A parabola can be drawn given a focus of ( - 8,0) and a directrix of y= - 2 What can be said about the parabola?
Answers
Answer:
The equation of the parabola is:
y
=
1
32
x
2
Explanation:
Please notice that we know that the parabola opens upward or downward, because the directrix is a horizontal line:
y
=
−
8
This tells use that the equation of the parabola of the form:
y
=
f
(
x
)
Not
x
=
f
(
y
)
.
Furthermore, we can see that it must open upward, because the y coordinate of the focus is above the directrix.
The vertex has the same x coordinate as the focus:
x
=
0
And its y coordinate is halfway between the focus and the directrix:
y
=
8
−
8
2
=
0
Therefore the vertex is
(
0
,
0
)
Use the vertex form of the equation of a parabola that opens upward or downward:
y
=
a
(
x
−
h
)
2
+
k
where the vertex is the point
(
h
,
k
)
.
Substitute the vertex into the equation:
y
=
a
(
x
−
0
)
2
+
0
Simplify:
y
=
a
x
2
The distance, f, from the vertex to the focus is,
f
=
8
; this allows use to find the value of
a
, using the equation:
a
=
1
4
f
a
=
1
32
The equation of the parabola is:
y
=
1
32
x
2
Step-by-step explanation:
Answer:
vertex is (-8,-1) with a p-value of 1 and it opens upward
Step-by-step explanation:
the vertex is the place in directly between the focus and the directrix, giving us (-8,-1)
the p-value is the equivalent distance between the focus and the vertex, or the vertex and the directrix, giving us 1
the parabola opens away from the directrix, meaning it opens upward
Related Questions
Give me the answer pls!
Answers
Answer:
Square Area = ( one side length)²
784 = (AB)²
AB = 28
circle radius = 14
pi = 3.142
semi circle parameter = pi × r
= 3.142 × 14 = 43.988
square parameter = 3 × 28 = 84
we dont calculate the 4th side.
parameter of the figure = 43.988+ 84= 127.988
At what values of x does the graph of y=e−x+2xe−x+x2e−x have a point of inflection?
Answers
Where the voice rises and falls. But inflection also describes a departure from a normal or straight course.
What is inflection point and how to find an inflection point?
Inflection points for the given equation x^2e^{-2x} are
f'(x) =\(2x2xe^{(-2x)}-2{(x2)} e^{(-2x)}\)
f'(x) =\(-2(x-1)xe {(^-2x)}\)
The point of inflection, also known as the inflection point, is when the function's concavity changes. Changing the function from concave down to concave up, or vice versa, signifies that. In other words, an inflection point is the location at which the rate of slope shift from a growing to a decreasing way, or vice versa, occurs. There is no doubt that those positions are neither local maxima nor minima. They are fixed points.On a curve, an inflection point is when the concavity changes, according to definition. (i.e., a shift in the sign of curvature). We are aware that the function is concave up if f " > 0, and that it is concave down if f " 0. The point of inflection on a graph is where the function switches from positive to negative, or from negative to positive, at a particular value of x = c.x= -b±√(b^2 - 4ac)/2a
x=4±√(16+16)4
x=4±4√2/4
x=\(\sqrt{2+2/2}\)
x=\(\sqrt{2-2/2}\)
We get,
x=\(\sqrt{(2+2)/2^{2}*\sqrt{2+2}\)
so, inflection points are,
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What's the answer to this question?
Answers
Why?: 5+3+2= 10
You then try looking at your 5 options, and choose the one that is closest to 10. 9.4 rounds to 9, but it is closest to 10 out of all the options...
Hope this helped!
A bag contains 4 white counters, 8 black counters, and 3 green counters. What is the probability of drawing(a) a white counter or a green counter? (b) a black counter or a green counter? (c) not a green counter?
