Write the equation of a parabola with the focus at (3, 0) and the directrix at x = –3.
x^2 = –3y
y^2 = –3x
x^2 = 12y
y^2 = 12x
Answers
The equation of the parabola whose focus is at (3, 0) and directrix at x = - 3 is y² = 12 · x. (Correct choice: D)
How to derive the equation of the parabola
In this problem we need to determine the equation of a parabola based on the information of the focus and the directrix. The vertex form of the parabola is described below:
4 · p · (x - h) = (y - k)²
Where p is the distance from the vertex to the focus. The coordinates of the vertex is the midpoint of the line segment of the least distance between the directrix and the focus.
First, determine the coordinates of the vertex:
(h, k) = 0.5 · (- 3, 0) + 0.5 · (3, 0)
(h, k) = (0, 0)
Second, calculate the distance from the vertex to the focus:
p = 3 - 0
p = 3
Third, write the vertex form of the parabola:
y² = 12 · x
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Related Questions
What should be added to 5/6 to get 41/24
Answers
Answer: 26/24
Step-by-step explanation:
First we have to convert 5/6 with a denominator of 24 so 6 times what makes 24, that is 4 & whatever you do with the denominator, you have to do it with the numerator. So 5 times 4 is 20, the new fraction is 20/24. Now, we need to find what we need to add with 20/24 to get 41/24, so we subtract 20/24 from 41/24 & that is 21/24. We can check if it's correct by adding both 21/24 and 20/24 & that makes 41/24.
5/6 + x = 41/24
x = 41/24 - 5/6
x = 41 - ( 5 multiplied by 4) / 24
x = 41 - 20 / 24
x = 22 / 24
x = 21/3 / 24/3
Final answer x = 7/8
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
Answers
A colony contains 1500 bacteria. The population increases at a rate of 115% each hour. If x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)x
f(x) = 1500(115)x
f(x) = 1500(2.15)x
f(x) = 1500(215)x
Answer:
A
Step-by-step explanation:
Which of the following examples would be continuous data?
How many people are late boarding an airplane?
The amount of diapers a newborn uses in a day.
The number of television shows on Netflix.
The volume of liquid in a pop can.
Answers
The example that would be continuous data is A. The volume of liquid in a pop can.
What is a continuous data?Continuous data is data that has no fixed value. Continuous data includes height, weight, temperature, and length. Some continuous data, such as a baby's weight in its first year or the temperature in a room throughout the day, will change over time.
Discrete data is a type of numerical data that consists of whole, concrete numbers that have specific and fixed data values determined by counting. Continuous data consists of complex numbers and varying data values measured over a specific time period.
In this case, the volume of the liquid is s continuous data.
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A spinner is spun 800 times.
The probabilities it lands on each colour
are shown below.
The probability it lands on red is the same
as the probability it lands on yellow.
Colour Red Green Brown Yellow
Probability. 0.3. 0.54
How many times would you expect it to
land on each colour?
Red: 0
Brown: Yellow:
O
Green:
0
Answers
Answer:
green 45 times or 40 a note
You want to have $300,000 when you retire in 30 years. If you can earn 4% interest compounded continuously, how much would you need to deposit now into the account to reach your retirement goal?
Answers
An amount of $ 92,495.60 must be the initial deposit to become into $ 300,000 by compound interest.
How much money must be deposited to obtain a given quantity for retirement?
In this problem we must determine the initial deposit that must become into $ 300,000 by compound interest after a period of 30 years. Compound interest model is a model where money gains interest continuously, whose formula is:
C' = C · (1 + r / 100)ⁿ
Where:
C - Initial deposit, in monetary units.C' - Final deposit, in monetary units. r - Interest rate, in percentage.n - Number of periods, in years.If we know that C' = 300,000, r = 4 and n = 30, then the initial deposit is:
C = C' / (1 + r / 100)ⁿ
C = 300,000 / (1 + 4 / 100)³⁰
C = 92,495.60
The initial deposit must be $ 92,495.60.
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find the Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ]
Answers
The Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ] is ( 5/√2, -5/√2)
The polar cordinates given are (r,θ)=(5,− π/4)
And we need to find the cartesian coordinates
We have,
x=rcosθ, y=rsinθ
x=5cos(− π/4) ,y=5sin(− π/4)
x= 5/√2 ,y=− 5/√2
So, the cartesian form is ( 5/√2, -5/√2)
The Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ] is ( 5/√2, -5/√2)
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Brett tallies up the transactions in his check register and comes up with a total balance of $248.53, but his bank statement says that his balance is $257.72. Which of the following are still outstanding?
I. A $44.09 check to the electronics store
II. A $73.98 check to the mechanic
III. A $49.96 paycheck deposit
IV. A $64.79 check deposit from Brett’s cousin
Answers
The third grade teachers had a pizza party. They ordered 11 large pizzas and each pizza had 8 slices. There were 4 classrooms in the grade. Estimate how many slices of pizza each classroom can have if the pizzas are shared equally.
