Any point on the parabola can be labeled (x,y) as shown.
1. What are the distances from the point (x,y)(x,y) to the focus of the parabola and the directrix?
Select two answers.
distance to the focus: √(x+3)2+(y−3)2
distance to the directrix: |y−4|
distance to the directrix: |x−4|
distance to the focus: √(x−2)2+(y+3)2
distance to the focus: √(x+3)2+(y−2)2
distance to the directrix: |y+4|
2. What is the correct standard form of the equation of the parabola?
Answers
Answer:
Part A)
2nd and 5th choice.
Part B)
[tex]\displaystyle y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{3}{4}[/tex]
Step-by-step explanation:
For the given parabola, our focus is (-3, 2), and our directrix is given by y = 4.
Part A)
We are given a point (x, y) on the parabola.
Since our directrix is an equation of y, the distance from (x, y) to the directrix will simply be the absolute value of the difference in y-values. So:
[tex]d_1=|y-4|=|4-y|[/tex]
Recall the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Our distance from (x, y) to the focus (-3, 2) can be determined using the distance formula. Let (x, y) be (x₂, y₂) and let our focus (-3, 2) be (x₁, y₁). Therefore:
[tex]d_2=\sqrt{(x-(-3))^2+(y-2)^2}=\sqrt{(x+3)^2+(y-2)^2[/tex]
Hence, for Part A, our answers are the 2nd and 5th choices.
Part B)
Recall that by the definition of a parabola, any point (x, y) on it is equidistant to the directrix and focus. Hence:
[tex]\sqrt{(x+3)^2+(y-2)^2}=|y-4|[/tex]
Solve for y. Square both sides. We may remove the absolute value since anything squared is positive:
[tex](x+3)^2+(y-2)^2=(y-4)^2[/tex]
Square:
[tex]x^2+6x+9+y^2-4y+4=y^2-8y+16[/tex]
Rearrange:
[tex](x^2+6x+13)+(-16)=(y^2-y^2)+(-8y+4y)[/tex]
Combine like terms:
[tex]x^2+6x-3=-4y[/tex]
Divide both sides by -4. Hence, our equation is:
[tex]\displaystyle y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{3}{4}[/tex]
Heyo! :D
Distance to the directrix is |y - 4|.
Distance to the focus is [tex]\sqrt{(x+3)^2+(y-2)^2}[/tex].
Hope this helps! If so, please lmk! Tysm and good luck!
Related Questions
Can someone please help me with these quadratic formula word problems. I'll give the best answer the brainiest and 25 points.
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Answer:
6.C10.BMARK ME AS BRAINLY#Carry On LearningSOMEONE HELP ME PLSS !
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volume = length x width x depth
-X + 5 = 1
What is the answer for this equation and the steps
Answers
Answer:
x=4
Step-by-step explanation:
-x=1-5 (subtract 5 from both sides to isolate the x variable)
-x= -4 (1-5= -4)
x=4 (divide both sides by -1 so the x will not be a negative.)
Therefore, your answer will be x=4. Hope this helps! :)
Answer:
4
Step-by-step explanation:
First, let's move "+5" on the other side. We should change "+" on "-":
-x=1-5
1-5=-4:
-x=-4 |• (-1)
x=4
Can you PLEASE help with this as SOON as you can. I will give BRAINLIEST!!!
Answers
Answer: 2(7c^2+y)
Step-by-step explanation:
Which three statements are true about the correlation shown by this scatter plot?
A. The correlation coefficient is approximately 0.96
B. The line of best fit can be used to make accurate predictions from the data.
C. The correlation coefficient is approximately 0.33.
D. The correlation coefficient indicates a strong positive correlation.
E. The line of best fit cannot be used to make accurate predictions from the data
F. The correlation coefficient indicates a weak positive correlation.
Answers
Answer:
A,C nd E
Step-by-step explanation:
The three statements are true about the correlation shown by this scatter plot are;
A. The correlation coefficient is approximately 0.96
C. The correlation coefficient is approximately 0.33.
E. The line of best fit cannot be used to make accurate predictions from the data
What is correlation?Correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when other data value is increased or decreased respectively.
The correlation coefficient is the degree of association between two quantities in terms of linear relation.
The range of correlation coefficient is -1 to 1
The correlation is -1, then that means as the one quantity increases, the other quantity decreases (linearly)
We can conclude that the correlation coefficient is approximately 0.96
The correlation coefficient is approximately 0.33.
The line of best fit can't be used to make accurate predictions from the data
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WILL GIVE BRAINLIEST
A cylinder has a total area of 3.41946cm2 and a diameter of 0.66cm. What is its height?
Answers
Total surface Area(A) = 2pi*r(r+h)
Diameter D= 2r
r=0.66/2=0.33cm
A=3.41946
3.41946=2*3.143*0.33(0.33+h)
3.41946=2.0744(0.33+h)
3.41946/2.0744=(0.33+h)
1.6484=0.33+h
1.6484-0.33=h
h=1.3184cm
Step-by-step explanation: Total surface area is different from area around the cylinder.
