A parabolà can be drawn given a focus of (7,9) and a
directrix of y = 5. Write the equation of the parabola
in any form.
Answers
from the provided focus point and directrix, we can see that the focus point is above the directrix, meaning is a vertical parabola and is opening upwards, thus the squared variable will be the "x".
keeping in mind the vertex is half-way between these two fellows, Check the picture below.
[tex]\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \begin{cases} h = 7\\ k = 7\\ p = 2 \end{cases}\implies 4(2)(y-7)=(x-7)^2\implies 8(y-7)=(x-7)^2 \\\\\\ y-7=\cfrac{1}{8}(x-7)^2\implies \boxed{y=\cfrac{1}{8}(x-7)^2+7}[/tex]
Final answer:
The equation of the parabola with a focus of (7,9) and a directrix of y = 5 can be written as (x-7)^2 = 16(y-5).
Explanation:
The equation of a parabola in standard form is given by:
(x-h)^2=4p(y-k)
Where (h,k) is the vertex of the parabola and p is the distance from the vertex to the focus and to the directrix. In this case, the focus is (7,9) and the directrix is y = 5. To find the equation of the parabola, we need to determine the value of p.
From the given information, we can see that the focus is a point on the parabola and the directrix is a line that is perpendicular to the axis of symmetry and does not pass through the vertex. Therefore, the distance from the vertex to the focus is equal to the distance from the vertex to the directrix. In other words, the value of p is the distance from the vertex to the line y = 5.
Since the directrix is a horizontal line, the vertex of the parabola is on the line y = 5. Therefore, k = 5. The distance from the vertex to the line y = 5 is equal to the distance from the vertex to the focus, which is p. Therefore, we have:
p = 9 - 5 = 4
So the equation of the parabola is:
(x-7)^2 = 4 * 4(y-5)
Simplifying, we get:
(x-7)^2 = 16(y-5)
Therefore, the equation of the parabola is (x-7)^2 = 16(y-5).
Related Questions
please solve with working thankyou
Answers
Answer:
m∠y=72°
Step-by-step explanation:
The question is
Find the measure of angle y
step 1
Find the measure of angle x
see the attached figure to better understand the problem
we know that
m∠x=67° -----> by corresponding angles
step 2
Find the measure of angle y
we know that
(m∠x+m∠y)+42°=180° -----> because form a straight line
substitute the measure of angle x
67°+m∠y+42°=180
m∠y+108°=180
m∠y=180°-108°
m∠y=72°
5. The parts that are added or subtracted in an algebraic
expression are called?
Answers
Answer:
They are known as terms in algebraic expression
Step-by-step explanation:
For the following right triangle, find the side length x. Round your answer to the nearest hundredth. 11, 19
Answers
If the unknown is the hypotenuse...
Following pyth. theorem,
x^2=11^2+19^2
x=21.95
If the unknown is a leg other than the hypotenuse...
Following pyth. theorem,
x^2=19^2-11^2
x=15.49
Solve the equation:
5x-2=X+4
Answers
Answer: x = 1.5
Step-by-step explanation:
5x - 2 = x + 4
Add 2 to each side
5x = x + 6
Subtract x from each side
4x = 6
Divide each side by 4
x = 1.5
Answer:
x = 3/2
Step-by-step explanation:
5x-2=x+4 (add 2 to both sides)
5x=x+4 + 2
5x=x+6 (subtract x from both sides)
5x - x = 6
4x = 6 (divide both sides by 4)
x = 6/4 = 3/2
7m+12 over 8= 2m-1 over 3
Answers
Answer:
m=-44/5
Step-by-step explanation:
(7m+12)/8=(2m-1)/3
cross product
8(2m-1)=3(7m+12)
16m-8=21m+36
16m-21m-8=36
-5m-8=36
-5m=36+8
-5m=44
m=44/-5
m=-44/5
20 millimeters long with an area of (20x-200) square millimeters. Write an expression that represents the perimeter (in millimeters) of the octopus pupil.
Answers
Answer:
Perimeter = (20 + 2x) mm.
Step-by-step explanation:
The octopus pupil has length 20 mm and the expression for its area is given by (20x - 200) square mm.
If the width of the octopus pupil is w, then 20w = 20x - 200
⇒ w = (x - 10) mm.
Therefore, the expression for its perimeter is 2(Length + Width) = 2 ( 20 + x - 10) = 2( 10 + x) = (20 + 2x) mm. (Answer)
The expression that represents the perimeter of the octopus pupil is 20 millimeters.
Explanation:To find the expression that represents the perimeter of the octopus pupil, you need to know the length and area of the pupil. The length is given as 20 millimeters, and the area is represented by the expression (20x-200) square millimeters. The perimeter of a shape is the sum of all its side lengths.
So, for the octopus pupil, the perimeter can be found by adding up the lengths of all its sides. Since the shape is not specified, we'll assume it's a regular shape with all sides equal in length.
To find the expression for the perimeter, we need to know the number of sides. If we assume it has n sides, then each side has a length of 20/n millimeters. Therefore, the perimeter expression would be 20/n multiplied by n, which simplifies to 20 millimeters.
