The equation of the parabola with focus (-2,4) and directrix y = 0 is (x + 2) = 8(y - 2). This is derived by finding the vertex and applying the general equation for a vertically oriented parabola.
To find the equation of a parabola with a given focus and directrix, we use the definition that a parabola is the set of all points that are equidistant from the focus and the directrix. In this case, the focus is at (-2,4) and the directrix is y = 0. The vertex of the parabola will thus be halfway between the focus and the directrix, which means it will lie on the line y = 2 (since the focus has a y-coordinate of 4 and the directrix is at y = 0).
The standard form equation of a vertically oriented parabola with its vertex at the origin is x = 4py, where p is the distance from the vertex to the focus (or to the directrix). For a parabola that is shifted to have a vertex not at the origin, the equation is (x-h)² = 4p(y-k) where (h,k) is the vertex.
In this scenario, because the vertex is not at the origin and the parabola opens upwards (since the directrix is below the focus), we'll adjust the standard form equation to take these factors into account. The vertex (h,k) is (-2,2), the focus is (-2,4), thus p = 2. Therefore, the equation is (x + 2)² = 4*2*(y - 2)
6. Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 147 of the first 156 customers have not received a star on their receipts. What is experimental probability of winning a free gallon of milk?
A. 11/156
B. 49/52
C. 2/39
D. 3/52*****?
The experimental probability of winning a free gallon of milk will be calculated as under -
It is given that, total number of outcomes = 156
Non-winning customers = 147 (it is given in the question)
Thus, the winning customers will be = Total outcomes - Non-winning customers
Expected winning customers = 156 - 147 = 9
The probability is calculated as -
Probability (Winning customer) = [tex] \frac{Winning Customers}{Total Customers} [/tex]
Probability (Winning customer) = [tex] \frac{9}{156} [/tex] = [tex] \frac{3}{52} [/tex]
Which expression is equivalent to 2m(3/2m+1)+3(5/3m-2)?
The expression is equivalent to [tex]\rm 3m^2+7m-6[/tex].
Given
Expression; [tex]\rm 2m \left (\dfrac{3}{2}m+1 \right )+3\left ( \dfrac{5}{3}m-2\right )[/tex]
How to find the equivalent expression to the given expression?To find the equivalent expression first multiply by term then combine like terms and simplify.
Therefore,
The expression is equivalent to;
[tex]\rm =2m \left (\dfrac{3}{2}m+1 \right )+3\left ( \dfrac{5}{3}m-2\right )\\\\=2m \times 3m + 1\times 2m + 5m \times 1-3\times 2\\\\=3m^2+2m+5m-6\\\\= 3m^2+7m-6[/tex]
Hence, the expression is equivalent to [tex]\rm 3m^2+7m-6[/tex].
To know more about Expression click the link given below.
https://brainly.com/question/10628562
How much of a 14% iodine solution should be added to 89 ounces of a 47% iodine solution to get a 29% solution
What is the standard deviation of the data set? 29, 36, 41, 53, 45, 30, 60
PLEASE HELP ME!! How much greater is the median number of employees at Restaurant A than the median number of employers at Restaurant B?
y = 2f(g(x))
dy/dx = 2f'(g(x)) * g'(x)
Differentiate again:
d^2y/dx^2 = 2f''(g(x)) * g'(x) * g'(x) + 2f'(g(x)) * g''(x)
d^2y/dx^2 = 2f''(g(x)) * (g'(x))^2 + 2f'(g(x)) * g''(x)
Am I correct in saying answer D?
What is the length of an arc cut off by an angle of 3 radians on a circle of radius 8 inches?
Find the fifth roots of 32(cos 280° + i sin 280°).
