The Equation of parabola with focus (3,1) and directrix y = 3 is [tex]10x^2 + 9y^2-60x -14y+91 =0[/tex]
What is Parabola?A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
Here, focus (3,1) and directrix y=3
Let the locus of parabola be (x, y)
We know that, in Parabola
Distance between locus to focus = Distance between locus to directrix line
[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex] = [tex]\frac{Ax_{1}+By_{1}+C }{\sqrt{A^2 + B^2 + C^2} }[/tex]
[tex]\sqrt{(x-3)^2+(y-1)^2} = \frac{0.x+1.y-3}{\sqrt{0^2+1^2+(-3)^2} }[/tex]
On squaring both sides, we get
[tex](x-3)^2 + (y-1)^2 = (\frac{y-3}{\sqrt{10} } )^2[/tex]
[tex]x^2 -6x + 9 + y^2 -2y + 1 = \frac{y^2 -6y +9}{10}[/tex]
[tex]10x^2 + 9y^2-60x -14y+91 =0[/tex]
Thus, The Equation of parabola with focus (3,1) and directrix y = 3 is [tex]10x^2 + 9y^2-60x -14y+91 =0[/tex]
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Questions are on the picture, a-e.
What is equilibrium?
Equilibrium price is the price at which the quantity demanded equals the quantity supplied. The equilibrium price is $1.12.
Above equilibrium price, quantity supplied would exceed quantity demanded and there would be a surplus. When price is below equilibrium price, quantity supplied would be less quantity demanded and there would be a scarcity.
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The variables x and y vary inversely. Use x = 4 and y = 8 to write an equation relating x and y. Then find y when x
= 2.
Answer:
y=[tex] \frac{32}{x} [/tex]16Step-by-step explanation:
y=
[tex] \frac{k}{x} [/tex]
when x=4 and y = 8
k =xy
k=4×8=32
:- y=
[tex] \frac{32}{x} [/tex]
when x = 2
y=
[tex] \frac{32}{2} [/tex]
:- y = 16
(x) = -2x - 3
g(x) = 3x + 1
Find (f .g)(x)
Answer:
Answer:-6x^2 -11x - 3
Step-by-step explanation:
(f.g)(x)=(-2x-3)(3x + 1)
= -6x^2 -11x - 3
help please I'm confused
Answer:
Milena level tro bau bola ehh
Answer:
1.3 < x < 6.7
Step-by-step explanation:
The property of triangles is that the length of the third side must be less than the sum of the lengths of the other 2 sides.
Minimum value : Taking 4.0 to be the 3rd side.
2.7 + x > 4.0x > 1.3Maximum value : Taking x to be the 3rd side
2.7 + 4.0 > xx < 6.7Range
1.3 < x < 6.7
Given the following equation what is the value of y if x = 7
15
Select the correct answer.
If f(x) = (x+1)-¹ and g(x)
= x^-2, what is the domain of f(x) = g(x)?
Answer:
Step-by-step explanation:
[tex]f(x)=g(x) \implies \frac{1}{x+1}=\frac{1}{x^{2}}[/tex]
This means the denominators cannot equal to (because then the fractions would be undefined) so the domain is [tex]x \in \mathbb{R} -\{-1,0\}[/tex]
Rahul drives 10 miles in 20 minutes. If he drove three hours in total at the same rate, how far did he go?
Before you try that problem, answer the question below.
How many minutes did Rahul drive in total?
Answer: 180 minutes
90 miles in 3 hours
Step-by-step explanation:
60 minutes = 1 hour
60 mins/20 mins = 3
60*3 = 180
30 miles per hour for 3 hours is 90 miles
PLEASE HELP WILL MARK BRSINLIEST!!!!!
Answer:
AC=18
Step-by-step explanation:
Let's look at the smaller triangle first. Side AB is 2.5, side BC is 3.5 and side AC is 4.5. Now, looking at the larger triangle, we see that side AB is 10, side BC is 14 and side AC is unknown.
So, how do we find side AC?
First, let's take a look at the other sides available to us—how about AB? On the smaller triangle, AB=2.5, and on the larger triangle AB=10. So, what's their relation?
Well, let's first divide the two by each other: 10/2.5, of which gets us 4. Now, this in itself gives us answer, but let's just double check to be sure. So, taking side BC on the smaller triangle, 3.5, and on the larger triangle, 14, we then divide the two again. 14/3.5 and- look at that! We get 4 again again.