Answers
Given:
\(\begin{gathered} White-counters(W)=4 \\ Black-counters(B)=8 \\ Green-counters(G)=3 \end{gathered}\)To Determine: The probability of drawing a white or a green counter
Solution
\(\begin{gathered} P(A)=\frac{n(A)}{n(S)} \\ P(A)=The\text{ probability of A} \\ n(A)=Number\text{ of A} \\ n(S)=Total\text{ Outcome} \end{gathered}\)\(\begin{gathered} For\text{ the given} \\ n(S)=4+8+3=15 \\ P(W)=\frac{4}{15} \\ P(B)=\frac{8}{15} \\ P(G)=\frac{3}{15}=\frac{1}{5} \end{gathered}\)So
\(\begin{gathered} P(WORG)=P(W)+P(G) \\ =\frac{8}{15}+\frac{1}{5} \\ =\frac{8+3}{15} \\ =\frac{11}{15} \end{gathered}\)Hence, the probability of
(b)
\(\begin{gathered} P(BORG)=P(B)+P(G) \\ =\frac{4}{15}+\frac{1}{5} \\ =\frac{4+3}{15} \\ =\frac{7}{15} \end{gathered}\)A machine puts lids on 45 jars per minute
How many jars can the machine put lids on in 30 minutes?
Enter your answer in the box.
Answers
Answer:
1350 jars in 30 minutes
Step-by-step explanation:
45 jars × 30 mins
Answer: 1350
Step-by-step explanation: 45 x 30 = 1350
Hope this helps!
The maximum resistance for a new spark plug wire is 840 ohms per inch. A 25-in. wire had a resistance of 20,250 ohms. Does this fall within the acceptable limit?
Answers
Answer:
Yes
Step-by-step explanation:
Let's calculate the resistance of one inch for our wire and compare it with the maximum:
20250 / 25 = 810 Ohm
810 < 840 ? Yes!
Yes, this is within the acceptable limit. Wire can be used.
Find the value of 5⁰ X 7⁰ X 3⁰
plz help asap
Answers
Answer:
5⁰ × 7⁰ × 3⁰ = 1
Step-by-step explanation:
5⁰ × 7⁰ × 3⁰ = ?
5⁰ = 1
7⁰ = 1
3⁰ = 1
1 × 1 × 1 = 1
What is the area of a circle with a radius of 4 ft?
(Use 3.14 for Pi.)
Answers
Step-by-step explanation:
A = Pi x r^2
r=4_____________
Answer:
50.26548
50.27 Rounded to the hundredths place .
Which inequality is true for x = 20?
Answers
Answer:
Step-by-step explanation:
The options are :
A. x + 30 < 3x
B. x - 5 < 2x - 35
C. x divided by 4 < x - 12
D. 2x < x + 22
Option (A) :
x + 30 < 3x
Put x = 20 on both sides
LHS = 20 + 30 = 50
RHS = 3(20) = 60
50<60
The option is correct.
Option (B) :
x - 5 < 2x - 35
Put x = 20 on both sides
LHS = x-5 = 20-5 = 15
RHS = 2x - 35 = 2(20) -35 = 5
15<5
The option is incorrect.
Option (C) :
x/4 < x - 12
Put x = 20 on both sides
LHS = 20/4 = 5
RHS = x - 12 = 20-12 = 8
5<8 (correct)
Option (D) :
2x < x + 22
Put x = 20 on both sides
LHS = 2x = 2(20) = 40
RHS = x+22 = 20 + 22 = 44
40<44
It is true. The option is correct.
Hence, option A, B and D are correct.
Answer:the last one
Step-by-step explanation:
The yearly cost of a life-saving cancer
treatment is growing exponentially. If the
current cost is $3,500 per year, which of
the following functions could represent the
annual cost of this cancer treatment in x years
Answers
Answer: x= 3500+ x^2
Step-by-step explanation:
x^2 is the formula for an exponential number. Add 3500 because that’s what you started with and then just add x^2
There are 946 milliliters in a quart. There are 2 pints in a quart
How many milliliters are in a pint?
Answers
Answer:
There are 473 millimeters in 1 pint.
Step-by-step explanation:
946 ml in 1 quart.
2 pints in 1 quart
hence,
946 ml in 2 pints
hence in 1 pint we have 946/2 ml
i.e. 473 ml in 1 pint.
:)
Answer:
473 milliliters
Step-by-step explanation:
If there are 946 mL in a quart and there are 2 pints in a quart, divide 946 by 2 to find how many mL are in one pint.
Here's an equation you can set up to solve the problem.
— 946 = 2x
— 946 / 2 = 2x / 2
— 473 = x
So, if we let x stand for the amount of mL in a pint, then 473 = x means there are 473 mL in a pint.
Which point could represent 5/3 ?
