Given:
Focus of a parabola = [tex]\left(1,\dfrac{1}{2}\right)[/tex]
Directrix: [tex]y=3[/tex]
To find:
The equation of the parabola.
Solution:
The equation of a vertical parabola is:
[tex]y-k=\dfrac{1}{4a}(x-h)^2[/tex] ...(A)
Where, [tex](h,k)[/tex] is center, [tex](h,k+a)[/tex] is focus and [tex]y=k-a[/tex] is the directrix.
On comparing the focus, we get
[tex](h,k+a)=\left(1,\dfrac{1}{2}\right)[/tex]
[tex]h=1[/tex]
[tex]k+a=\dfrac{1}{2}[/tex] ...(i)
On comparing the directrix, we get
[tex]k-a=3[/tex] ...(ii)
Adding (i) and (ii), we get
[tex]2k=\dfrac{7}{2}[/tex]
[tex]k=\dfrac{7}{4}[/tex]
Putting [tex]k=\dfrac{7}{4}[/tex] is (i), we get
[tex]\dfrac{7}{4}+a=\dfrac{1}{2}[/tex]
[tex]a=\dfrac{1}{2}-\dfrac{7}{4}[/tex]
[tex]a=\dfrac{-5}{4}[/tex]
Putting [tex]a=\dfrac{-5}{4},h=1,k=\dfrac{7}{4}[/tex] in (A), we get
[tex]y-\dfrac{7}{4}=\dfrac{1}{4\times \dfrac{-5}{4}}(x-1)^2[/tex]
[tex]y-\dfrac{7}{4}=\dfrac{-1}{5}(x^2-2x+1)[/tex]
[tex]y-\dfrac{7}{4}=-\dfrac{1}{5}(x^2)-\dfrac{1}{5}(-2x)-\dfrac{1}{5}(1)[/tex]
[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x-\dfrac{1}{5}+\dfrac{7}{4}[/tex]
On further simplification, we get
[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{35-4}{20}[/tex]
[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex]
Therefore, the equation of the parabola is [tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex].
Note: Option C is correct but the leading coefficient should be negative.
When Daniel left his house in the morning, his cell phone battery was partially
charged. Let B represent the charge remaining in Daniel's battery, as a percentage,
hours since Daniel left his house. The table below has select values showing the linear
relationship between t and B. Determine how much battery life Daniel's phone
would have 1.5 hours after leaving his house.
t
B
1
27.5
2.5
19.25
4
11
Answer:
24.75 percents
Step-by-step explanation:
1) Find AC
2
А
24
118°
220
B
Jackson bought a jar of 240 marbles. The percent bar graph shows the percentage of each color marble in the jar.
How many of the marbles are blue?
Answer:
84
Step-by-step explanation:
Blue marbles = 35%
35% = 0.35
240(0.35)
84
Answer:
84
Step-by-step explanation:
0.35×240=84
hope this helps
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 18
and AC 36, what is the length of AD?
A
D
36
18
B
Answer:
8 is the length
Step-by-step explanation:
The length of AD is 9 units from the given right triangle ABC.
What is a right triangle?A right angled triangle is a triangle with one of the angles as 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.
Given right triangle ABC with altitude BD drawn to hypotenuse AC.
Given that, AB = 18 and AC = 36
Using Pythagoras theorem
AC²=AB²+BC²
⇒ 36²=18²+BC²
⇒ BC²=1296-324
⇒ BC²=972
⇒ BC=31.18 units
We know that, area of a triangle =1/2 × Base × Height
= 1/2 × 31.18 × 18
= 280.62 square units
Now, area of a triangle ABC with base AC and height BD
That is, Area = 1/2 ×36×BD
⇒ 18BD=280.62
⇒ BD=280.62/18
⇒ BD=15.6
Consider ΔBDA
AB²=AD²+BD² (Pythagoras theorem)
18²=x²+15.6²
⇒ x²=18²-15.6²
⇒ x=9 units
Therefore, the length of AD is 9 units from the given right triangle ABC.
To learn more about the right angle visit:
https://brainly.com/question/3770177.
