 8 pounds?
Answers
Using the formula they gave us:
Cost of shipping = 2.79 + 0.38(8)
Cost of shipping = 2.79 + 3.04
Cost of shipping = 5.83(currency unit)
For each table, calculate the mean weight for each group, xa and xb, and find the difference of the mean
of group a and the mean of group b (xa - xb).
Answers
The mean weight for each group and the difference between them, calculate the mean weight for group a and group b separately, and then subtract the mean of group b from the mean of group a.
To calculate the mean weight for each group (xa and xb), follow these steps:
1. Add up all the weights of group a and divide by the total number of data points in group a to find the mean weight (xa).
2. Repeat the same process for group b, adding up all the weights and dividing by the total number of data points to find the mean weight (xb).
3. Finally, subtract the mean of group b (xb) from the mean of group a (xa) to find the difference between the two means (xa - xb).
In summary, to find the mean weight for each group and the difference between them, calculate the mean weight for group a and group b separately, and then subtract the mean of group b from the mean of group a.
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What are the solutions of x^2=-7x-8
Answers
The solutions to the quadratic equation x² = -7x - 8 are x equals \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
x² = -7x - 8
To find the solutions of the quadratic equation x² = -7x - 8, we can rearrange it into standard quadratic form, which is ax² + bx + c = 0, and apply the quadratic formula.
x² = -7x - 8
x² + 7x + 8 = 0
a = 1, b = 7 and c = 8
Plug these into the quadratic formula: ±
\(x = \frac{-b \± \sqrt{b^2 -4(ac)}}{2a} \\\\x = \frac{-7 \± \sqrt{7^2 -4(1*8)}}{2*1} \\\\x = \frac{-7 \± \sqrt{49 -4(8)}}{2} \\\\x = \frac{-7 \± \sqrt{49 - 32}}{2} \\\\x = \frac{-7 \± \sqrt{17}}{2} \\\\x = \frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\)
Therefore, the values of x are \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).
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Based on the measurements you completed above, which two segments are congruent? Select the appropriate answer below.
Answers
Answer:
can you please add the options or even a picture of the segments?
in theyx, y-plane above, the circle has center (h, k)left parenthesis, h, comma, k, right parenthesis and radius 10. what is the value of k ?
Answers
We can say that the value of k will be equal to the y-coordinate of the center of the circle (since k represents the y-coordinate of the center).
To answer this question, we need to use the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
Where h and k represent the coordinates of the center of the circle, and r represents the radius. In this case, we are given that the circle has center (h, k) and radius 10. So we can write:
(x - h)^2 + (y - k)^2 = 10^2
We are asked to find the value of k. To do this, we need to look at the equation of the circle and notice that the y-coordinate is paired with k. This means that we can isolate k by rearranging the equation as follows:
(y - k)^2 = 10^2 - (x - h)^2
y - k = ±√(10^2 - (x - h)^2)
k = y ±√(10^2 - (x - h)^2)
Since we don't have any information about the x-coordinate, we can't solve for a specific value of k. However, we can say that the value of k will be equal to the y-coordinate of the center of the circle (since k represents the y-coordinate of the center). Therefore, the answer is:
k = y
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3. you want to determine whether the race of the defendant has an impact on jury verdicts. you assign participants to watch a trial with either a hispanic or caucasian defendant, and you measure on a 1 (not at all) to 7 (very) scale how guilty the defendant is. what is the best dv scale of measurement?
Answers
The best discrete variable of measurement for the situation is an interval.
What is the Scale of Measurement?Finding the scale of measurement for the variables is the next step in selecting a statistical test after identifying the independent and dependent variables. The dependent variable must be measured using an interval or ratio scale for each of the parametric tests that we have covered so far. Many psychologists also subject variables with roughly interval scales of measurement to parametric tests. You must decide whether to use "scale" or "interval" scores when performing parametric tests of means.
Given the condition about whether the race of the defendant has an impact on jury verdicts,
and measure on a 1 (not at all) to 7 (very) scale how guilty the defendant,
The best scale of measurement for the condition is an interval.
Although the interval scale has characteristics of nominal and ordered data, it also allows for the quantification of data point differences. The variables' actual positions in the order as well as their differences are both displayed by this form of data. They can be combined or split, but not added to or subtracted from.
The fact that zero is an existing variable adds another characteristic to this scale. Zero in the ordinal scale indicates that there is no data.
Hence the scale of measurement is an interval.
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What's the slope intercept form, simplifying all fractions.
3x +6y = 42
Answers
Step-by-step explanation:
Solving
3x + -6y = 42
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '6y' to each side of the equation.
3x + -6y + 6y = 42 + 6y
Combine like terms: -6y + 6y = 0
3x + 0 = 42 + 6y
3x = 42 + 6y
Divide each side by '3'.
x = 14 + 2y
Simplifying
x = 14 + 2y
The slope of the equation 3x +6y = 42 is - 1 / 2.
How to find the slope of an equation?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
Therefore, the equation a line can be represented in slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
3x + 6y = 42
6y = -3x + 42
divide both sides by 6
y = -3x / 6 + 42 / 6
y = - 1 / 2 x + 7
Therefore, the slope is - 1 / 2.