Answers
Answer:D
Step-by-step explanation:
5/3 is 2/3 and its also between 0 and 1
Answer:
the answer is C
Step-by-step explanation:
i got it right
SOMEONE PLEASE HELP!! ITS ALMOST DUE!! ILL MARK BRAINLIEST!!!
Answers
Answer:
5.8
Step-by-step explanation:
c=(square root of 5^2 + 3^2)
math please help 5-8
Answers
Answer:
5. 4.6
6.1.3
7.15
8.55
Step-by-step explanation:
Mannnnn Im from south korea and this is justttttt.... Holy crab I lost my words
If f (x) =2x^3 + 2x -3 and g(x) = -0.5 |x-4|. What is the value for f(x) = g (x) ?
A. X = 0
B. X = -1.75
C. X = 4
D. X = 0.5
Answers
Answer:
D. x = 0.5
Step-by-step explanation:
A graphing calculator is the quickest way to get to an answer here.
f(x) = g(x) for x = 0.5
__
We can find the y-intercepts of the two functions to be ...
f(0) = -3
g(0) = -2
We know the x-intercept of g(x) is x=4. The x-intercept of f(x) will be a value less than 1, because f(1) = 1. (The function crosses the x-axis between x=0 where f(x) < 0 and x=1, where f(x) > 0.)
Considering these intercept points, we know the value of x for f(x)=g(x) will be between x=0 and x=1. There is only one answer choice in that interval:
x = 0.5
Which equation represents this sentence? 10 points! Twenty-eight is the product of four and a number. 28=4n 28=4+n 28=4n 28=4n
Answers
Answer:
28=4n
Step-by-step explanation:
since it is said that 28 is the product of 4 and a number
therefore, 28 is the final answer and we use n to represent the unknown number, and it is also said product of 4 and the unknown number thereby giving us our final answer 28=4n
which table represent a linear function
Answers
Answer:
The last answer is correct. (x: 1,2,3,4 ; y: -5,0,5,10)
Step-by-step explanation:
In a linear function, the rate of increase/decrease is constant (the same). For the last answer, since for every x increase, y increases by 5, it is linear and has a constant rate of change.
Lisa wrote a business plan for an entrepreneurship class, and now she has to make bound copies. Lisa could use a printer who charges a setup fee of $40 and $5 for every copy printed. Another possibility is to go to the office supply store, where she could pay an up-front fee of $30 and $10 per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How many copies is that?Write a system of equations, graph them, and type the solution.
Answers
The equation for the first option would be
\(y=40+5x\)Where "x" is the number of copies and y the cost.
The second equation will be
\(y=30+10x\)If we graph both equations we have
As we can see, they will be equal in terms of cost with 2 copies. The cost will be 50.
We can see it at the intersection of the two graphs! we can also do it with algebra, if the costs are equal (same "y") we can say
\(\begin{gathered} 40+5x=30+10x \\ \\ 10=5x \\ \\ x=2 \end{gathered}\)The number of copies is 2.
Solve the quadratic equation by completing the square. 2x^2-8x-5=0Completing the square gives us: (x- Answer )^2 = AnswerEnter your solutions below from smallest to largest. If a solution is repeated type that answer for both values of x. If your answer is not an integer then type it as a decimal rounded to the nearest hundredth.x=Answer and x=Answer
Answers
ANSWER
(x-2)^2 = 13/2
x = 4.55 or x = -0.55
STEP BY STEP EXPLANATION
please help me solve
Answers
Answer:
130 degrees
Step-by-step explanation:
DE+DA=130
Write a recursive formula and an explicit formula for the following arithmetic sequence.
-5, 1, 7, 13, 19, ...
A recursive formula is a₁ = a₁ = ₁
(Simplify your answers.)
Answers
The recursive formula is aₙ₊₁ = aₙ + 6 and the explicit formula is aₙ = -5 + (n-1)6 for the given sequence.
What is the recursive formula of an arithmetic sequence?The recursive formula to find the nth term of an arithmetic sequence is:
aₙ = aₙ₋₁ + d for n ≥ 2
where aₙ is the nth term of an A.P.
In arithmetic, sequence d represents the common difference.
Where aₙ is the nth term of the sequence and a₁ is the first term
Given the sequence -5, 1, 7, 13, 19, ...
