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
Parlings vary directly with mots. If 7.5 mots are worth 37.5 parlings, how many parlings will get you 13 mots?
Answers
Answer:
65 parlingsStep-by-step explanation:
Use ratios:
7.5 mots / 37.5 parlings = 13 mots / x parlingsx = 13*37.5/7.5x = 65With Big Phone Company, you pay $0.39 for the connection and $0.03 per minute
With LittlePhone Company, you pay $0.25 for the connection and $0.07 per minute
If you plan on making a call that will take at least 4 minutes, which company offers the better
deal?
A. Both companies will charge the same amount.
B. There is not enough information.
C. BigPhone company offers the better deal for this call.
D. LittlePhone company offers the better deal for this call
Answers
Big Phone Company offers a better deal for this call.
Option C is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Big Phone Company:
Cost after 4 minutes.
= 0.39 + 4 x 0.03
= 0.39 + 0.12
= $0.51
LittlePhone Company
Cost after 4 minutes.
= 0.25 + 4 x 0.07
= 0.25 + 0.28
= $0.53
Thus,
The Big Phone Company charges less as compared to the LittlePhone Company after using it for 4 minutes.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
from the adjoining figure, find the value of x
Answers
Answer:
x = 2°
Step-by-step explanation:
x + 2x + 30 = 180°
3x + 30 = 180°
3x = 180°/30°
3x = 6°
x = 6°/3°
x = 2°
I need this answered!
Simplify the following expression:
5s + 72 - 6
use s = -8 and z = -3
I Record your answer in this box:
Answers
Answer:
I believe its -82
Step-by-step explanation:
5 × -8 + 7 × -3 = -82
A cyclist travels 18 km from home to the park.
She leaves home at 16:00 and arrives at the park at 16:45.
What is her average speed in km/h?
Answers
Answer: 24 km/h
Step-by-step explanation:
She traveled 18 km in 45 minutes, this could be simplified to .4 km/min or 24 km/h
Which word best describes a parallelogram with diagonals that are congruent and perpendicular?
A. rectangle
B. rhombus
C. square
D. trapezoid
Answers
help please !! thank you!
Answers
Answer:
.5
Step-by-step explanation:
if you put ur mouse on -2 then move to the right 1.5 you will get .5
Hope this Helps!!!
Answer:
-.5
Step-by-step explanation:
1.5 +-2 is -.5 hope this helps
Help meeeeee! plsssssssssssssssssssssssssssss
Answers
Step-by-step explanation:
Store a must offer 30%
I hope this helped :)
Describe fully the single transformation which takes shape A to shape B
Answers
sorry sir i dont really know
The length of one leg of an isosceles right triangle is 7 units. What is the length of the hypotenuse?
Answers
=
14
,
⇒
the length of each leg
=
14
√
2
=
7
√
2
Check :
(
7
√
2
)
2
+
(
7
√
2
)
2
=
196
=
14
2
(OK)
Find the Mean,
3, 9, 13, 8, 10, 2
Mean
can someone help me?
Answers
Answer:
7.5
Step-by-step explanation:
3 + 9 + 13 + 8 + 10 + 2 = 45
There are 6 numbers so we divide 45 by 6
45/6 = 7.5
help please!!!!!!!!!!!!!!!!!!!!!!!
Answers
9514 1404 393
Answer:
a) $336
b) $1036
Step-by-step explanation:
a) The interest is computed using the formula ...
I = Prt
where P is the amount invested at rate r for t years.
I = $700·0.08·6 = $336
The interest earned is $336.
__
b) The balance of the account is the sum of the original amount and the interest earned:
balance = $700 +336 = $1036
The balance of the account is $1036.
1 - 2k + 5k <_ -4 + 3k
Answers
Answer:
No solution.
Step-by-step explanation:
1-2k+5k<-4+3k Combine like terms on each side wherever you can.
1+3k<-4+3k Subtract -3k on both sides (it's less confusing when you get
-3k -3k rid of the variable first).
1<-4 1 is not less than or equal to -4, so there is no solution.
I hope this helped you out!! Have a great day (*^3^)╭
A cube is cut in to three parts by vertical slices find the volume of the shaded area The length and width of original is 20 cm and cut part is 10 cm
Answers
Answer:
4000 cm^3
Step-by-step explanation:
Note that no image was attached for reference purposes
Step one:
We are given that the original length and width of the cube is 20cm
if the cut part is 10cm
hence the dimension of the cut part is
lenght = 20cm
Width= 20cm
Hieght= 10cm
Step two:
the volume of the cut part will be
Volume= 20*20*10
Volume= 4000 cm^3
Pls help, I know the answer but what I wrote in the box isn't correct
How do I show the answer?