#SPJ2
Please help me on this! Name it like A, B, C, D
Answer:
B. -2_x_4÷3 this answer are not sure
Answer:
D
Step-by-step explanation:
-5 < 6x +3
-8 < 6x
-(4/3) < x
I use < to represent 'no no smaller than'
A cell phone company charges a one-time activation fee, as well as a monthly service charge for a cell phone plan with unlimited minutes and data. The total cost is modeled by the function C(x) = 99 + 85x. Which statement represents the meaning of the function?
Answer:
C(x) is the total cost, x is the number of months of service, $99 is the one-time activation fee, and $85 is the service charge per month.
Step-by-step explanation:
Because I'm always right.
If kobe had 30 girls and Shaq had 20 girls... How many more girls does Kobe have than Shaq?
Answer:
10 more shawties
Step-by-step explanation:
30-20 = 10
The triangle and the trapezoid have the same area. Base b2 is twice the length of base b1. What are the lengths of the bases of the trapezoid? The area of the triangle is 65 cm squared
Answer:
[tex]b_1 \approx 7.2[/tex]
[tex]b_2 \approx 14.4[/tex]
Step-by-step explanation:
Given
[tex]Area = 65cm^2[/tex] --- Area of the triangle
[tex]b_2 = 2b_1[/tex] --- the bases of the trapezoid
The missing parameters is:
[tex]h=6 cm[/tex] --- Trapezoid height
Required
Determine b1 and b2
Since the areas of the trapezoid and the triangle are the same, then:
[tex]Area = \frac{1}{2}(b_1 + b_2) *h[/tex]
So, we have:
[tex]65 = \frac{1}{2}(b_1 +b_2) * 6[/tex]
Substitute[tex]b_2 = 2b_1[/tex]
[tex]65 = \frac{1}{2}(b_1 +2b_1) * 6[/tex]
[tex]65 = \frac{1}{2}(3b_1) * 6[/tex]
[tex]65 = 3b_1 * 3[/tex]
[tex]65 = 9b_1[/tex]
Solve for [tex]b_1[/tex]
[tex]b_1 = \frac{65}{9}[/tex]
[tex]b_1 \approx 7.2[/tex]
Substitute [tex]b_1 \approx 7.2[/tex] in [tex]b_2 = 2b_1[/tex]
[tex]b_2 \approx 2 * 7.2[/tex]
[tex]b_2 \approx 14.4[/tex]
Are the triangles congruent ? Please answer correctly !!!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!
Answer:
no
Step-by-step explanation:
they are not
Answer:
No
Step-by-step explanation:
because the angles are not equal. If they were they would have the same numbers.
What is -8w-4 simplified?
[tex]\huge\red{\boxed{\tt{\colorbox{pink}{ANSWER:}}}}[/tex]
[tex] - 4(2w + 1)[/tex]
[tex]\huge\red{\boxed{\tt{\colorbox{pink}{Solution:}}}}[/tex]
[tex] - 8w - 4[/tex]
Bind the expression with the common factor -4
[tex] - 8w - 4[/tex]
#❀CARRY ON LEARNING❀#❀KEEP ON LEARNING❀#❀LEARNING IS FUN❀#❀LETS LEARN❀#❀NoToCopyPaste❀❀hope it helps(◕ᴗ◕✿)❀❀Keep safe!❀シ︎Answer: −4(2w+1)
Step-by-step explanation: Hope this help :D
Someone PLSSS HELP TYSM IF U DO
-41.2 minus (-37.4) is -3.8.
If this is incorrect, please, don't refrain to tell me. Thank you.
Answer: -3.8
Hope this helps!
MARKED BRAINLIEST!!!
Answer:
(3,-4)
Step-by-step explanation:
Sorry if it is wrong
What is the concept of cause and effect?
A.
when an action causes something to come into effect
B.
when an action is caused but there is no resulting effect
C.
when an action doesn't actually have a resulting effect
D.
when an action leads to an effect that is not desired
Answer:
A. when an action causes something to come into effect
Step-by-step explanation:
Mark as brainliest please. Hope the answer helps :)
For a school fundraiser, Percy bought a big box of rubber ducks and wrote prize amounts, in dollars, on the bottom of each rubber duck. The prize amounts were $5, $10, $20, $50, and $100. The number of ducks with each prize amount varied so that the total value for all the ducks with each prize amount was always $500.
