Find the standard form of the equation of the parabola with a focus at (-4, 0) and a directrix at x = 4. (2 points)
Answers
since the focus point is at -4, 0 and the directrix is a vertical line at x = 4, is a horizontal parabola, and it opens to the left-hand-side.
now, notice the distance "p", is just 4 units, however, the parabola is opening to the left-side, thus "p" is negative, then is -4, the vertex is half-way between the focus point and the directrix.
[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} \boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\ (x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\ \begin{cases} h=0\\ k=0\\ p=-4 \end{cases}\implies (y-0)^2=4(-4)(x-0)\implies y^2=-16x \\\\\\ -\cfrac{1}{16}y^2=x[/tex]
Related Questions
How many lines of symmetry does the figure have?
0
1
2
3
Answers
so answer is
1
hope it helps
need help with this inequality
Answers
|x-4| </ 1
x-4 </ 1
and
x-4 >/ -1
+4 both sides
x </ 5
x >/ 3
this is shown in the graph
A wheel in this scale drawing is 4 cm wide. The ratio of the drawing is 1:14. How wide is the actual wheel in cm?
Answers
1:14 means that for every 1 cm it is drawn at it is actually 14 cm
so multiply 4 x 14 = 56
it is actually 56 cm wide
) there are exactly 20 students currently enrolled in a class. how many different ways are there to pair up the 20 students, so that each student is paired with one other student
Answers
There are at least two ways to see this (possibly more).
One way is to note that, first, we have to select 2 students for the first pair; that's C(20, 2) (where by C(20, 2) I mean "20 choose 2"; that is, 20! / (18! * 2!). )
Then, for each way of selecting 2 students for the first pair, I have to select 2 of the remaining 18 students for the second pair, so I multiply by C(18, 2).
Continuing in this manner, I get C(20, 2) * C(18, 2) * ... * C(2, 2).
But it doesn't matter in this situation the order in which I pick the pairs of students. Since there are 10! different orders in which I could pick the individual pairs, then I want to divide the above by 10!, giving me the answer
[C(20, 2) * C(18, 2) * ... * C(2, 2)] / 10!.
This is the same as your answer, because C(n , 2) = n(n - 1) / 2, so we can simplify the above as
[(20 * 19) / 2 * (18 * 17) / 2 * ... * (2 * 1) / 2] / 10!
= 20! / [2^10 * 10!]
= 20! / [(2!)^10 * (10!)].
Another way is to reason as follows:
1. First, arrange the 20 students in a line; there are 20! ways to do this
2. We can get a pairing by pairing the 1st and 2nd students in line together, the 3rd and 4th students together, etc.
3. But if I switch the order of the 1st and 2nd student, then this doesn't give a different pairing. I don't want to count both orderings separately, so I divide by 2!
4. The same argument from step 3 holds for the 3rd and 4th student, the 5th and 6th student, etc., so I need to divide by 2! nine more times
5. Finally, the particular order in which I selected the ten pairings are unimportant--for example, the following orderings don't produce different pairings:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
3, 4, 1, 2, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
So I need to further divide by the number of ways I can arrange the ten pairs, which is 10!.
To convert 2.7 hours into seconds, which two ratios could you multiply by?
Answers
amount of minutes x 60 (for seconds) = amount of seconds.
IN this case
2.7 x 60 = 162 minutes
162 x 60 = 9720 seconds.
so the two rations are 1:60 or (hr: min) then 1:60 or (min: seconds)
hope this helps :D
Bob's Skate Shop had a profit of $3,563 during the month of August. The company models its profit using P=x^2+10x-12
, where x is the number of skateboards the company sells. How many skateboards did the company sell during the month of August? A. 50 B. 55 C. 60 D. 75
Answers
The company sold 55 skateboards.
Every evening Jenna empties her pockets and puts her change in a jar. At the end of the week she counts her money. One week she had 38 coins all of the dimes and quarters.When she added them up she had a total of $6.95
Answers
d = dimes
q = quarters
d+q = 38 coins
q=38-d
0.25q + 0.10d=6.95
0.25(38-d)+0.10d=6.95
9.5-0.25d+0.10d=6.95
-015d=-2.55
d=-2.55/-0.15 = 17
q=38-17 =21
21*0.25 =5.25
17*0.10 = 1.70
5.25+1.70 = 6.95
she had 21 quarters and 17 dimes
Find the product and quotient of 24.6 and 1.2
Answers
Quotient: 24.6 / 1.2 = 20.5
The product of 24.6 an 1.2 is 2.88 and quotient of 24.6 and 1.2 is 2.