What is x/ 2 - 8 > 22!
Answers
Answer:
x>60
Step-by-step explanation:
when solving for X that is
Answer:
x>60
Step-by-step explanation:
x/2-8>22
+8 +8
-------------------
x/2>30
x>60
Select all of the zeros of the polynomial
g(x)=x^4+6x^3+6x^2−24x−40
(A). -2
(B). 2
(C). 1
(D). 4
(E). -4
(F). 8
Answers
Answer:
-2, 2
Step-by-step explanation:
those are the answers uwu
A: -2.
B: 2.
someone please do this for me:(
Answers
Answer:
Step-by-step explanation:
2x⁵ + 3x²- 2 → Quintic trinomial
12x → Linear monomial
7x³ -1 → Cubic binomial
3 - 4x → Linear binomial
4x - 5x³ + 1 → Cubic trinomial
2x²(x³ - 1) = 2x⁵ - 2x² → Quintic binomial
x²(4x - 1 + x²) = 4x³ - x² + x⁴ → Quartic trinomial
(x - 2)(x + 3) = x² + x - 6 → Quadratic trinomial
(x² - 1)(x² + 1) = x⁴ - 1 → Quartic binomial
solve the inequality 9-12>-13
A. q>1
B. q>-1
C. q>25
D. q>-25
Answers
Answer:
C
Step-by-step explanation:
Part A
Recall the function V that you wrote in Question 1 to represent the volume of the soil in the frame. Choose an online tool or paper to graph the
function V to identify the x-intercepts. List them in order from least to greatest.
Answers
Answer:
4321
Step-by-step explanation:
rreer5t66
helpppppppppppp...plsss
Answers
Answer:
c=72
Step-by-step explanation:
8
=
9
8
⋅
8
=
8
⋅
9
Answer:
91
Step-by-step explanation:
For questions like these, you multiply the denominator times what it equals
Like in this case you do 8x9
I hope this helps!
A pool has a circumference of about 150.82 meters. Find the radius.
Answers
Answer:
96.0 or 96.01499407
Step-by-step explanation:
r = C / (pi x 2)
What is the approximate value of a local maximum for the polynomial?
–4.5
–2.5
0.5
2.5
Answers
Answer:
0.5
Step-by-step explanation:
The local minimum is the hill made between 0 and 1 on the y axis. Since it is between 0 and 1, 0.5 is the best choice.
Answer:
2.5
Step-by-step explanation:
Please help me I’ll mark you brainiest
Answers
The soil in Sean's backyard is made up of 45% sand. If he has 1000 lbs of soil in his yard, how many pounds of sand are there?
Answers
Answer: 450 lbs
Step-by-step explanation:
45/100 is 45%
Since there are 1000 lbs we multiply 45/100 by 10, giving us 450/1000
Therefore 45% of 1,000 is 450
450 pounds of sand is present in the soil.
What is percentage?
'A percentage is a number or ratio expressed as a fraction of 100. A percentage is a dimensionless number, that is, it has no unit of measurement.'
Total weight of soil in Sean's backyard = 1000 pounds
Percentage of sand in the soil = [tex]\frac{45}{100}[/tex]
Total amount of sand in the soil = ( [tex]\frac{45}{100}[/tex] × 1000 ) lbs
= 450 lbs
Hence, we can conclude, 450 pounds of sand is present in the soil in Sean's backyard.
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If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far away from zero is he?
Answers
Answer:
He is on 4.
Step-by-step explanation:
HELP ASAP MARKING BRAINLIEST
Answers
I hoped this helped! +*♡
Help please :( !
Compare . Who picked fruit at a faster pace ?
Answers
Answer:
Shawn.
Step-by-step explanation:
We can solve for apples per hour and pears per hour. For Shawn, to get the apples per hour, we do 4/2 which is 2 bushels of apples per hour. For pears, we do 5/2 which is 2.5 bushels of pears per hour.
When Carla is picking, we can do:4/3 which is 1 and 1/3, which is her apple bushel picking per hour. For her pears, she picks them at 2 bushels of pears per hour.
Since Shawn picks her apples quicker per hour, and her pears quicker per hour, Shawn picks at a faster fruit pace.
Please help! Ralph buys a computer for $675. The sales tax rate is 6%. How much did Ralph pay for the computer?
Answers
Answer:
$715.50 my dudeeee
Step-by-step explanation:
..........
Ralph pays a total of $715.5 for the computer including the sales tax amount.
What is Percentage?Percentage is defined as the part of a number in a whole of 100. % is the symbol used to denote the percentage.
Percentage of a number in a whole can be calculated by dividing that number with the whole and then multiply to 100.
Actual price of the computer = $675
Sales tax rate = 6%
Ralph has to pay the actual price and in addition the sales tax to buy the computer.