The first term (a₁) = -5
a₂ = 1
a₃ = 7
a₄ = 13
a₅ = 19
The common difference (d) = a₅ - a₄= a₄ - a₃= a₃ - a₂ = 6
So, aₙ₊₁ - aₙ = 6
aₙ₊₁ = aₙ + 6
The explicit formula of the given sequence is given by,
aₙ = a₁ + (n-1)d
aₙ = -5 + (n-1)6
Hence, the recursive formula is aₙ₊₁ = aₙ + 6 and the explicit formula is aₙ = -5 + (n-1)6 for the given sequence.
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Rob lost 77 pounds in the 1st 6 months of his diet then 16 pounds in the next 2 months find his average change in way each month
Answers
Answer:
7 is a good answer. Do you know how good of an answer 7 is. I don't think you do. If you don't know the answer always choose 7.
given constants $a,$ $b,$ and $c,$ let $\alpha$ and $\beta$ be solutions to the equations \[a \cos \theta b \sin \theta
Answers
A constant is fixed, which is arbitrary since you don't know what that fixed number is the arbitrary denotes that no particular value has been ascribed.
The order of a differential equation is equal to the number of arbitrary constants in its general solution.
The highest-order derivative that a differential equation has is used to define the equation's order. The highest-order derivative of a differential equation is defined as its degree, which is expressed as a power. The formula:
c1=a1+ib1
and c2=a2+ib2
the solution will be
y(x)=(a1+ib1+a2+ib2)cos(ax)+i(a1+ib1−a2−ib2)sin(ax)
If and only if
a2=a1
and b2=−b1
will be the solution real because of complex conjugates using this property.
Know more about arbitrary
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Full question
Can arbitrary constants in solutions to 2nd-order linear differential equations be complex?
A parking manager recorded the number of cars in a city parking lot. She found that 90% of the parking spaces in the lot were occupied. If there are 30 spaces in the parking lot, how many are occupied with a car?
Answers
Answer:
divide 90 and 30 to see what you got
Step-by-step explanation:
number 1 hshshhhshsh
Answers
Answer:
i am saying
Step-by-step explanation:
a) 5nt7equals 12
Answer:
C
Step-by-step explanation:
I don't want to explain again because my question got deleted for some reason. I hope you understand and have a phenominal day!
(6p+4)+(-5p+8)
Plz i need help
Answers
Answer:
p+12
Step-by-step explanation:
I'm assuming you want me to simplify this equation. Okay, first, we eliminate the redundant parenthesis. Now, we have 6p+4+-5p+8, we can simplify this to 6p+4-5p+8 because adding a negative has the same effect as subtraction. Now, we combine like terms (6p and -5p, and 4 and 8). From this, we have 1p+12 (4+8=12, and 6p-5p=1p, or just p). We can simplify this even more to get p+12. I hope this helps!
Ms. Thomspon needs 15/2 yards of red fabric and 7 1/2 yards of silver fabric. which comparison is true.
Answers
Step-by-step explanation:
To compare the two amounts of fabric, we need to express them with a common denominator:
15/2 = 30/4
7 1/2 = 15/2
Now we can compare the two amounts:
30/4 > 15/2
This is true because 30/4 is equal to 7.5 yards, which is greater than 7.5 yards (or 15/2 yards) of silver fabric.
Therefore, Ms. Thompson needs more red fabric than silver fabric.
Simplify.
2x-4
²-8+12
O
O
O
-6
x+6
x-6
-
x-2
²-82+12
Answers
The simplified value of (2x - 4)² is 4x² - 16x + 16.
First, let us understand the algebraic identities;
Algebraic identities are equations in which the left hand side of the equation is identically equal to the right hand side of the equation.
Some of the identities are:
(a + b)² = a² + 2ab + b²(a - b)² = a² - 2ab + b², etc.We are given (2x - 4)².
Use the identity (a - b)² = a² - 2ab + b² to expand to the given expression.
So, a = 2x and b = 4.
Put it into the identity, we will get;
Therefore,
(2x - 4)² = (2x)² - 2 * 2x * 4 + (4)² = 4x² - 16x + 16
Thus, the simplified value of (2x - 4)² is 4x² - 16x + 16.
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PLS HELP WILL MARK BRAINLIEST
Answers
Find the inverse of each of the given functions.
f(x) = 4x-12
ƒ¹(x) =