What is product and quotient?Product is of two or more numbers is the result of multiplying these numbers, and
Quotient of two numbers is the result of division of these numbers.
Now the given numbers are 2.4 and 1.2.
Now for product of these numbers let us multiply these numbers. So we have,
2.4 x 1.2 = 2.88
Hence the product of 2.4 and 1.2 is 2.88
Again for quotient of 2.4 and 1.2, let us divide these numbers. So we have,
2.4 ÷1.2 = 2
Hence the quotient of 2.4 and 1.2 is 2.
Therefore,The product of 24.6 an 1.2 is 2.88 and quotient of 24.6 and 1.2 is 2.
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In January 2008, the temperature in parts of Minnesota fell from 46 F degrees to -14 F degrees over a 24 hour period. What was the average temperature change per hour?
Answers
60/24 = 2.5 degree drop per hr...so the average temp change is -2.5 degrees per hr
The average temperature change per hour is -2.5 F per hour.
What is temperature?Temperature is simply an average measure of the kinetic energy for particles of matter.
Here,
at t = 0 hour, Temp. = 46 F
at t = 24 hours, Temp. = -14 F
Now, average temp change per hour = (T₂-T₁)/(t₂-t₁)
= (-14-46)/(24-0)
= -60/24
= -2.5 F per hour
Thus, the average temperature change per hour is -2.5 F per hour.
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A student club with 30 members need to chose an executive committee. there are five members of the committee and all have equal votes. how many possible sets of members are there for the committee
Answers
write in order from least to greatest
Answers
HELP PLZ? You want to help build an awards podium for a track meet. If the podium has the dimensions shown, what is its volume?
Answers
volume = l x w x h
area 1 = 3 x 1.5 x 2 = 9 cubic feet
area 2 = 2 x 1.5 x 2 = 6 cubic feet
area 3 = 1.5 x 1 x 2 = 3 cubic feet
9+6+3 = 18 cubic feet total
The volume of Podium is: 18 cubic feet.
Step-by-step explanation:The volume of Podium is equal to the volume of 3 cuboids of different heights.
We know that a volume of cuboid with length l, width b and height h is given by:
Volume= l×b×h
Hence,
Volume of cuboid numbered as 3 is:
Volume= 1×2×1.5= 3 cubic feet.
Volume of cuboid numbered as 2 is:
Volume=2×2×1.5=6 cubic feet.
Similarly volume of cuboid numbered as 1 is:
Volume= 3×1.5×2=9 cubic feet.
Hence, the Volume of Podium is:
3+6+9=18 cubic feet.
a model train engine is 6 inches long the real train is 42 feet long what is the scale factor
Answers
Describe the two possible ways to use the angle of depression that is outside a right triangle to find the measure of an angle inside the triangle?
Answers
=> Angle of depression = 90° - up angle
=> up angle = 90° - angle of depression
2) The angle of depression is equal to the bottom angle of the right triangle.
=> bottom angle = angle of depression.
G the base of a solid is the circle x2 + y2 = 9. cross sections of the solid perpendicular to the x-axis are equilateral triangles. what is the volume, in cubic units, of the solid
Answers
Final answer:
To find the volume of the solid, we can use the formula V = A * h, where A is the area of the base and h is the perpendicular height. Given that the base is a circle and the cross sections of the solid are equilateral triangles, we can calculate the volume by integrating the expression for the area of the cross section from -3 to 3.
Explanation:
To find the volume of the solid, we can use the formula V = A * h, where A is the area of the base and h is the perpendicular height.
Given that the base is a circle with equation x^2 + y^2 = 9, we can determine the radius of the circle to be 3 units.
The cross sections of the solid perpendicular to the x-axis form equilateral triangles. The side length of an equilateral triangle is equal to the radius of the circle, which is 3 units. Since the height of each elemental cylinder is 2y, and the height of an equilateral triangle is h = √(3^2 - (3/2)^2) = √(9 - 9/4) = √(36/4 - 9/4) = √(27/4), the volume of each elemental cylinder is 4π(3^2 - x^2)^(1/2) dx = 4π(27 - 4x^2)^(1/2) dx.
To find the total volume of the solid, we integrate the expression 4π(27 - 4x^2)^(1/2)dx from x = -3 to x = 3.
∫(4π(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π∫(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π∫(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π∫(27 - 4x^2)^(1/2)dx from -3 to 3 = 4π(3^3/3 - (-3)^3/3) = 36π units^3.
