The focus of a parabola is (2, 5) and the directrix is y = 3. Find the equation of the parabola in standard form.
Answers
The equation of the parabola in standard form whose focus is (2, 5) and directrix is y = 3 is equal to the quadratic equation y = 0.25 · x² - x + 5. (Correct answer: C)
How to derive the equation of a parabola
Since the directrix is a horizontal line, then we have a parabola with a vertical axis of symmetry. The standard equation of the parabola is described below:
y - k = [1/(4 · p)] · (x - h)² (1)
Where:
(h, k) - Location of the vertex.p - Distance between vertex and focus.By analytical geometry we understand that the least distance between the focus and the directrix is twice as the distance between the vertex and the focus. First, we find the coordinates of the vertex:
V(x, y) = 0.5 · F(x, y) + 0.5 · D(x, y)
V(x, y) = 0.5 · (2, 5) + 0.5 · (2, 3)
V(x, y) = (1, 2.5) + (1, 1.5)
V(x, y) = (2, 4)
By Pythagorean theorem we find that the distance between vertex and focus is 1. Then, the equation of the parabola in standard form is:
y - 4 = 0.25 · (x - 2)²
y - 4 = 0.25 · (x² - 4 · x + 4)
y - 4 = 0.25 · x² - x + 1
y = 0.25 · x² - x + 5
The equation of the parabola in standard form whose focus is (2, 5) and directrix is y = 3 is equal to the quadratic equation y = 0.25 · x² - x + 5. (Correct answer: C)
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Related Questions
tis the season slope formula
Answers
The slope is the change in vertical axis of a graph to its horizontal axisor the rise to run of a line.
The slope formulaThe slope is the change in vertical axis of a graph to its horizontal axis. This can also be the rise to run of a line.
The formula for calculating the slope of a line is given asL
Slope = rise/run
It can also be expressed as:
Slope = change in y-axis/change in x-axis
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Select the correct answer.
To solve this system of equations using substitution, what could be substituted in place of y in the first equation?
4x=5-2y
y-2x=7
Answers
Answer: y=2x+7
(this is a rearranged version of y-2x=7 from question)
Step-by-step explanation:
4x=5-2y
y-2x=7
i would rearrange the 2nd value into y intercept form y=mx+b
so move the -2x to the other side of the = sign by doing the opposite, +2x on both sides to isolate the y
y=2x+7
you didn't give any options for "correct answer" so i can't give
you A B C or D answers
The angle marked a=92 degrees.
work out the angle marked x.
Answers
Answer:
x is 92 degrees
The lines x and a are parallel and congruent, meaning they are evenly proportioned and have the same length.
I don’t know how to do this question and my math teacher is not helpful
Answers
Answer:
i think its 4.7
Step-by-step explanation:
Answer:
AC is an enlargement of AE
scale factor = 11.7 ÷ 5.2 = 2.25
CD is an enlargement of AB
10.5 ÷ 2.25 = 4.666666...
= 4.7 (rounded to nearest tenth)
Need help to proportion this question help please
Answers
Step-by-step explanation:
1. So first you have to cross multiple the two terms
2.Solve the algebraic equation
By dividing with 12 on both sides
(Note :That's a 32 in the picture sometimes i really write bad)
Tom bought a computer for 15% off from the list price of p dollars. if the sales tax was 8%, how much did he pay for the computer including sales tax?
Answers
The amount paid for the computer including sales tax is 0.918p
How to determine the amount paid?The price paid is given as:
Price = p
A 15% off means that he pays 85%.
So, we have:
Amount = 85% * p = 0.85p
A sales tax of 8% means:
Total = 0.85p * (1 + 8%)
Evaluate the product
Total = 0.918p
Hence, the amount paid is 0.918p
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Daniel has $600 in a checking account, has $12,000 in a savings account, owns a $12,000 car, and owns a $35,000 house. what is the total value of his large assets?
Answers
The total value of Daniel's large assets is $59,600
Calculating Total assetsFrom the question, we are to determine the total value of Daniel's assets
From the given information,
Daniel has $600 in a checking account and he has $12,000 in a savings account.
He also owns a $12,000 car and a $35,000 house
Then,
The total value of his assets = $600 + $12,000 + $12,000 + $35,000
The total value of his assets = $59,600
Hence, the total value of Daniel's large assets is $59,600
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Answer: 47,000
Step-by-step explanation:
large assets: House+car
12,000+35,000=47,000
A circular grass lawn has an area of 314 square metres.
12.
Find the circumference of the lawn.
