Answer:
y=0.12/1(x-5)^2 -3
y=1/10(x-10)^2 -4
Step-by-step explanation:
Given the directrix and focus of the parabolas, the equation of the parabolas are [tex]y=\frac{1}{6}(x^{2} +10x - 2)[/tex] and [tex]y=\frac{1}{20}(-x^{2} +20x - 80)[/tex].
What is equation of a parabola?Equation of a parabola is given by-
Distance of a point (x, y) on parabola from directrix = Distance of a point (x, y) on parabola from focus
focus = (-5, -3)
directrix = y = -6
[tex]\sqrt{(x+5)^{2}+(y+3)^{2} } = (y+6)\\\\ (x+5)^{2}+(y+3)^{2} = (y+6)^{2}\\\\x^{2} +25+5x = 6y+27\\\\y=\frac{1}{6}(x^{2} +10x - 2)[/tex]
focus = (10,-4)
directrix = y = 6
[tex]\sqrt{(x-10)^{2}+(y+4)^{2} } = (y-6)\\\\ (x-10)^{2}+(y+4)^{2} = (y-6)^{2}\\\\x^{2} +100-20x = -20y+20\\\\y=\frac{1}{20}(-x^{2} +20x - 80)[/tex]
Learn more about equation of parabola here
https://brainly.com/question/21685473
#SPJ2
Please help me, GodBless.
Answer:
Rate of change is 1
Step-by-step explanation:
Well rate of change in a function is basically slope
theres 1 rise and.1 run
1/1=1
So rate of change is 1
Falls City has a current population of 3,300 and is increasing 4.1% every year. How large will the population be in 8 years? Round your answer to the nearest whole number.
Angela purchased a car using a simple interest loan. The loan had an interest rate of 5% and was for three years. Angela paid $450 in interest. The principal amount of the loan was for $
Answer:
$3000
Step-by-step explanation:
Given data
Rate=5%
Time=3 years
Simple interest= $450
We know that the expression for simple interest is
SI=PRT/100
Substitute
450=P*5*3/100
cross multiply
P*15= 45000
Divide both sides by 15
P= 45000/15
P=$3000
Hence the principal amount is $3000
William is building a planetary path for people to walk through the planetary path will have a model of the sun and model of the planet William uses two different scales He uses 1 cm to 1000 km for the diameter of each planet and 1m to 1000000km for the distance of the sun to each planet William makes a model of planet Venus the model has a diameter of 12.1 work out the real diameter of venus
Answer:
The actual diameter of Venus is 12,100 kilometers.
Step-by-step explanation:
Since William is building a planetary path for people to walk through, and the planetary path will have a model of the sun and model of the planet, and William uses two different scales, he uses 1 cm to 1000 km for the diameter of each planet and 1m to 1000000km for the distance of the sun to each planet, if William makes a model of planet Venus and the model has a diameter of 12.1, to work out the real diameter of Venus the following calculation must be performed:
1 cm = 1000 km
12.1 cm = X km
1 = 1000
12.1 = X
12.1 x 1000/1 = X
12,100 = X
Thus, the actual diameter of Venus is 12,100 kilometers.
Can someone explain to me what to do and what is the correct answer please? I would really like to know what to do, thank u in advance if u help me!<3
What is the simplified form of the expression below?
3+ 4i
4 - 2i
Answer:
7 + 2i is the simplified form
Step-by-step explanation:
PLEASE HELP HURRY WILL GIVE BRAINLIST IF CORRECT
Answer:
26 per week
Step-by-step explanation:
A rectangular prism with a length of 5 inches a width of 4 inches and a height of 3 inches is how many square inches
Answer:
20
Step-by-step explanation:
length x width = area
4 x 5 = 20
(not 100% sure, but I hope this helps)
Is (2, 3) a solution to the equation y = x - 1?
yes or no
and pls explain for i can lead this already
Answer: No
Step-by-step explanation: Because if you substitute the 2 for x and 3 for y it is not equal
Seth is using a large shoe box to store his baseball cards. The length of the box is 12 inches, and the height is 6 inches. If the volume of Seth's box is 288 cubic inches, how wide is the box?