Correct Answer:
z1= 2(cos 56 deg + i sin 56 deg)
z2= 2(cos 128 deg + i sin 128 deg)
z3 = 2(cos 200 deg + i sin 200 deg)
z4 = 2(cos 272 deg+ i sin 272 deg)
z5 = 2(cos 344 deg+ i sin 344 deg)
Step-by-step explanation:
De Moivre's Theorem--> e^i theta = cos theta + i sin theta
The fifth root of 32 is 2 and 280/5 is 56
z1= 2(cos 56 deg + i sin 56 deg)
360deg/ 5 = 72 deg
(If it was asking for cubed root u would do 360/3. whatever the root is you divide that by 360)
z2= 2(cos 56 + 72) + (i sin 56 + 72)
z2= 2(cos 128 deg + i sin 128 deg)
z3 = 2(cos 128 + 72) + ( i sin 128 + 72)
z3 = 2(cos 200 deg + i sin 200 deg)
z4 = 2(cos 200 + 72) + (i sin 200 + 72)
z4 = 2(cos 272 deg + i sin 272 deg)
z5 = 2(cos 272 + 72) + (i sin 272 + 72)
z5 = 2(cos 344 deg + i sin 344 deg)
deg means degrees
How do u find the height of the base??
A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. What is the probability of a lock without all even digits? There to get a lock code with all even digits. There are 3,024 different 4-digit lock codes. There are to get a lock code without all even digits. The probability of a 4-digit lock code without all even digits is
Answer:
it's 24, 3000, and 3000/3024
Step-by-step explanation:
The probability for a 4-digit lock code using numbers 1-9 with no repeats and not all even is 2,904/3,024.
Explanation:To solve this, we need to find the total number of possible 4-digit lock codes using digits 1-9 with no repeats and not all even, then divide it by the total number of 4-digit lock codes using digits 1-9 with no repeats. Specifically, the lock code includes 5 different even numbers (2,4,6,8), and 4 different odd numbers (1,3,5,7,9). If the lock code is all even, we will have 5*4*3*2 = 120 possibilities. However, the total possibilities for 4-digit lock codes are 9*8*7*6 = 3,024. Thus the number of codes that are not all even digits is 3,024 - 120 = 2,904. Therefore, the probability for a 4-digit lock code not having all even digits is 2,904/3,024.
Learn more about Probability here:https://brainly.com/question/22962752
#SPJ12
In p.
e. A parachute is laid out on the gym floor. The parachute has a radius of 16 feet. Which measurement is closest to the circumference of the parachute in feet.
The circumference of the parachute is Option A (100.48 feet).
To find the circumference of the parachute, we use the circumference formula for a circle:
C = 2πr
Given the radius (r) is 16 feet, we substitute it into the formula:
C = 2π(16) = 32π
Using the approximate value of π (3.1416), we get:
C ≈ 32 × 3.1416 = 100.48 feet
Thus, the measurement closest to the circumference of the parachute in feet is 100.48 feet (Option A).
Complete question:
In PE a parachute is laid out on the gym floor. The parachute has a radius of 16 feet. Which measurement is closest to the circumference of the parachute in feet?
A. 100.48ft
B. 198.4ft
C. 49.6ft
D. 803.84ft
A town has a population of 5000 and grows at 2% every year. What will be the population after 5 years, to the nearest whole number?
The population of a town with an intial population of 5000, that grows at 2% every year would be 5520 after 5 years
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the population of the town after x years.
The population of 5000 grows at 2% every year. Hence:
100%+2% = 1.02, this gives:
y = 5000(1.02)ˣ
After 5 years:
y = 5000(1.02)⁵ = 5520
The population of a town with an intial population of 5000, that grows at 2% every year would be 5520 after 5 years
Find out more on equation at: https://brainly.com/question/2972832
statement must be true??
Given that AB is the bisector of DC. The third options of all the options are True.
B is the midpoint of DC.
In geometry, to bisect an entity means to disassociate it into two equal parts. A bisector is a line, ray, or segment that divides an entity into two equal parts. For illustration, a line that bisects an angle divides the angle into two angles with equal measures. A segment that bisects a line segment divides the line segment into two segments with equal lengths. A ray that bisects an angle extends from the vertex of the angle and divides the angle into two angles with equal measures.