The following statistics represent weekly salaries at a construction company.
Mean $550. First quartile $480
Median $630 third quartile $700
Mode $605. 91st percentile $891
The most common salary is ?
The salary that half the employees salaries surpass is ?
The percent of employees salary that serve because $700 is ?
Percent of employees salaries that were less than $480 is
The percent of employees salaries this surpass $891 years
if the company has 104 is the total weekly salary of all employees he is $?
I don't know how to solve the questions
Answers
Answer:
The most common salary is $605. The salary that half the employees salaries surpass is $630. The percent of employees salary that serve because $700 is 75%. Percent of employees salaries that were less than $480 is 25%. The 9% percent of employees salaries this surpass $891 years. The total weekly salary of 104 employees is 57200.
Step-by-step explanation:
It is given that mean is $550, first quartile is $480, median is $630, third quartile is $700, mode is $605 and 91st percentile is $891.
First quartile is at 25% of the data, median is at 50% of the data, third quartile is at 75% of the data.
The mode of a set of data values is the value that occurs most often.
The most common salary is mode, therefore the most common salary is $605.
The salary that half the employees salaries surpass is $630. Because median is the half of the data.
The percent of employees salary that serve because $700 is 75%. Because $700 is third quartile.
Percent of employees salaries that were less than $480 is 25%. Because $480 is first quartile.
The percent of employees salaries this surpass $891 years is 9%. Because $891 is 91 percentile. Therefore 9% employees get more than $891.
If the company has 104 employees than the total salary of employees is
[tex]104\times 550=57200[/tex]
because means is $550, therefore the total weekly salary of 104 employees is 57200.
The most common salary is [tex]605USD[/tex].
The salary that half the employees' salaries surpass is [tex]630USD[/tex].
The percent of employees salary that serves because [tex]700USD[/tex] is [tex]75[/tex]%.
The percent of employees' salaries that were less than [tex]480USD[/tex] is [tex]25[/tex]%.
The [tex]9[/tex]% percent of employees' salaries surpass [tex]891USD[/tex] years.
The total weekly salary of [tex]104[/tex] employees is [tex]57200[/tex].
Given Mean is [tex]550USD[/tex], the first quartile is [tex]480USD[/tex].
The Median is [tex]630USD[/tex], the third quartile is [tex]700USD[/tex], the Mode is [tex]605 USD[/tex] and the [tex]91st[/tex] percentile is [tex]891USD[/tex].
The first quartile is at [tex]25[/tex]% of the data, the median is at [tex]50[/tex]% of the data, the third quartile is at [tex]75[/tex]% of the data.
The mode of a set of data values is the value that occurs most often, So the most common salary is a mode, therefore the most common salary is [tex]605USD[/tex].
As the median is half of the data, the salary that half of the employees' salaries surpass is [tex]630USD[/tex].
Given that [tex]700USD[/tex] is the third quartile, so the percent of employees ' salary that serves
The Percent of employees' salaries that were less than is % as first quartile.
The percent of employees salaries this surpass $891 years is [tex]9[/tex] %. Because [tex]891USD[/tex] is [tex]91[/tex] percentile. Therefore more than [tex]891USD[/tex].
If the company has [tex]104[/tex] employees then the total salary of employees is
[tex]104\times550=57200[/tex] because means is [tex]550USD[/tex], therefore the total weekly salary of [tex]104[/tex] employees is [tex]57200 USD[/tex].
Therefore, the most common salary is [tex]605USD[/tex]. The salary that half the employees' salaries surpass is [tex]630USD[/tex]. The percent of employees salary that serves because [tex]700USD[/tex] is [tex]75[/tex]%. The percent of employees' salaries that were less than [tex]480USD[/tex] is [tex]25[/tex]%.The [tex]9[/tex]% percent of employees' salaries surpass [tex]891USD[/tex] years and the total weekly salary of [tex]104[/tex] employees is [tex]57200[/tex][tex]USD[/tex].
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What is the constant high temperature at which organisms are able to live in thermal vents and volcanoes? A. 250 degrees Celsius B. 250 degrees Fahrenheit C. 250 degrees Kelvin D. 250 degrees Newton
Answers
Answer:
it is actually 250 degrees Fahrenheit
Step-by-step explanation:
10 times as many as 1 hundred is
Answers
Compare the functions f(x) = x5 and g(x) = 5x by graphing both functions in several viewing rectangles. find all points of intersection of the graphs correct to one decimal place. (enter your answers as a comma-separated list. round any decimal answers to one decimal place.)