This tells us that 4 is then our multiplier, so we can write the equation as follows: 4.5 (of which we get from the smaller triangle) *4=?. So, with the equation 4.5*4, we get 18 as our answer for ?, or simply the unknown side "a".
I really need help with this.
Answer:
300 cm cubed or 300 cm^3
Step-by-step explanation:
(b x h ) / 2 = Area of triangle
5 x 12 = 60
60 / 2 = 30
Because it is a prism, the cross-sectional area is the same throughout the prism. Therefore, you just need to multiply the area by the height/width, which is 10cm.
30 x 10 = 300 cm cubedor 300 cm^3
Answer:
1/2BA*2+l*w
1/2*12*5*2+10*13+12*10+10*5
=360cm
Look at the image below.
Find the area of the parallelogram.
Answer:
Below.
Step-by-step explanation:
Area = base * perpendicular height
= 3 * 5
= 15 square units.
The area of the parallelogram is 15 square units.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal
Area of a two dimensional shape is the total region which is bounded by the object's shape.
If the base and height is known,
Area of a parallelogram = base × height
Given base = 3
Height = 5
Area = 3 × 5 = 15 square units
Hence the required area of the parallelogram is 15 square units.
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Answer:
-20.5
Step-by-step explanation:
Using a basic calculator, you divide 10.25 by -.5 which easily gives -20.5
Convert: 8 tons = _____ pounds
4 pounds
80 pounds
8,000 pounds
16,000 pounds
Answer:
16,000 pounds hope this helps!
[tex]\sqrt{272}[/tex] Simplify.
√272 is a real number, and the simplified expression of √272 is 4√17
How to simplify the expression?The expression is given as:
√272
Expand
√272 = √16 * 17
Take the square root of 16
√272 = 4√17
Hence, the simplified expression of √272 is 4√17
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Given the following quadratic sequence -2, 0, 3,7
1. Write down the value of the next two terms of this sequence
2. Determine the n term of this sequence
3. Which term of the sequence will be equal to 322?
Answer:
1) 12
2) an=n²+n-6/2
3) the 25th term
Step-by-step explanation:
check explanation in the attached image
Graph the set {x | -7 < x < - 1} on the number line. Then, write the set using interval notation. Thank you!
To graph this on a number line, we'll have open holes at -7 and -1. Then shade between those open holes to complete the graph. The open holes tell the reader "do not include the endpoint". The x values span from -7 to -1, excluding both endpoints. Use of filled in holes, or closed endpoints, will signal that we include the endpoint.
The answer in interval notation is (-7, -1) which unfortunately looks identical to ordered pair notation. The parenthesis tell the reader to exclude the endpoints. If you wanted to include the endpoint, then use a square bracket instead.
Summary:Graph: Plot two open holes at -7 and -1, then shade in betweenInterval notation: (-7, -1)Need help for this please
Step-by-step explanation:
what is the problem ?
we only need to use the formula that can be found easily on the internet.
the area of a circle is
pi×r²
r being the radius (half of the diameter). in our case :
14/2 = 7 m
and we shall use 22/7 as approximation for pi.
so, we get as circle area
22/7 × 7² = 22 × 7 = 154 m²
What is the value of 50 x 3 - 120 / 40
Answer:
The answer is 150-3
That is 147
Step-by-step explanation:
Do This
(50 x 3)-(120/40)
150-3
147 is your answer
SOMONE PLEASE HELP ME I WILL GIVE YOU 30 POINTS AND BRAINLESS??
Given: mZRPQ = 23°; m ZTPR = 85
If ZSPR and ZRPQ are complementary angles, then what is the measure of ZTPS?
A. 5
B. 18°
C. 23°
D. 67°
Answer:
I would think 23°
Step-by-step explanation:
I could be wrong but I would think 23° because if I remember correctly they're congruent.
A person works and earns $3853 dollars but on a pay stub pays 49% to tax. What is the sales Tax?
Answer:
1887.97 (3853 * 0.49)
Step-by-step explanation:
3853 * 0.49
Please help me with this really need the answer please
Teresa is maintaining a camp fire. She can
keep the fire burning for 4 hours with 6 logs.
She wants to know how many logs (y) she
needs to keep the fire burning for 18 hours.