Answers
Answer:
[tex]C= 62.8m[/tex]
Step-by-step explanation:
Let's round [tex]\pi = 3.14[/tex]. Area of a circle if [tex]\pi r^2[/tex]. In our case, we can easily find out the radius[tex]\pi r^2 = 100\pi \rightarrow r=10m^[/tex]. At this point, it's easy to find the length of the circumference by doubling it and multiplying again by [tex]\pi[/tex]:
[tex]C= 2\pi r = 62.8 m[/tex]
Point A in this figure is to be rotated 90° in a clockwise direction. The center of the rotation is the origin. A (0,5) C (6,3) B (2,-2) Where does point A end up?
Answers
Answer:
B
Step-by-step explanation:
To rotate triangle ABC about the origin 90° clockwise we would follow the rule (x,y) → (y,-x), where the y-value of the original point becomes the new x-value and the x-value of the original point becomes the new y-value with the opposite sign.
What is the value of f(3) in the function below?
f(x) = 2x
O A. 16
OB. 8
OC. 4
O D. 6
Answers
So we replace "x" with the necessary value (3):
[tex]f(3) \: = \: 2 \: \times \: 3[/tex]
[tex]f(3) \: = \: \boxed{ \bold{6}}[/tex]
Answer:[tex]\text{Opción A. } \boxed{ \bold{55}}[/tex]
MissSpanishHelp!! I don’t understand how to answer this
Answers
Answer:
The answer is option A
Step-by-step explanation:
The solution is in the image
Select the correct answer. what is the approximate solution to this equation? a. b. c. d.
Answers
The approximate solution to the given equation is x ≅ 148.4. The correct option is C. x ≈ 148.4
Solving equationsFrom the question, we are to determine the approximate solution to the given equation,
The given equation is
[tex]4lnx -8 =12[/tex]
First, add 8 to both sides
[tex]4lnx -8+8 =12+8[/tex]
[tex]4lnx =20[/tex]
Now, divide both sides by 4
[tex]ln x =\frac{20}{4}[/tex]
[tex]ln x = 5[/tex]
Take the exponents of both sides
[tex]e^{lnx} = e^{5}[/tex]
x = 148.413
x ≅ 148.4
Hence, the approximate solution to the given equation is x ≅ 148.4. The correct option is C. x ≈ 148.4
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The formula for final velocity given acceleration and time is Vf=Vi+a•t
Rewrite the formula for solve Vi
Answers
Answer:
It is the third option
Step-by-step explanation:
Trust me
A rectangular piece of material with sides 150 cm and 100 cm is used to make a circular table cloth. the diameter of the completed cloth must be 0.9 m and 5 cm is provided for the hem. how much material is wasted?
Answers
The material wasted is 7915.375 sq cm.
What is area of rectangle?The product of its length and breadth.
Area = length* breadth
Given:
length= 150 ac, breadth = 100 cm
d= 0.9m 5cm
r= 47.5 cm
Area of rectangle,
= l * b
= 150*100
= 15000 sq. cm
Area of Circular cloth,
= πr²
=3.14*47.5*47.5
=7084.625 sq cm.
Hence, the wasted material is = 15000-7084.625
= 7915.375 sq cm
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URGENT I don't know which one it is
Answers
Which of the following is the correct graph of the solution to the inequality -13> -5x + 2 > -28?
Answers
Answer:
3 < x < 6
Step-by-step explanation:
1) Subtract 2 from the whole equation.
- 13 - 2 > -5x > -28 - 2
2) Simplify.
-15 > -5x > -30
3) Divide the whole equation by -5.
-15/-5 < x < -30/-5
4) Simplify.
3 < x < 6
identify the domain of the functions shown in the graph
Answers
Answer:
D. 2<=x<=6
Step-by-step explanation:
domain: all possible x-values
Sheryl has a basket of ripe apples and peaches. The number of apples in the basket is 12 more than twice the number of peaches. If there are
36 apples in the basket, how many peaches are in the basket?
Answers
Answer: 432
Step-by-step explanation:
12
x 36
--------
72
+ 36
-------
432
Solve the inequality.
-2c-7-9
Enter the correct answer
Answers
Answer:
-2c-16
Step-by-step explanation:
do 7-9 because it's the only thing you can solve.