As it is given that AB is the bisector of DC,
therefore, B, being the foot of AB on CD is the midpoint of DC.
Since DC is bisected by AB,
therefore, [tex]\angle[/tex] ABD = [tex]\angle[/tex] ABC.
Learn more about bisector here:
https://brainly.com/question/31893955
#SPJ4
Rewrite the expression log(3x) as an equivalent logarithmic expression using only addition.
Given that f(x) = x2 − 4x − 3 and g(x) = the quantity of x plus three, over four, solve for f(g(x)) when x = 9.
−6
3
6
9
Final answer:
The solution to f(g(x)) when x = 9 is -6.
Explanation:
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain), where each input is related to exactly one output.
Given:
f(x) = x2 - 4x - 3, g(x) = (x + 3) / 4
To find f(g(x)) when x = 9:
Calculate g(9): Substitute x = 9 into g(x) to get (9 + 3) / 4 = 12 / 4 = 3Substitute g(9) into f(x): Substitute g(9) = 3 into f(x) to get f(3) = 32 - 4(3) - 3 = 9 - 12 - 3 = -6Therefore, f(g(x)) when x = 9 is -6.
can someone please explain how to do this.
PLLLLLLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Find the value of n.
The sum of the digits of a two-digit number is 16. if the digits are reversed, the new number is 18 less than the original number. find the original number.
plz help me!!!!!!!
Instructions: Select the correct answer from each drop-down menu. When p2 – 4p is subtracted from p2 + p – 6, the result is . To get p – 9, subtract from this result.
-3p-6. 4p+3
5p-6 4p-15
4p+6. 4p+12
A line has a slope of -5 and passes through (1,-1). Which is the equation of the line in point-slope form?
Which of the following shows the true solution to the logarithmic equation 3log2(2x)=3
A.x=-1
B.x=1
C. x=-1 and x=1
D. x0 x=-1 and x=1
Answer:
Option B is correct.
Step-by-step explanation:
Given logarithmic equation,
[tex]3log_2(2x)=3[/tex]
[tex]log_2(2x)=\frac{3}{3}[/tex]
[tex]log_2(2x)=1[/tex]
since base of the log function is 2.
we take power of 2 on both sides.
[tex]2^{log_2(2x)}=2^1[/tex]
2x = 2
x = 1
Therefore, Option B is correct.
What is the value of x?
How long does it take for a letter to get from orlando to los angeles?
I need step by step instructions on how to get the y-intercept for the following function:
f(x)=x^3-18x^2+107x-210.
For the triangle above, find sin A. a. 36° c. 0.9323 b. 50° d. 0.385
An average infant is 20 inches long and weighs 7.6 pounds. if the child grows to 80 inches and keeps the same proportions,how much will the child weigh
They traveled 200 kilometers in total, and they biked 40 kilometers more than they were bussed. how many kilometers did they travele by bike
Which is the correct form of the quadratic formula? A) x = b ± b2 - 4ac a B) x = b ± b2 - 4ac 2a C) x = - b ± b2 - 4ac a D) x = - b ± b2 - 4ac 2a
The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).
Hence, option D) is the correct answer.
What is a Quadratic Equation?Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x using the quadratic formula;
x = (-b±√(b² - 4ac)) / (2a)
The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).
Hence, option D) is the correct answer.
Learn more about quadratic equations here: brainly.com/question/1863222
#SPJ2
At the start of the year northern lights had $8000 worth of merchandise. What do we know about northern lights?
A. The company ended with a net income last year
B. It’s a retail business
C. The company ended with a net loss last year
D. It’s a service business
Answer:
B. It's a retail Business
Step-by-step explanation:
Just by knowing that they have money worth in merchandise, you can say that they sell as a retail business, the first option A. is not posible because they dont have an income they just have inventory worth money. the C. is not possible because having $ 8000 positive value does not constitute loss and D. it's a service business, could be but the merchandise does not suffice all information.
The mean of a set of five numbers is 4.8. Given that the sixth number is x and the mean of these six numbers is 5.5, find the value of x.