Choose 1 answer: 20 slices 50 slices 300 slices 320 slices
Answers
Answer:
20 slices
Step-by-step explanation:
If there were 11 large pizzas with 8 slices per pizza, that would mean that there are a total of 88 slices of pizza.
If there are four classrooms, that means that if each classroom had 20 slices, there would be enough for everyone with 8 pieces leftover.
20 x 4 = 80
Translate the sentence into an equation.
The square of a number is equal to the square root of that number.
Answers
The equation of the sentence, the square of a number is equal to the square root of that number, is [tex]x^{2} =\sqrt{x}[/tex].
According to the question,
We have the following information:
The square of a number is equal to the square root of that number.
Now, let's take this number to be x.
Now, square of this number will be [tex]x^{2}[/tex] and the square root of this number will be [tex]\sqrt{x}[/tex].
Now, according to the sentence, we will have the following expression:
[tex]x^{2} =\sqrt{x}[/tex]
Hence, the equation of the sentence, the square of a number is equal to the square root of that number, is [tex]x^{2} =\sqrt{x}[/tex].
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Jacob held different part-time jobs during his summer holiday. The table below shows the total money he earned for different amounts of time, in hours.
What type of association will the scatter plot for this data represent between the number of hours worked and the total money earned?
1. A positive nonlinear association
2. A positive linear association
3. A negative nonlinear association
4. A negative linear association
Answers
Given the table on the total money earned, the type of association the scatter plot would represent is 2. A positive linear association
What is a positive linear association?When two variables are said to have a positive linear association, it means that they move in the same direction together. When one of them increases, the other increases as well. It also means that they are increasing by a uniform amount. For instance, when one variable increases by 3, the other increases by 6, always.
The hours worked here are increasing as well as the money earned by Jacob. The hours worked is increasing by 1, and the money earned is increasing by 4. This is therefore a positive linear association.
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Change 4 1/6to an improper fraction.
Answers
Answer:
4 1/6 = 25/6
Why?:
Multiply the denominator with the mixed number 4.
Add the numerator 1 and get 25.
Then, you keep the denominator (Which is 6) on the bottom.
And finally, you get
25/6
Answer:
25/6
Step-by-step explanation:
first start by multiplying 6 and 4, which leads you to 24
then add the 1 from the numerator and you get 25 as your numerator.
for the denominator, leave six as it is so it becomes 25/6
What is the x-intercept of the line with the equation 7x+4y=-28?
Answers
Step by step
Substitute 0 for y and solve for x
7x + (4)(0) = -28
Divide both sides by 7 to solve for x
7/7 x = -28/7
x = -4
Explanation: to find the X intercept you need to make y=0 which basically eliminates the 4y leaving you with 7x=-28 then you just divide both both sides by 7 which leaves you at x=-4
A cube has an edge measuring 7 inches.
What is the volume of the cube, in inches?
Answers
line x is the perpendicular bisector of segment ZY
what does YT equal
Answers
Answer:
Step-by-step explanation:
ZT=YT
x+3=3x-11
x-3x=-11-3
-2x=-14
x=-14/-2=7
YT=3×7-11=21-11=10
YT=10
The Monty Corporation has a staff of sales people who are paid a monthly salary of $1,600.00 plus an incremental commission based on the table below. If Sally sells $29,700.00, what is her total gross pay for the month
Answers
Answer:
Step-by-step explanation:
-28,100 if you subtract 29,700.00 - 1,600.00 = -28,100
A bank found that 2.5% of its loans to new small businesses become delinquent. If 400 small businesses are selected randomly from the bank’s files, what is the probability that at least 12 of them are delinquent? Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.
.3155
Answers
The probability that at least 12 are delinquent is given as 0.3155
How to solve for the probabilityProbability can be defined as the likelihood of getting an outcome out of other outcomes.
We have the mean u = np
where n = 400
p = proportion = 2.5% = 0.025
= 400 x 0.025
= 10
we have to find the population standard deviation
= [tex]\sqrt{np(1-p)}[/tex]
= √400 x 0.025 (1 - 0.025)
= 3.1225
P (X ≥ 12)
= P(X ≥ 11.5)
= 11.5 - 10 / 3.1225
= 1 - P(z < 0.4804)
= 1 - 0.6845
= 0.3155
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The weight of substance X is halved per minute. In the beginning, the weight of substance X is 5kg.
(a) Find the weight of substance X after 4 minutes.
(b) After how many minutes will the weight of substance X first go below 0.5kg?
Please give your answer as an integer.
EMERGENCY PLEASE HELPPPP
Answers
Answer:
a: 0.3125kg
b: 4
Step-by-step explanation:
for a we simply calculate 5 * 0.5 ^ 4.
we then see that the weight after 4 minutes is smaller than 0.5kg, but if we go back to 3 minutes (by multiplying our solution to a by 2), giving us 0.625kg, which is now bigger than 0.5kg. meaning 4 minutes is the first whole amount that will give us a weight smaller than 0.5kg.
Please help I’ve been stuck on this question for awhile thanks:)
Does anyone know how to do this?