Answers
f(x) = x⁵ and g(x) = 5x
are shown in the figure below.
The initial plot interval is -2 ≤ x ≤ 2.
In order to determine the points of intersection (to 1 decimal place accuracy) more graphs (shown in accompanying figures) were necessary.
The points of intersection are
x = -1.5, x = 0, and x = 1.5
Answer:
The points of intersection are x = -1.5, 0, and 1.5 (accurate to 1 decimal place)
To compare the functions f(x) = x^5 and g(x) = 5x, graph both functions and find their points of intersection.
Explanation:To compare the functions f(x) = x^5 and g(x) = 5x, we can graph both functions in several viewing rectangles. By finding the points of intersection of the graphs, we can compare their values at those points.
Start by graphing the function f(x) = x^5 using a graphing calculator or software. This will give us a curve with a steep increase as x gets larger.Next, graph the function g(x) = 5x in the same viewing rectangle as f(x). This will give us a straight line that increases more gradually as x gets larger.Identify the points of intersection between the graphs of f(x) and g(x). These are the x-values at which the two functions have the same y-value. Round these x-values to one decimal place and list them as the points of intersection.52.85 rounded to nearest tenth
Answers
Answer:
The required number is 52.9.
Step-by-step explanation:
Given : Number 52.85
To find : The number rounded to nearest tenth?
Solution :
Rounded to the tenth means round the number so that only one number left after the decimal.
Rules of rounding :
1) If the hundredth place value is >5 or =5 then add 1 to first digit and remove second.
2) If the hundredth place value is <5 ,then hundredth place number is removed.
Now, In the number 52.85
The hundredth place value is 5 so, 1 is added to the 8
Then the required number is 52.9.
Find the general solution of the given system. dx dt = −6x + 4y dy dt = − 7 4 x + 2y
Answers
[tex]\begin{bmatrix}-6&4\\\\-\frac74&2\end{bmatrix}[/tex]
has eigenvalues given by
[tex]\begin{vmatrix}-6-\lambda&4\\\\-\frac74&2-\lambda\end{vmatrix}=\lambda^2+4\lambda-5=(\lambda+5)(\lambda-1)=0[/tex]
The eigenvalues are thus [tex]\lambda_1=-5[/tex] and [tex]\lambda_2=1[/tex].
For the eigenvalue [tex]\lambda_1[/tex], the corresponding eigenvector [tex]\eta_1[/tex] satisfies
[tex]\begin{bmatrix}-1&4\\\\-\frac74&7\end{bmatrix}\begin{bmatrix}\eta_{1,1}\\\eta_{1,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}[/tex]
[tex]\implies\eta_{1,1}=4\eta_{1,2}[/tex]
so that we can choose [tex]\eta_1=\begin{bmatrix}4\\1\end{bmatrix}[/tex].
For [tex]\lamda_2=1[/tex], we have
[tex]\begin{bmatrix}-7&4\\\\-\frac74&1\end{bmatrix}\begin{bmatrix}\eta_{2,1}\\\eta_{2,2}\end{bmatrix}=\begin{bmatrix}0\\0\end{bmatrix}[/tex]
[tex]\implies7\eta_{2,1}=4\eta_{2,2}[/tex]
and we can choose [tex]\eta_2=\begin{bmatrix}4\\7\end{bmatrix}[/tex] for the corresponding eigenvector.
Then the general solution to the ODE system is given by
[tex]\begin{bmatrix}x(t)\\y(t)\end{bmatrix}=C_1\begin{bmatrix}4\\1\end{bmatrix}e^{-5t}+\C_2\begin{bmatrix}4\\7\end{bmatrix}e^t[/tex]
Is the GCF of any two odd numbers is always odd?
Answers
This is because an odd number must have all odd factors. If it has even 1 even factor, the result is an even number. For example, 4*9*9*3 would be even because of the 4.
Riverside bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. the loan (principal plus interest) must be repaid at the end of the year. midwest bank also offers to lend you the $50,000, but it will charge an annual rate of 6.2%, with no interest due until the end of the year. how much higher or lower is the effective annual rate charged by midwest versus the rate charged by riverside
Answers
The effective annual rate of Midwest is 0.2% lower than the rate charged by Riverside.