Percy then put all the rubber ducks in his school’s swimming pool. At the fundraiser, participants used a long net to catch a duck from the pool. They won the amount written on the bottom of the rubber duck, and then they threw the duck back into the pool before the next person’s turn. Since the ducks were returned to the pool after they were caught, the chances of winning any particular amount remained the same.
Amir paid $15 to play the game once. If we assume he randomly selected a du
Answer:
i dont know
Step-by-step explanation:
HELP HELP ASAP ASAP WILL MARK BRAINLIEST
ANSWER BOTH PLEASE EASY POINTS
Answer:
1.) Hypotenuse.
The hypotenuse is the longer side.
2.)Leg
Answer:
1.) Hypotenuse
2.) Leg
Step-by-step explanation:
The legs or bases of a triangle are the sides connected to the right angle.
The hypotenuse is the side across from the right angle and is always the longest side.
Hiiioo :D can someone please help. I really need help. Much love ❤️❤️❤️
Answer:
The answer is the second one!
Have a wonderful day/night! <3
Can Someone please help me out with this problem
Step-by-step explanation:
find the area as if it was a rectangle so do 14x12 then subtract the area of half a circle with a diamater of 12
PLEASE HELP WHAT ONE
Its not C
Answer:
D. (-3, 4)
Step-by-step explanation:
Help I'll give Brainly
Answer:i think D
Step-by-step explanation:
Which function has a graph with
x-intercepts of (-2, 0) and (7,0)?
The photo is the answers
The probability that a student guesses the correct answer to a five-choice multiple choice question is P(correct)=0.2. How many correct answers should a student expect to guess on a test with 60 five-choice multiple choice questions?
Answer:
12 correct answers
Step-by-step explanation:
It is given that :
The probability of a student guessing the correct answer for a five choice multiple choice question is [tex]$\text{P(correct)}=0.2$[/tex]
Number of multiple choice questions = 60
So the number of correct answers that a student are expected to guess correctly on the test is :
[tex]$=60 \times 0.2$[/tex]
= 12
Please answer this!!! No links !!!
What’s the answer ? Pleaseee help
Answer:blue
Step-by-step explanation:
the dark one
724 Ft
Surface Area = 2×(17×4 + 17×14 + 4×14) = 724 feet^2
Can someone help me with this. Will Mark brainliest.
Answer: I think it’s False I’m not sure
Answer:
it's false because isosceles is convex quadrilateral with line of symmetry
Laurie needs at least 40 pounds of topsoil for a new flower bed. Each bag of topsoil is 200 ounces. Laurie determines that if she buys 3 bags of topsoil she will have enough for the flower bed. Is Laurie correct? Why or why not?
Answer:
No she will not have enough topsoil for the flower bed.And she is not correct.Because every pound is 16 ounces.so 600 ounces is only 37.5 pounds
Step-by-step explanation:
3×200=600600÷16=37.5Hope this helps :)
what is the hypothesis of a triangle with a base of 11cm and height of 9cm
Answer:
14.21 cmExplanation:
you mean the hypotenuse* lol
the hypotenuse = √(11²+9²)
the hypotenuse = √(121+81)
the hypotenuse = √(202)
the hypotenuse ≈ 14.21 cm
Plzzzzzz heeelllpp. 20 pointsss
Answer:
Hello.
The answer to this question is
− √ 2 − √ 3 /2
And in Decimal Form: − 0.25881904
Step-by-step explanation:
Give brainliest :)
how would you do log(3250) without a calculator
Answer:
Step-by-step explanation:
It depends on what level you are. Logs are most easily developed by using a series for the natural logarithms (instead of base 10, you use base e). Even that is a difficult process using a series that you won't be introduced to until your second calculus course..
For now, I'd be content to use a calculator. The series does not converge terribly quickly.
Find area of square
Pls help
Answer:
49/64 yd²
Step-by-step explanation:
since where finding a square we do
A = bxh
A = 7/8×7/8
A = 49/64
Which of the following equations represents this statement
Answer: 5n = 35
Step-by-step explanation:
The product of a number n and the number 5 is 35. This statement can be formed into an equation as:
n × 5 = 35
5n = 35
The equation is 5n = 35
If we want to get the value of the number, it'll be:
5n = 35
n = 35/5
n = 7
The number is 7