She assumes all logs are the same.
How many logs does Teresa need to
maintain the fire for 18 hours?
Answer:
27
Step-by-step explanation:
she needs 24 logs to keep the fire for 16 hours(4×6). And for next 2 hours she's gonna need 3. altogether it's 27.
please help will mark Brainliest!!.
4. For exercise, Francesca walks laps around a track. She walked 0.9 of a lap around the track in 5 minutes. If each lap is 440 yards, how fast did
Francesca walk?
•88 yards per minute
•360 yards per minute
•90 yards per minute
• 79.2 yards per minute
Answer:
79.2 yards per minute
Step-by-step explanation:
First you 440 times 0.9. which equals 396. Then you divide the answer by 5 to get 79.2.
Which polynomial expression is equal to (a + 3)(a − 3)(a² + 9)?
Answer:
a⁴ - 81
Step-by-step explanation:
Identity applied :
(a + b)(a - b) = a² - b²
Simplifying :
(a + 3)(a − 3)(a² + 9)(a² - 9)(a² + 9)a⁴ - 81Describe the end behavior of each function.
3) f(x) = -x^4+x^2 -x+1
Answer:
End Behavior is
y -> -inf as x -> -inf
y -> -inf as x -> +inf
Step-by-step explanation:
I am not sure if your teacher has explained how to look at the equation and determine the end behavior of that function without a graph. Here is a picture that explains it.
Help asap please. Thank you!!!!
Answer:
Step-by-step explanation:
You've plotted 3 points where x = 0, 1 and 2
= where y = 1, 1 1/2 and 9/4
They are correct.
I suggest you plot 1 more where x = -1 and another where x = 3
Where x = -1 , y = (3/2)^-1 = 2/3.
x = 3 , y = (3/2)^3 = 27/8 = 3 3/8.
Which graph represents the function f(x) = –x2 + 5? On a coordinate plane, a parabola opens down. It goes through (negative 3, negative 4), has a vertex at (0, 5), and goes through (3, negative 4). On a coordinate plane, a parabola opens up. It goes through (negative 2, 9), has a vertex at (0, 5), and goes through (2, 9). On a coordinate plane, a parabola opens down. It goes through (negative 6, negative 9), has a vertex at (negative 5, 0), and goes through (negative 2, negative 9). On a coordinate plane, a parabola opens up. It goes through (negative 8, 9), has a vertex at (negative 5, 0), and goes through (negative 2, 10).
Answer:
The graph in the attached figure
Step-by-step explanation:
we have the quadratic function
[tex]f(x)=-x^2+5[/tex]
This is a vertical parabola open downward
The vertex is a maximum
Remember that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^2+k[/tex]
where
a is a coefficient
(h,k) is the vertex
In this problem
a=-1
(h,k)=(0,5) ----> vertex
The y-intercept is the point (0,5) ---> value of y when the value of x is equal to zero (is the same point that the vertex)
The x-intercepts are the points --->values of x when the value of y is equal to zero
using a graphing tool
The graph in the attached figure
Answer:
A on edge
Step-by-step explanation:
i took the test
. Estimate the sum of 277 and 854 and write them in Roman numerals.
Answer:
The answer is MC = 1100. The real answer is 1131 but I have estimated the answer to the nearest hundred.
Step-by-step explanation:
I just added them up to get the real answer. The real answer is 1131 but I have estimated the answer to the nearest hundred.
A box contains orange balls and green balls. The number of green balls is ten more than four times the number of orange balls. If there are 110 balls altogether, then how many green balls and how many orange balls are there in the box?
Answer:
there are 50 orange balls
Step-by-step explanation:
let green balls be x
orange balls be y
green balls = orange balls + 10
x = y+10
orange balls + green balls = 110
x + y = 10
y + 10 + y = 110
2y + 10 = 110
2y = 110 -10
2y = 100
y = 50
thus there 50 orange balls
Contagious diseases can spread quickly. Suppose 3 people are ill during the first week of an epidemic, and each person who is ill spreads the disease to five people by the end of the next week. By the end of the 8th week of the epidemic, how many people have become ill?
Answer:
1875
Step-by-step explanation:
3x5 = 15
15x 5 = 75
75x 5 = 375
375 x 5 = 1875
1875 because at the end of the next week, which basically turns 8 weeks into 4, and the number of contaminants multiply by 5 each other week.