Answers
The length of BC is 50 miles (approx).
What is Trigonometry?
Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.
Solution:
In the triangle ABC,
The perpendicular = BC
The Base = AB = 6 miles
by using the trigonometric ratio "tan"
tan (58) = BC / AB
8.33 = BC / 6
49.98 miles = BC
BC = 50 miles (approx)
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Please help: Which numbers are in order from least to greatest?
A.
0.561, 8.627, 5.325
B.
4.057, 4.122, 5.008
C.
1.742, 1.558, 1.671
D.
6.705, 6.527, 6.211
Answers
Simplify the experession
6²-3³)÷7
Answers
Answer:
9/7 or 1.285714
Step-by-step explanation:
Answer:9/7
Step-by-step explanation:
4y-5x=3(4x-2y+1) in standard form
Answers
Answer:
7x+10y=3
Step-by-step explanation:
Standard Form= Ax+By=c
Distribute first
4y-5x=12x-6y+3
Add 6y
10y-5x=12x+3
Add 12x
7x+10y=3
Complete the chart to show similarities and differences between multiplying by 0.1, 0.01, 10, 100. Tell how many places the decimal point appears to move and in which direction when you multiply by each
Answers
Answer:
they all are being multiplied by 10
Step-by-step explanation:
0.01 x 10 = 0.1
0.1 x 10 = 1
1 x 10 = 10
10 x 10 = 100
Identify the domain and range of the relation, and determine whether the relation is a function.
{(0, 3),(-1/3,0),(-5, 2),(1/3,4)}
Answers
range: {3,0,2,4}
it is a function
8 (x + 2 ) when x = 6
Answers
Answer:
64
Step-by-step explanation:
8(x+2) when x=6
replace x with 6
8(6+2)
distribute 8
48+16= 64
A relation contains the points (1,-4), (3, 2), (4, -3), (x, 7), and (-4, 6).
For which value of a will the relation be a function?
O-4
O-3
O 3
O 4%
Answers
For x = -3 the relation will be a function.
We know that a relation is a function when for each input there is exactly one output.
In this question, we need to find the value of x for which the relation will be a function.
We need to select the value of x such that x ≠ 1, 3, 4, -4
This means x must be -3
Therefore, For x = -3 the relation will be a function.
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What is the slope of the line shown?
A. slope = 2
B. slope = 1/2
C. slope = -1
D. slope = 1
Answers
Answer:
I think b 1/3
Step-by-step explanation:
slope is rise over run
Answer:
1/2
Step-by-step explanation:
find 2 clear points A(2,0) B(8,3)
use the formula of the angular coefficient
[tex]c = \frac{y2 - y1}{x2 - x1} [/tex]
Kalia’s parents give her simple interest on any money she saves for college. Which equation and solution represents the total interest, T, earned when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10?
T = 100 • (10 + 0.1); $1,010
T = 100 • (10 + 0.01); $1,001
T = 100 • 0.1 • 10; $100
T = 100 • 0.01 • 10; $10
Answers
The equation and solution representing the total interest, T, earned by Kalia when the principal amount is $100, the annual simple interest rate is 1%, and the number of years is 10, is D. T = 100 • 0.01 • 10; $10.
What is the simple interest?Simple interest is interest that does not compound.
Simple interest does not accumulate interest, unlike compound interest, which is added to the principal for subsequent interest.
Principal = $100
Simple interest rate = 1%
Period of savings = 10 years
The simple interest in dollars = T
T = 100 x 0.01 x 10
T = $10
Thus, Option D correctly represents the total interest earned by Kalia.
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What is the slope of the line passing through the points (2, 4) and (5, 6)?
A. 6/11
B. -2/3
C. 7/10
D.2/3
Answers
Answer:
D, 2/3
Step-by-step explanation:
Using the Slope formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] we can find the slope of the line.
Input values:
[tex]m=\frac{6-4}{5-2}=\frac{2}{3}[/tex]
[tex]m=\frac{2}{3}[/tex]
PLS ANSWER THIS QUESTION
FAST
WILL MARK BRAINLIEST
Answers
Angle x= 45
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.acc to the question-
N + M = 90X + X= 902X=90X=45Hence, Angle x= 45
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The hire purchase price of a refrigerator is $6509.A deposit of $500 is made and the reminder is paid in equal monthly payments of $250. Calculate the number of monthly payments that must be made.
Answers
Step-by-step explanation:
The hire purchase price of a refrigerator is $6509.A deposit of $500 is made and the reminder is paid in equal monthly payments of $250. Calculate the number of monthly payments that must be made.
amount paid over x months:
$6509 - $500 = $6,009
Equal payments of $250:
$6,009 / $250 = 24.036 months of payments
[Depending on if they want the answer rounded up, answer may become 25]
Answer:
hire purchase= $6509
deposit=$500
monthly payment=$250
no of monthly payment that must be made=hire purchase - deposit divided by monthly payment
$6509-$500/$250=$6009/$250= 24.036 month