Answers
Answer:
AC=11.38 cm
Step-by-step explanation:
The Law of Cosines
It relates the length of the sides of a triangle with one of its internal angles.
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
[tex]c^2=a^2+b^2-2ab\cos x[/tex]
The figure shows two triangles and we are required to calculate the length of the side AC, knowing two sides and the angle between them. Thus, applying the formula:
[tex]AC^2=17^2+13^2-2*17*13*\cos42^\circ[/tex]
[tex]AC^2=289+169-442*0.7431[/tex]
[tex]AC^2=129.53[/tex]
[tex]AC=\sqrt{129.53}[/tex]
AC=11.38 cm
Abigail’s parents pay her $5 an hour for weeding the yard and pay her little sister $3 an hour for raking leaves.
Write an expression in two different ways to represent the amount their parents will pay Abigail and her sister for working the same number of hours
I dont get help me
Answers
Answer: (MAKE ME BRAINLIST PLEASE)
Answer: For Abigail W = $5t
For her younger sibling W= $3t
Bit by bit clarification:
How about we address the compensation with W
t as the time spent on work in hours
Abigail will be paid $5 every hour, her all out compensation will be
W(abg) = $5t
Her younger sibling will be paid $3 every hour, her complete compensation will be
W(lts) = $3t
Simplify the expression:
4b - 24 + 19
4p - 5p - 30p
4.2v - 5 - 6.5v
Answers
4b - 24 + 19 ——> 4b - 5
The second expression only has variables so we simplify the whole expression
4p - 5p - 30p = -31p
The third expression we will only simplify the variables
4.2v - 5 - 6.5v ——> -2.3v - 5
2/5k - 3/5 + 1/10k ?
Answers
Answer:
Since it is not an equation u wont get a numerical value
so basically its just fraction addition and subtraction
which is ((2/5)-(3/5)+(1/10))k
so answer is (-1/10)k
Step-by-step explanation:
[tex] \frac{2}{5} k \: - \frac{3}{5} + \frac{1}{10} k[/tex]
[tex] \frac{4}{10} k + \frac{1}{10} k - \frac{3}{5} [/tex]
[tex] \frac{5}{10} k - \frac{3}{5} [/tex]
[tex] \frac{k}{2} - \frac{3}{5} [/tex]
Roscoe hit a ball straight up at a speed of 96 ft/s. His bat hit the ball at a height 3 ft above the ground. After how many seconds did the ball hit the ground? (Give your answer to the nearest hundredth of a second.)
Answers
Answer:
t = 6.031 seconds
Step-by-step explanation:
Roscoe hit a ball straight up at a speed of 96 ft/s.
His bat hit the ball at a height 3 ft above the ground.
We need to find how many seconds did the ball hit the ground.
Using equation of motion to find height of the ball.
[tex]h=-16t^2+96t+3[/tex]
When it hits the ground.
h = 0
[tex]-16t^2+96t+3=0[/tex]
It is a quadrctic equation where a = -16, b = 96 and c = 3
[tex]t=\dfrac{-96\pm \sqrt{96^2-4(-16)(3)} }{2(-16)}\\\\t=-0.031\ s, 6.031\ s[/tex]
Neglecting negative value.
So, after 6.031 seconds the ball will hit the ground.
Given :
Roscoe hit a ball straight up at a speed of 96 ft/s.
His bat hit the ball at a height 3 ft above the ground.
To Find :
After how many seconds did the ball hit the ground.
Solution :
When the ball reaches the same height from which it is thrown ( i.e. 3 ft ) its displacement will be zero.
So, using equation of motion :
[tex]s = ut + \dfrac{at^2}{2}\\\\96t - \dfrac{10t^2}{2} = 0\\\\5t^2 - 96t = 0\\\\t( 5t - 96 ) = 0\\\\t = \dfrac{96}{5}\\\\t = 19.2 \ s[/tex]
Now, time taken to reach ground from 3 feet of height is :
[tex]s = ut + \dfrac{at^2}{2}\\\\3 = 96t + 5t^2 \\\\5t^2 + 96t - 3 = 0[/tex]
t = 0.03 s
Therefore, time taken is T = 19.2 + 0.03 = 19.23 seconds.