Amount of sales tax = 6% × 675
= (6/100) × 675
= 0.06 × 675
= $40.5
Ralph should add $40.5 to the actual price.
Total payment made for buying the computer = $675 + $40.5
= $715.5
Hence Ralph pays a total amount of $715.5 for the computer.
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Luke goes to summer camp with $45 in spending money. The amount of money he has left after n days at camp is modeled by the recursive function f(n) = f(n-1)-7. Modify the explicit function, and simplify it to slope-intercept form.
Answers
Answer:
Please mark as Brainliest :)
Step-by-step explanation:
Answer:
Sample Answer
Step-by-step explanation:
Please help me I need the answer now!!
Answers
Answer:
an ordered pair
the point where all the lines intersect (which is located by the ordered pair above)
No solutions (in case for example you have parallel lines, so no point there they intersect)
Infinitely Many Solutions (this is when for example you have one single equation, each point of the line is a solution and there are infinite points)
Step-by-step explanation:
basically a "system" means finding a solution that is valid for each equation, like a logical AND
so in this case it means finding a point that lies on each line, and that point can only exists (the intersection of those lines) or not exist (they are parallel)
if the system is made of one single linear equation then you have infinite solutions
A bag contains 49 coins consisting of quarters and dimes. There are 2.5 times as many quarters as there are dimes in the bag. Write a system of equations that models this situation. How many dimes are in the bag?
pls write step by step so that I can understand :)
Answers
Answer:
Dimes = 35
Quarters = 14
Step-by-step explanation:
Let
quarters = q
Dimes = d
Total coins = 49
There are 2.5 times as many quarters as there are dimes in the bag
Dimes = 2.5q
Quarters + Dimes = Total
q + 2.5q = 49
3.5q = 49
q = 49/3.5
q = 14
d = 2.5q
= 2.5 * 14
= 35
d = 35
Therefore,
Dimes = 35
Quarters = 14
Answer:
The system of equations that models this equation area:
d + q = 49
q = 2.5d
Brent spends $ 420 on his monthly bills. Of this amount, 15 % is for utilities, 1/5 is for Internet service, and 1/7 is for phone service. If the rest of the total amount is for food, how much money does Brent have for food?
Answers
Answer: $213
Step-by-step explanation:
First find out how much is spent on the other things:
Utilities
= 15% * 420
= $63
Internet services
= 1/5 * 420
= $84
Phone service
= 1/7 * 420
= $60
The amount left for food is therefore:
= 420 - money spent on other things
= 420 - 63 - 84 - 60
= $213
HELP ASAP
1.Which number or symbol is a variable in the following algebraic expression?
5 + 4y x 32
a 5
b 4
c y
d 2
2.Convert the following word phrase to an algebraic expression:
9 less than a number.
a x - 9
b 9 -x
c 9 ÷ x
d x ÷ 9
Answers
Answer: 1.C 2.B
Step-by-step explanation:
Find the slope and the y intercept please help what do I do
Answers
Answer:
Slope: -7
y-intercept: (0,12)
Answer:
here give my friend the brainliest ^^;
Step-by-step explanation:
Solve the inequality -2x - 8<4
Answers
Use a quadratic equation to find two real numbers with a sum of -43 and a product of 306.
Answers
Answer:
Real numbers = 39 and 9
Step-by-step explanation:
The standard form of a quadratic equation is ax² + bx + c = 0
Given the following data;
a = 1
b = -43
c = 306
Quadratic equation formula is;
[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]
Substituting into the equation, we have;
[tex] x = \frac {-(-43) \; \pm \sqrt {43^{2} - 4*1*306}}{2*1} [/tex]
[tex] x = \frac {43 \pm \sqrt {1849 - 1224}}{2} [/tex]
[tex] x = \frac {43 \pm \sqrt {625}}{2} [/tex]
[tex] x = \frac {43 \pm 25}{2} [/tex]
[tex] x_{1} = \frac {43 + 25}{2} [/tex]
[tex] x_{1} = \frac {68}{2} [/tex]
[tex] x_{1} = 39 [/tex]
[tex] x_{2} = \frac {43 - 25}{2} [/tex]
[tex] x_{2} = \frac {18}{2} [/tex]
[tex] x_{2} = 9 [/tex]
Therefore, the two real numbers are 39 and 9.
The quadratic equation now becomes;
x² - 43x + 306 = (x - 39)(x - 9) = 0
Guys I need help ASAP I am giving 55 points
Answers
Answer:
The answer is 80°
Step-by-step explanation:
pls give brainliest!
all angles = 360°
100+100+80=280°
360°-280°=80°
16/x = 2/7 cross multiplication
Answers
Answer:
x=56
Step-by-step explanation:
16 x 7= x * 2
[tex]x=\frac{16 x7}{2}[/tex]
x=56
Hope this helps :)