Step-by-step explanation: *First, decide which volume formula to use: v = lwh
*Next, substitute in for what you do know (leave variable for unknown): 288 = 12 · w · 6
*Then simplify the side of the equation with the variable: 288 = 72 · w
*Now divide each side of the equation by 72 to solve for w:
288 ÷ 72 = w
4 in = w
What is the quotient of 1,234 and 4?
Answer:
308.5 lol
Step-by-step explanation:
The polynomial V(x)=x^3+9x^2-16x-144 represents volume of a shipping crate. Explain how to find the area of the base of the crate? if the polynomial H(x)=x+4 represents the height of the crate
Answer:
x = − 9 , − 4 , 4
Step-by-step explanation:
Each crate is in the shape of a rectangular solid. Its dimensions are length, width, and height. The rectangular solid shown in the image below has a length
4 units, width 2 units, and height 3
units. Can you tell how many cubic units there are altogether? Let’s look layer by layer.
Breaking a rectangular solid into layers makes it easier to visualize the number of cubic units it contains. This
4 by 2 by 3 rectangular solid has 24 cubic units.
A rectangular solid is shown. Each layer is composed of 8 cubes, measuring 2 by 4. The top layer is pink. The middle layer is orange. The bottom layer is green. Beside this is an image of the top layer that says
Altogether there are 24 cubic units. Notice that 24 is the length × width × height .
The top line says V equals L times W times H. Beneath the V is 24, beneath the equal sign is another equal sign, beneath the L is a 4, beneath the W is a 2, beneath the H is a 3.
The volume, V , of any rectangular solid is the product of the length, width, and height.
V = L W H
We could also write the formula for the volume of a rectangular solid in terms of the area of the base. The area of the base, B , is equal to length × width . B = L ⋅ W
We can substitute
B for L ⋅ W in the volume, formula to get another form of the volume formula.
The top line says V equals red L times red W times H. Below this is V equals red parentheses L times W times H. Below this is V equals red capital B times h.
We now have another version of the volume formula for rectangular solids. Let’s see how this works with the
4 × 2 × 3
rectangular solid we started with. See the image below.
Besides the solid is V equals Bh. Below this is V equals Base times height. Below Base is parentheses 4 times 2. The next line says V equals parentheses 4 times 2 times 3. Below that is V equals 8 times 3, then V equals 24 cubic units.
Help me with this please
Answer:
21 degrees.
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
as BC ║DE ⇒ ∠CBA=∠BAD
⇒ ∠x=180-∠BAD -∠CAB
⇒ ∠x=180-105-54=21
Identify if they are function or not
Answer:
1=function
2=not function
3=function
4=function
5=function
6=not function
7=not function
8=function
CAN SOMEONE HELP ME FIND THE AREA OF THE LIGHT GRAY PART WITH AN EXPLANATION :)
(IF YOU WANT ME TO GO TO A LINK I'M NOT, SO YOUR ANSWER WILL BE REPORTED IF YOU DECIDE TO INCLUDE ONE)
Answer:
91 or 525
Step-by-step explanation:
Multiply the objects width (How long it is), times height. For the smaller object inside the bigger object, it is 91. For the bigger object, it is 525.
Find the equation the line with the given information below:
slope = 3, y-intercept = (0, 2).
Answer:
y=3x+2
Step-by-step explanation:
y=mx+b
b=2
m=3
plug in
y=3x+2
(2x+1)^2+4x(x-1)-3+3(-4x^2
Answer:
−4x2−2
Step-by-step explanation:
if T= 101+102+103+...+199 find T
...............................................
Give an example to show that when two prime numbers are added, the result
may be an odd number.
Answer:
2+3=5
Step-by-step explanation:
prime numbers =2 and 3
sum =5 which is odd
Please help!!
A circle has a circumference of 1007 cm. What is the radius of the circle?
Answer:
3/2 I'm not sure I think it's that
Grayson is deciding between two truck rental companies. Company A charges an initial fee of $40 for the rental plus $2 per mile driven. Company B charges an initial fee of $100 for the rental plus $1 per mile driven. Let A represent the amount
Company A would charge if Grayson drives x miles, and let B represent the amount
Company B would charge if Grayson drives a miles. Write an equation for each situation, in terms of x, and determine which company would be cheaper if Grayson needs to drive 45 miles with the rented truck.