Square CDFG below contains several angles. Which pairs of angles in square CDFG are complementary? Select all that apply. С C D 27° 63° | М 64° 26° G F UL Angles DCM and MCG Angles MGF and MGC Angles FGM and MCD Angles DCM and DMC
Answers
Answer:
angles FGM and MCD, angles DCM and DMC
Step-by-step explanation:
Answer:
angles FGM and MCD, angles DCM and DMC
Step-by-step explanation:
What is the slope of the line that passes through the points (-6,8) and (-16,33)? write your answer in the simplest form
Answers
Answer:
slope or m= -5/2
Step-by-step explanation:
Use SUBSTITUTION to solve the system
y=4x
2y-2x=12
Answers
y
=
2
x
−
10
y=2x−10 into
y
=
4
x
−
8
y=4x−8.
2
x
−
10
=
4
x
−
8
2x−10=4x−8
2 Solve for
x
x in
2
x
−
10
=
4
x
−
8
2x−10=4x−8.
x
=
−
1
x=−1
3 Substitute
x
=
−
1
x=−1 into
y
=
2
x
−
10
y=2x−10.
y
=
−
12
y=−12
4 Therefore,
x
=
−
1
y
=
−
12
x=−1
y=−12
Are x+x^2 and u+u^2 the same function? If x and u are for all real numbers? A- these are the same function B- If x and u are two different numbers, the functions are different C- there is not enough information to answer this question.
Answers
Answer:
(a) These are the same function
Step-by-step explanation:
Given
[tex]x + x^2[/tex] and [tex]u + u^2[/tex]
Required
Are they the same?
Yes, they are the same function and this is proved below.
[tex]x + x^2[/tex]
Represent as a function:
[tex]f(x) = x + x^2[/tex]
[tex]u + u^2[/tex]
Represent as a function
[tex]f(u) = u + u^2[/tex]
Let x = u
Substitute u for x in [tex]f(x) = x + x^2[/tex]
[tex]f(u) = u + u^2[/tex]
This implies that:
[tex]f(x) = f(u)[/tex]
[tex]x + x^2 =u + u^2[/tex]
PS: The information that x and u are real numbers are for all real numbers; So, we can not assume that x and u are different numbers
Hence:
(b) and (c) are wrong
Please hurry it’s 100 points
Answers
Answer:
I Believe B
Step-by-step explanation:
Hope this helps:)
Answer:
B
Step-by-step explanation:
Its B
Substitute y=-2x+5 into 2y=2x-8 and solve for x
(help me asap please)!!
Answers
Answer:
x = 3
Step-by-step explanation:
2y = 2x - 8
2(-2x + 5) = 2x -8
-4x + 10 = 2x - 8
+4x +4x
10 = 6x - 8
+8 +8
18 = 6x
divide both sides by 6
x = 3
Hope this Helps!!!
What is the equivilent of +367 on a numberline?
Answers
Answer:
367
Step-by-step explanation:
367 because it is positive
A company claims that their new bottle holds 25% more laundry soap. If their original container held 80 fluid ounces of soap, how much does the new container hold?
Answers
Answer: The new container folds 100 fluid ounces.
Step-by-step explanation:
Given: A company claims that their new bottle holds 25% more laundry soap.
If original container hold 80 fluid ounces.
Then, Quantity of soap in the new container = 80 fluid ounces + 25% of 80 fluid ounces
= [80+0.25 x 800] fluid ounces [ 25% = 0.25]
= 80+ 20= 100 fluid ounces
Hence, the new container folds 100 fluid ounces.
Answer:
66.25
Step-by-step explanation:
{(2,5), (-3, 4), (-4,-4), (x,-5)}
What value of x will make the relation a function?
-3
-4
5
2
Answers
Answer:5
Step-by-step explanation:
because idrk my teacher just answered this question and i thought i would share :)
Dan made 90 free throws in 30 minutes Alex made 60 free throws in 20 minutes compare the unit rates
A) Dan made more free throws per minute
B) Alex made more free throws per minute
C) they made the same free-throw‘s per minute
Answers
Answer:
A is the answer ..........
Step-by-step explanation:
A line includes the points (3, 7) and (2, 2). What is its equation in slope-intercept form?
Answers
Answer:
y=5x-8
Step-by-step explanation:
