Answers
Answer:
p = -3v: (4, -1)f: (4, -4)d: y = 2Step-by-step explanation:
The equation ...
(x -h)² = 4p(y -k)
is the equation of a parabola with vertex (h, k) and vertex-focus distance of p. When p is negative (as here), it means the focus is below the vertex, and the parabola opens downward. The directrix is p units on the other side of the vertex from the focus.
The vertex for equation ...
(x -4)² = -12(y +1)
is (h, k) = (4, -1). The value of p is (-12/4) = -3, so the focus is (4, -1-3) = (4, -4), and the directrix is y = -1+3 = 2.
_____
Additional comment
As a check on the graph, you can remember that any point on the parabola is equidistant from the focus and directrix. You will notice the vertex is halfway between the focus and directrix, so you know that relationship is true there.
You will also notice that a horizontal line from the focus to the parabola intersects the same distance away from the focus as from the directrix. Thus the parabola distance relation holds at that point as well.
Related Questions
1)
Find the value of x and y
Answers
May I please receive help?
Answers
First, we know that a² + b² = c². We will just be using this in a different way! b² = c² - a²
b² = 32² - 28²
b² = 1024 - 784
b² = 240
b = 15.49
Hope this helps!
whats 8 to the power of 6 please
Answers
Answer:
262144
Step-by-step explanation:
Hope I was able to help you with your question , have a great day :)
Answer:
Step-by-step explanation:
I think 8 to the power of 6 Is 262144
One package of blueberries cost $3. How many packages of blueberries can you buy for $9?
Round the answer to the nearest whole number!
Answers
Answer:
3 packages
Step-by-step explanation:
To find how many packages you can buy for $9, you have to divide 9 by 3.
Since each package costs $3.
So, 9/3 = 3
So you can buy 3 packages of blueberries.
Answer:
3 Packages
Step-by-step explanation:
1 package costs $3
2 packages cost $6 (because 3+3=6)
3 packages cost $9- And we have exactly $9 so we can buy 3 packages.
Can someone please help me with this and tell me the points?
Answers
Answer:
Graph: Refer to attached image
Solution: (-5,-3)
Step-by-step explanation:
First graph to two equations.
Refer to the image attached to see what the equations would look like when graphed.
Wherever they intersect is the solution.
They intersect at (-5,-3) therefore (-5,-3) is the solution to the system of equations
Please help me!!!! Thank you
Answers
[tex]\huge \rm༆ Answer ༄[/tex]
In the given question, the two sides of the given triangles are parallel, so the the two corresponding angles of the Triangles are equal to one another.
Therefore, the Triangles are similar by AA similarity criteria ~
And since they are similar, the ratio of sides of one Triangle will be equal to ratio of corresponding sides of the other Triangle.
that is ~
[tex] \sf \dfrac{5}{7} = \dfrac{5 + 6}{y} [/tex][tex] \sf y = 11 \times \dfrac{7}{5} [/tex][tex] \sf y = \dfrac{77}{5} [/tex][tex] \sf y = 15.4[/tex]Hence, value of l = 15.4 units ~
Find the midpoint of PQ¯¯¯¯¯¯¯¯ with endpoints P(0, 2) and Q(6,−2). Then write an equation of the line that passes through the midpoint and is perpendicular to PQ¯¯¯¯¯¯¯¯ . This line is called the perpendicular bisector.
Answers
Answer:
The midpoint of PQ is (3,0) and the equation if the line perpendicular to PQ is y=3/2(x-3).
Step-by-step explanation:
To find the midpoint, find the average of the x and y values. (0+6)/2=3 and (-2+2)/2=0
In order to make a perpendicular line, we must find the slope first of the original line.
(y2-y1)/(x2-x1) is the formula for slope
(-2-2)/(6-0)= -4/6=-2/3
Now we know the slope which is all we need to start making the equation using the point slope form which is y-y1=m(x-x1) (let m be slope) and we use the midpoint (3,0) as our point. since it is perpendicular, we will take the slope and flip it as well as change the sign
y-0=3/2(x-3) or y=3/2(x-3)
if you'd like, you can distribute and put it in slope intercept form
y=3/2x+9/2
how to find a and b in the equation below.
3(a+b)=28
Answers
we have: 3(a+b)=28 => a + b = 28/3
=> a = 28/3 - b and b = 28/3 - a
ok done. Thank to me :>
Round your answer to the nearest hundredth
Answers
Answer:
9.49
Step-by-step explanation:
Using the Pythagorean Theorem, we know a²+b²=c².
So 3²+9²=(BA)²
9+81=(BA)²
90=(BA)²
From this, we know BA=√90
BA=9.486
Rounding to the nearest hundredth, this is 9.49
Please consider a brainliest! Thank you!