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you have $20.56. you buy an apple for 79 cents and a granola bar for $1.76. how much money did you spend?how much money do you have?
Answers
Let:
M = Total money = $20.56
Ca= Cost of the apple = 79 cents = $0.79
Cg = Cost of the granola bar = $1.76
Ms = Total money spent
Mr = Remaining money
So, the total money spent will be:
Ms = Ca + Cg = $0.79 + $1.76 = $2.55
And the remaining money will be:
Mr = M - Ms = $20.56 - $2.55 =$18.01
A researcher is investigating the effect of sleep deprivation on learning. She recruits 30 participants and randomly assigns half to a "no sleep" group and half to a "regular sleep" group. The "no sleep" group are required to stay up all night and report to a testing room at 2PM the following day. The "regular sleep" group are instructed to have a normal night's sleep and report to the testing room at 9AM the following day. Unfortunately, a water pipe broke outside the testing room window and there was noisy construction crew working the whole day of testing. Which of the following statements is true?
a. The study may be affected by a situational variable.
b. The construction noise may contribute to variability in test scores.
C. The study has a confounding variable. The groups differ in the time they are to report to the testing room.
d. All of these are true.
Answers
The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.
The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.
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Devin drove her truck. The fuel remaining in the truck's tank (in liters) as a function of distance (in kilometers) is graphed.
What is the approximate average fuel consumption rate, between the 100th kilometer and 400th kilometer?
Answers
Between the 100th and 400th kilometers, the average fuel consumption rate is 5/6 liters per kilometer.
What is the rate of change?A consequence of dividing the variation in a variable's function by the variation in the variable. For example The rate at which a distance changes in relation to time is known as velocity.
Given, Devin drove her truck. The fuel remaining in the truck's tank (in liters) as a function of distance (in kilometers) is graphed.
Since in the domain [100, 400] graph shows somewhat linear properties.
from the graph Fuel consumption at 100 = 375 liters
Fuel consumption at 400 = 125 liters
rate in a linear function between two points = (y₂ - y₁)/ (x₂ - x₁)
thus rate between [100, 400] = (375-125)/400-100
rate between [100, 400] = 250/300
rate between [100, 400] = 5/6litere per kilometer
therefore, the average fuel consumption rate, between the 100th kilometer and 400th kilometer is 5/6 liters per kilometer.
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-4.5x(-2) =
i need help solving this equation
Answers
Answer:
9x
Step-by-step explanation:
-4.5X(-2)
-4.5x * -2
9x
if a load of bread cost 25 cents two years ago, how much does it cost now?
Answers
Answer:.80
p-by-step explanation:
what is y - 1 = 1/4 (x-1) in slope intercept form
Answers
Answer:
y=4x-5
Step-by-step explanation:
y = 4x-5. Step-by-step explanation: Slope-intercept form : y=mx+b. y+1 = 4(x - 1).
What is the volume of a hemisphere with a radius of 44. 9 m, rounded to the nearest tenth of a cubic meter?.
Answers
The volume of a hemisphere with a radius of 44.9 m is approximately 189582.2 cubic meters, rounded to the nearest tenth.
To calculate the volume of a hemisphere, you can use the formula
V = (2/3)πr^3
where V is the volume, π is pi (approximately 3.14), and r is the radius. In this case, r = 44.9 m.
So, (2/3)π(44.9)^3 = 189582.234 cubic meters.
This is the exact volume, but since the question asked for the volume rounded to the nearest tenth, the final answer would be 189582.234 cubic meters. It's worth mentioning that a hemisphere is half of a sphere, thus, the volume of a full sphere with a radius of 44.9 m would be double of this value.
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Use a trigonometric ratio to solve for x. Round to two decimal places as necessary.
Answers
Answer:
x ≈ 26.83
Step-by-step explanation:
using the sine ratio in the right triangle
sin59° = \(\frac{opposite}{hypotenuse}\) = \(\frac{23}{x}\) ( multiply both sides by x )
x × sin59° = 23 ( divide both sides by sin59° )
x = \(\frac{23}{sin59}\) ≈ 26.83 ( to 2 decimal places )
Will spent $3.75 for 3 pounds of granola. What is his unit rate in dollars per pound?
Answers
Answer:
$1.25 per pound
Step-by-step explanation:
Step 1:
$3.75 : 3 Rate
Step 2:
$3.75 ÷ 3 Divide
Answer:
$1.25 : 1
Hope This Helps :)
The required rate for granola in dollars per pound is 1.25.
What is Unitary method ?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
Given that,
The total money spent on granola is $3.75.
And, the amount of granola is 3 pounds.
The unit rate for the given case can be found using unitary method as,
Money spent for 3 pounds = $3.75
Then, money spent for 1 pound = 3.75/3 = $1.25
Hence, the rate of granola $1.25 per pound.
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I need A helping Hand Pleaseee
Answers
I got this because I found two points on the graph to use. To get from one point to the next, you had to go up 50cm, and right 10 minutes. So 50/10 is the slope, or rate of change.
5 cm is the answer.
Hope this helps!!!
x tends to 0 (sinax-sinbx)/x
Answers
Answer:
1xxx double answer po
Step-by-step explanation:
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