Further Explanation:
Riverside Bank:
Principal = $50,000
Duration = 1 year
APR = 6.5%
The amount paid after 1 year is
A = 50000(1 + 0.065/12)¹² = $53,348.59
Midwest Bank:
Principal = $50,000
APR = 6.2%
Duration = 1 year
The amount paid after 1 year is
A = 50000*(1 + 0.062) = $53,100.00
The amount charged by Midwest is lower:
Let r = the effective annual rate of Riverside Bank.
Then
50000*(1 + r) = 53348.59
1 + r = 53348.59/50000 = 1.067
r = 0.067 = 6.7%
Effective annual rate:
The viable yearly financing cost is the loan fee that is really earned or paid on a venture, advance or other money related item because of the aftereffect of intensifying over a given timeframe. It is additionally called the powerful loan cost, the viable rate or the yearly comparable rate.
Instructions to Calculate the Effective annual Rate:
1. Determine the expressed loan fee. The expressed financing cost (additionally called yearly rate or ostensible rate) is generally found in the features of the credit or store understanding.
2. Determine the quantity of aggravating periods.
3. Apply the EAR Formula: EAR = (1+ I/n)n – 1.
Subject: mathematics
Level: college
Keywords: Riverside Bank, Midwest Bank, The amount charged by Midwest is lower, Effective annual rate, Instructions to Calculate the Effective annual Rate.
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When you convert 0.63 to a fraction, which of the following could be the first step of the process
Answers
[tex]0.63 \\ = \frac{0.63}{1} \times \frac{100}{100} \\ = \frac{0.63 \times 100}{100} \\ = \frac{63}{100} [/tex]
Answer:
[tex]0.63 = \frac{63}{100} [/tex]
What addition doubles fact can help you find 4+ 3? Explain how you know
Answers
By using the commutative law of addition, the result of the addition would be 7.
What is commutative property of addition?The commutative property of addition says that it doesn't matter how we add two numbers, the result of the addition would be same.
For two numbers x and y, we have:
x + y = y + x
Thus, if we take 3 numbers as a,b and c, then:
a + b + c = b + a + c = b + c + a = a + c + b = c + a + b = c + b + a
And so for any amount of numbers.
We have been Given that the expression 4 + 3, we need to determine what addition shows that the statement is true.
We know that the sum of 4 and 3 is 7, we can explain that by using the commutative law of addition as shown;
According to the law, A + B = B+ A
4 + 3 = 3 + 4 = 7
Therefore, By using the commutative law of addition, the result of the addition would be 7.
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While passing a slower car on the highway, i accelerate uniformly from 12 m/s to 24 m/s in a time of 10.0s. How far do you travel during this time and what is the magnitude of your acceleration
Answers
vf-vi=at (final velocity minus initial velocity is equal to acceleration times time)
We know vf, vi, and t so we can solve for acceleration:
24-12=a10
12=10a
a=1.2
That is the acceleration, we will need to integrate with respect to time twice...
v=⌠a dt
v=at+vi , we know a=1.2m/s^2 and vi=12m/s
v=1.2t+12,
x=⌠1.2t+12 dt
x=1.2t^2/2+12t+xo, we can just let xo=0 for this problem...
x(t)=0.6t^2+12t
Now we know that this acceleration lasts for 10 seconds so the distance traveled in that time is:
x(10)=0.6(10^2)+12(10)
x(10)=60+120
x(10)=180 meters
Karen bought 4⁄5 pound of broccoli and 2⁄10 pound of cauliflower. How many more pounds of broccoli did she buy?
Answers
Chase makes 2 gallons of soup for a dinner party. He serves 10 cups of soups to his guests. How many cups of soup will he have left over?
Answers
1 gallon = 16 cups
2 gallons = 16 x 2 = 32
32-10=22
there will be 22 cups left over
Answer:
Step-by-step explanation:
1 gallon = 16 cups
2 gallons = 16 x 2 = 32
32-10=22
there will be 22 cups left over
You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. you will deposit your savings in an account that pays 5.2% interest. how much will you have just after you make the 3rd deposit, 3 years from now?
Answers
Fv=pmt [(1+r)^(n)-1)÷r]
Fv future value?
PMT payment per year 4200
R interest rate 0.052
N time 3 years
Fv=4,200×(((1+0.052)^(3)−1)÷(0.052))
Fv=13,266.56
Mary is making Magic Marshmellow cake . The recipe calls for 3/4 cup of milk and 2 eggs per serving. The wants to make enough cake for 20 people . How much milk will Mary need?
Answers
and surely you know how much that is.