WILL MARK BRAINLIEST TO FIRST ANSWER!!!!!!
NO LINKS WILL BE ACCEPTED!!!!!!
Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
Answers
Answer:
y=3 x=1
Step-by-step explanation:
Took the quiz
Liza types 180 words in 3 minutes. At
that rate, how many minutes does it
take her to type 1,260 words?
Brainliest to a person who gets it right.
Answers
Answer:
21 minutes
Step-by-step explanation:
180 divided by 3 is 60 wpm
1260 divided by 60 is 21
need help in a math question
Answers
Answer:
- [tex]\frac{7}{6}[/tex]
Step-by-step explanation:
I hope this helps
Ali uses 1.5 cups of flour to bake a dozen cupcakes. at this rate,how many cups of flour will she need to bake 30 cupcakes?
A.3.75c
B.3c
C.2.4c
D.2.75c
Answers
Answer:
A
Step-by-step explanation:
1.5 c flour = 12 cupcake
0.75 c flour = 6 cupcake
1.5 + 1.5 + 0.75 = 3.75 c flour
45. You decide to market your own custom computer software. You must invest $3,255 for
computer hardware, and spend $2.90 to buy and package each disk. If each program sells
for $13.75, write a system of equations and determine how many disks you must sell to
break even.
Answers
The rectangle and the trapezoid have the same area. What is the length l of the rectangle?
Please show work
Answers
Answer:
length = 18 ft
Step-by-step explanation:
A(rect) = 9l
A(trap) = 1/2(9)(24+12) → 4.5(36) → 162
9l = 162
l = 162/9
l = 18
=====================================================
How to get the answer:
We first need to compute the area of the trapezoid
area of trapezoid = height*(base1+base2)/2
A = h*(b1+b2)/2
A = 9*(12+24)/2
A = 9*(36/2)
A = 9*18
A = 162
The trapezoid has an area of 162 square feet.
---------
The rectangle also has an area of 162 sq ft.
area of rectangle = length*width
A = L*W
A/W = L
L = A/W
L = 162/9
L = 18
The length of the rectangle is 18 feet.
---------
Side note: both rectangle and trapezoid have the same height (9 feet). Notice how the average of the 12 ft and 24 ft sides leads to 18 ft, which is exactly the value of L. It's not a coincidence these two facts line up.
the ortiz will travel fron indianapolis to denver this summer.The driving distance between the two cities is 1058 miles. They need to find out about how much the gas will cost round trip. Their car gets about 20 miles per gallon. They usually spend about $2.89 per gallon. a write and solve an algebraic equation to find out how many miles they will travel. Explain your steps. b. Write and solve an algebraic equation to find out how many gallons of gas they will use. Explain your steps. c. Write and solve an algebraic equation to find out how much ortiz's will spend on gas round trip. Explain your steps. d. suppose you know the total cost of the gas, do not know the price pe gallon. Explain how you would work backward to solved the problem
Answers
Answer:
a. 2116 miles
b. 105.8 gallons
c. $305.76
d. cost per gallon = total cost / number of gallons = total cost/105.8
Step-by-step explanation:
a.The round-trip distance is the sum of the distances there and back. It is double the one-way distance.
round-trip distance = 2 × one-way distance
round-trip distance = 2 × 1058 miles = 2116 miles
__
b.The gas used will be the distance divided by miles per gallon.
gas used = round-trip distance / miles-per-gallon
gas used = (2116 mi)/(20 mi/gal) = 105.8 gal
__
c.The cost of gas will be the product of cost per gallon and number of gallons.
cost of gas = cost-per-gallon × gallons
cost of gas = $2.89/gal × 105.8 gal = $305.762 ≈ $305.76
__
d.The relation used in the previous step can be used to find the cost per gallon. Divide that equation by gallons to get ...
(cost of gas)/gallons = cost-per-gallon
For the same trip, the number of gallons is 105.8, so the equation becomes ...
cost-per-gallon = (cost of gas)/105.8
Mark has already run 33.4 miles this week. He can run 2.5 miles in one hour. Construct an equation that represents the total number of miles run based on how many hours he runs for. What is the total number of miles he ran if he runs for 17 hours?