A=
B=
_______ is $_____ cheaper than _____ when driving 45 miles.
Plz before in 10mins.
Answer:
A is 10 dollar cheaper than B
Step-by-step explanation:
A : 40 dollars plus 45*2=90
90+40= 130 dollars
B:100 dollars 45*1=45
100+45= 145 dollars
Answer:
A is 15$ cheaper than b
Step-by-step explanation:
A= 40+(45*2) = 40+90=130$
b= 100+45 =145$
slope of (9,3) (19,-17) using slope formula
The cost of renting a bicycle, y, for
x hours can be modeled by a linear
function. Renters pay a fixed insurance
fee of $12 plus an additional cost of $10
per hour, for a maximum of 6 hours.
What is the range of the function for this
situation?
F {22, 32, 42, 52, 62, 72}
G {1, 2, 3, 4, 5, 6}
H {12, 24, 36, 48, 60, 72}
J {22, 34, 46, 58, 70, 82}
Answer:
F
Step-by-step explanation:
1(10) + 12= 22
2(10) + 12= 32
etc.....
Which is an equivalent form of the first equation that when added to second equation eliminates the x terms? 4/5 x-3/5y=18
Answer:
[tex]-8x + 6y = -180[/tex]
Step-by-step explanation:
Given
[tex]\frac{4}{5} x-\frac{3}{5}y=18[/tex]
[tex]8x + 12y = 11[/tex]
Required
Equivalent form of the first equation that eliminates x when added to the second
To do this, we simply make the coefficients of x to be opposite in both equations.
In the second equation, the coefficient of x is 8.
So, we need to make the coefficient of x -8, in the first equation.
[tex]\frac{4}{5} x-\frac{3}{5}y=18[/tex]
Multiply by -10
[tex]-10 * [\frac{4}{5} x-\frac{3}{5}y=18][/tex]
[tex]\frac{-40}{5} x+\frac{30}{5}y=-180[/tex]
[tex]-8x + 6y = -180[/tex]
When this is added to the first equation, the x terms becomes eliminated
Sidney has $100 in a savings account. The interest rate is 10% per year and is not
compounded. How much interest will she earn in 3 years?
Answer:
130 dollars
Step-by-step explanation:
This time I don't think I done messed it up
Have a good day!
One angle of an isosceles triangle measures 46°. Which other angles could be in that isosceles triangle?
Answer:
67 degrees for both of the other angles or 46 degrees and 88
Step-by-step explanation:
An isosceles triangle has two angle that are the same size so it could only be these.
The top of a tall building has four triangular faces that slope toward a single point. What shape best models the top
of the building?
А cube
c. triangular pyramid
B cone
Dsquare pyramid
Choose
Answer:
Option D, square pyramid
Step-by-step explanation:
The base of a square pyramid is a square of side of length "A"
and the height of the pyramid is "h"
From the four sides of base of pyramid, four surfaces arises that are slanting and meet at a point at the top at height "h"
Hence, option D is correct
Find the product.
-7(-a 2)(-5)
Answer:
3
5
(
−
2
)
Step-by-step explanation:
Simplify then multiple the numbers
please dont put any links or I'll report:(
Answer:
1000
Step-by-step explanation:
volume of prism formula=b*w*h(base times width times height)
10*10*10(10^3)=1000
Answer: 1,000 m
Step-by-step explanation:
To find volume you have to multiply: LengthxWidth,Height so you would do 10x10x10 and get 1,000 m
HOPE THIS HELPS ^^
What is the area of a rectangle with side lengths 2/5 feet and 4/6 feet?
Answer:
[tex]\frac{4}{15}[/tex] (4/15)
Step-by-step explanation:
[tex]\frac{4}{6}=\frac{2}{3}[/tex]
[tex]\frac{2}{5}*\frac{2}{3};[/tex]
1- Multiply the numerators:
[tex]2*2=4[/tex]
2- Multiply the denominators:
[tex]5*3=15[/tex]
3- Thus:
[tex]\frac{2}{5}*\frac{2}{3}= \frac{4}{15}[/tex]
Hope this helps ;)