--> -2c-16
like terms first : -7-9 = -16
-2c-16
then you divide : -2/2 and -16/-2
c = 8
score distribution of the test result of 33 students in a science class containing 50 items
Answers
=66%
Given limit of f (x) = negative 4 as x approaches c and limit of g (x) = one-fifth as x approaches c. what is limit of left-bracket startfraction g (x) over f (x) endfraction right-bracket as x approaches c? negative startfraction 20 over 1 endfraction negative five-fourths negative four-fifths negative startfraction 1 over 20 endfraction
Answers
Since the limit of f(x) is non-zero, the limit distributes over the quotient and
[tex]\displaystyle \lim_{x\to c} \frac{g(x)}{f(x)} = \frac{\displaystyle \lim_{x\to c}g(x)}{\displaystyle \lim_{x\to c}f(x)} = \frac{\dfrac15}{-4} = \boxed{-\frac1{20}}[/tex]
Plot the points (0,6),(3,15.8) and (9.5,0) using the graphing tool, and find the function
Answers
Answer:
f(x)=11.1035−0.920848x
Step-by-step explanation:
Why is it that when you convert 3/4 into a decimal it’s 0.75??
Answers
Answer:because it’s like a quarter
Step-by-step explanation:
A quarter is 25c, 25•3=75
1 - 0.25
2 - 0.50
3 - 0.75
4 - 1.00
hope this helps !!!!!
A box contains 60 raffle tickets. The tickets are numbered 1 to 60 inclusive. What is P(multiple of 12) when a ticket is drawn from the box?
Answers
Answer:
[tex]the \: probability \: is \: \frac{5}{60} \\ when \: simplified \: becomes \: \frac{1}{12} [/tex]
Step-by-step explanation:
The solution is in the image
find the area of the circle if radius is 6 and there is only 3/4 of the circled
Answers
Answer:
84.8
Step-by-step explanation:
Begin by finding the total area of the circle. You have been given the radius.
A = πr²
A = π(6)²
A = 36π
A = 113
If there is only 3/4 of the circle, then multiply the entire area by 3/4 to find the final answer.
113 x 3/4 = 84.8
A. Name the smallest angle and the largest angle of the following triangles: F 6 S 5 1. A J 5.03 7 5 G B H 5.1 2. D 4 3 E
Answers
Answer:
(smallest, largest) = (B, C), (D, E), (G, J)
Step-by-step explanation:
Side lengths of a triangle are proportional to the sine of the opposite angle. In a triangle, a larger angle will always have a larger sine. That means the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.
__
ΔABCThe shortest side is 5 units, opposite angle B. The longest side is 7 units, opposite angle C.
smallest angle: Blargest angle: CΔDEFThe shortest side is 3 units, opposite angle D. The longest side is 5 units, opposite angle E.
smallest angle: Dlargest angle: EΔGHJThe shortest side is 5 units, opposite angle G. The longest side is 5.1 units, opposite angle J.
smallest angle: Glargest angle: J_____
Additional comment
Angles in a triangle may exceed 90°. The sine function actually is decreasing for angles above 90°. However, since the total of angles of a triangle must be exactly 180°, there cannot be two angles in a triangle such that the smaller angle has the larger sine.
In one country, approximately 144,000 of 900,00 residences are rentals. Determine the percentage of residences in the country that are rentals
Answers
The 62.5% of residences in the country that are rentals if the total number of residence in the country is 144,000.
What is the percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
We are assuming:
Total number of residence in the country = 144,000
In which 900,00 residences are rentals.
Percentage of residences in the country that are rentals:
= (90000/144000)×100
= 0.625×100
= 62.5%
Thus, the 62.5% of residences in the country that are rentals if the total number of residence in the country is 144,000.
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What is the probability of drawing four queens from a standard deck of cards, given that the first card drawn was a queen? Assume that the cards are not replaced.
3/20825
4/52
1/20825
3/52
Answers
The probability of drawing three queens from a standard deck of cards is 0.000162.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Total cards = 54
No. queens in a deck = 4
Probability of drawing a queen card = 4/54
Now that 1 queen has been taken, the no. of cards becomes = 53
and
no. of queens = 3
Probability of getting a queen again = (3/53)(4/54)
Two queens have already been removed.
No. of cards in the deck = 52
No. of queens in the deck = 2
Probability of drawing three queens
= (2/52)(3/53)(4/54)
= 0.000162 approximately
The probability of drawing three queens from a standard deck of cards is 0.000162.
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find the measure of the indicated angle
?
82°
58⁰
__ degrees
Answers
Because it’s supposed to equal 180 degrees
So 82+58=140+40=180
please solve it fast
Answers
This are function used to determine the term of a sequence. The second and the third term of the sequence is 6 and 18
Recursive functionsThis are function used to determine the term of a sequence. Given the following functions
an+1 = 3an
Given that a1 = 2
a2 = 3a1
a2 = 3(2)
a2 = 6
For the third term a3
a3 =3a2
a3 = 3(6)
a3 = 18
Hence the second and the third term of the sequence is 6 and 18
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