Answers
Answer:
y = 2.5x + 33.4, y = 75.9 miles
Step-by-step explanation:
Equation is y = 2.5x + 33.4
17 = 2.5 x + 33.4
y = 2.5 (17) + 33.4
y = 42.5 + 33.4
y = 75.9 miles
please help with question 3
Answers
Answer:
p = - [tex]\frac{2}{3}[/tex] , p = 2
Step-by-step explanation:
Using the discriminant to solve for p
Δ = b² - 4ac
The condition on the discriminant for 2 eeal and equal roots is
b² - 4ac = 0
Given
p²x² - (p + 2)x + 1 = 0
with a = p² , b = - (p + 2) , c = 1 , then
(- (p + 2) )² - 4p² = 0
(p + 2)² - 4p² = 0
p² + 4p + 4 - 4p² = 0
- 3p² + 4p + 4 = 0 ( multiply through by - 1 )
3p² - 4p - 4 = 0 ← in standard form
(3p + 2)(p - 2) = 0 ← in factored form
Equate each factor to zero and solve for p
3p + 2 = 0 ⇒ 3p = - 2 ⇒ p = - [tex]\frac{2}{3}[/tex]
p - 2 = 0 ⇒ p = 2
A plumber charges $8.00 per hour for her work, plus a $27 materials fee. If you pay her $107.00, for how many hours did the plumber work?
Answers
Answer:
10 hours
Step-by-step explanation:
Amount paid= material fee + ($8)(number of hours worked)
Let the number of hours the plumber worked be t.
$107= $27 +$8t
107 -27= 8t
80= 8t
8t= 80
Divide both sides by 8:
t= 80 ÷8
t= 10
Thus, the plumber worked for 10 hours.
What is the sum of 15/6
Answers
Answer: b because i did the eqaution on paper
Step-by-step explanation:
Can you help me answer this one please ?
Answers
Answer:
d. Right 5 and down 3
Step-by-step explanation:
If you have a given graph and then find that it is altered, the changes to the x (something added to or subtract from x) will be on the graph by translating (sliding) the graph left or right. Horizontal changes are probably the opposite of what they seem like they should be: x+_ moves the graph left and x-_ moves the graph right.
A number added on to the end of the equation will shift (translation, again) the graph up (a number added on) or down (a number subtracted). So in this case the x-5 moves the graph to the right 5 units and the - 3 at the end of the equation moves the graph down three units.
It takes 1 3/4 cups of cherries to make a cherry pie. Emma wants to make 3 cherry pies. How many cups of cherries will Emma need
Answers
Answer:
5 1/4 please give brainliest
Step-by-step explanation:
1 x 3 = 3 3/4 x 3 = 2 1/4
Answer:
5 1/4 please give brainliest
Step-by-step explanation:
1 x 3 = 3 3/4 x 3 = 2 1/4
A bank account, initially with $3200, earns interest at a rate of 5.5% compounded monthly. Write an equation for the amount of money in the account at a time,x.
Answers
Answer: The compound interest formula is an equation that lets you estimate how much you will earn with your savings account.
Step-by-step explanation:
there are 1200 students in a school. if 2/5 are girl what is the number and percentage of boys? find it
Answers
to find the number, multiply 1200 by 60%, or 0.60, and you get 720 boys.
final answer: 720 boys, 60%
Step-by-step explanation:
Hope it will help you...
HELPPPPPPPPPPPPPpppp
Answers
8.722 / (-3.56)
Expand [tex]\frac{8.722}{-3.56}[/tex] by multiplying both numerator and denominator by 1000.
[tex]\frac{8722}{-3560}[/tex]
Reduce the fraction [tex]\frac{8722}{-3560}[/tex] to the lowest terms by extracting and cancelling out 178.
-[tex]\frac {49}{20}[/tex] = -2.45
who ran faster, noah or lin?
Answers
PLEASE HELP.
A group of bacteria has a population of 100,000. The growth rate is 20%. How much bacteria will there be in 10 years? Use the exponential formula.
Answers
Answer:
200,000 i don't know apologies if it's wrong
Step-by-step explanation:
100,000*.20*10
200,000*10
200,000
The height, h, in feet of the tip of the minute hand of a wall clock as a function of time, t, in minutes can be modeled by the equation h = 0. 75 cosine (StartFraction pi Over 30 EndFraction (t minus 15)) 8. Which number (from 1 to 12) is the minute hand pointing to at t = 0? 3 6 9 12.
Answers
Answer:
9
Step-by-step explanation:
Answer:
Step-by-step explanation:
Question 3(Multiple Choice Worth 1 points)
(01.05 LC)
Which calculation can be used to find the value of y in the equation y3 = 27?
y=y equals 27 over 3
y=y equals cube root of 27
y=y equals square root of 27 over 3
y=y equals square root of 27
Answers
Answer:
y = y is equal to 27 over 3
Step-by-step explanation:
being y3 = 27
the y3 is found by multiplying and is passed to the other side by dividing, becoming y = 27/3
Find x .
Please help I’m begging
Answers
Answer:
x = 103
Step-by-step explanation:
Using the far right intersection, we can figure out that in inner angle is 32 degrees.
32 + 34 = 66 which is the angle of the left side of the middle cross.
x = 37 + 66 = 103