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What is the y and c intercepts of the linear equation
4.) y=-5x+10
Answers
Answer:
x-intercept is 2, y-intercept is 10.
Step-by-step explanation:
y=-5x+10
y=mx+b
-------------
m=-5 which means that the slope of this equation is -5.
And to find the y-intercept,
plug in x=0 into the equation and find out the value of y.
y=-5(0)+10=0+10=10
So the y-intercept is 10.
And to find the x-intercept,
plug in y=0 into the equation and find out the value of x.
0=-5x+10
-5x=0-10
-5x=-10
5x=10
x=10/5=2
So the x-intercept is 2.
Please answer this correctly
Answers
Answer:
2
Step-by-step explanation:
Conversion factor: 1/8
1) Cup = Fluid Ounce / 8
2) Cup = 32 / 8
3) Cup = 4
Answer:
2
There are 4 cups in a 32 fl oz carton, so she needs to get 2 more.
A system of equations is shown:
4c + 2d = 11
(7/2) d = 41 - 220
What is the solution to the system?
C = ?
D = ?
Answers
Answer:
c = 793/28 , d = -358/7
Step-by-step explanation:
Solve the following system:
{4 c + 2 d = 11 | (equation 1)
(7 d)/2 = -179 | (equation 2)
Multiply equation 2 by 2:
{4 c + 2 d = 11 | (equation 1)
0 c+7 d = -358 | (equation 2)
Divide equation 2 by 7:
{4 c + 2 d = 11 | (equation 1)
0 c+d = -358/7 | (equation 2)
Subtract 2 × (equation 2) from equation 1:
{4 c+0 d = 793/7 | (equation 1)
0 c+d = -358/7 | (equation 2)
Divide equation 1 by 4:
{c+0 d = 793/28 | (equation 1)
0 c+d = -358/7 | (equation 2)
Collect results:
Answer: {c = 793/28 , d = -358/7
Which describes how to find the solution 5k >22
Answers
Answer:
k > 4.4Step-by-step explanation:
[tex]5k>22\qquad\text{divide both sides by 5}\\\\\dfrac{5k}{5}>\dfrac{22}{5}\\\\k>4\dfrac{2}{5}\to k>4.4\to k\in(4.4,\ \infty)[/tex]
which graph represents a function?
Answers
Answer:
Graph C) represents a function.
Step-by-step explanation:
Graph C) is the only graph that passes the vertical line test, a way to determine if a graph is a function. All other graphs do not pass the vertical line test. The vertical line test states that if a vertical line drawn intersects the graph of the relation more than once, then the relation is a NOT a function.
The function is indeed a relationship that has only one outcome for each input value (x-value) and output value (y-value). As a result, all functions could be regarded as relationships. However, not all relations are functions because not all of them satisfy the criterion, so each unique input generates just one output.
The third option seems to be the only graph in the present situation that satisfies the vertical line test and determines if a graph is a function. The vertical line test fails on all other graphs. According to the diagonal line test, if a vertical line drawn over the graph of a relation meets it again, the relation is not a function.Therefore, the final answer is "Option C".
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Complete each function table.
1. Input (v)
0
*+6
Output (y)
3
Answers
Answer:Tueyndi
Step-by-step explanation:
Answer:1.6,9,14
Step-by-step explanation:
so x+6 input is x so you put the number in the input where the x is so 0+6=6,and 3+6=9 and so on.....
At a sale, a suit is being sold for 73% of the regular price. The sale price is $511. What is the regular price?
Answers
Answer:
700 dollars,
Step-by-step explanation:
what you do is divide 511 by 73 then multiply the number by 100
Lyril inspects sneakers at a
factory. Of the first 64 pairs of
sneakers she inspected 48 were
acceptable. What is the
experimental probability that
the next pair of sneakers will be
acceptable?
40 points
Answers
Answer:
0.8
Step-by-step explanation:
Of the 60 sneakers inspected, 48 were acceptable. The experimental probability is therefore:
P = 48/60
P = 0.8
What is the value expression of - 1.6 × (- 25 ) =
Answers
Answer:
40
Step-by-step explanation:
-1.6(-25)=40
Answer:
40
Why didn't you just use a calculator
How do you find the unit rate of 72/12
Answers
Answer:
6 : 1Step-by-step explanation:
[tex]\dfrac{72}{12}=\dfrac{72:12}{12:12}=\dfrac{6}{1}=6:1[/tex]
✓-2x = x please solve
Answers
Answer:
the sign =3x
Step-by-step explanation:
you just need to do the step
sign-2x+2x=x+2x
sign=3x
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -1, 2, 3
Answers
Answer:
f(x) = x³ - 4x² + x + 6
Step-by-step explanation:
The polynomial function f has zeros at -1, 2, and 3.
So, the least degree of the polynomial will be 3{As it has three roots}.
Then, if the function is of x variable then (x + 1), (x - 2) and (x - 3) will be the factors of the polynomial.
Therefore, we can write
f(x) = (x + 1)(x - 2)(x - 3)
⇒ f(x) = (x + 1)(x² - 5x + 6)
⇒ f(x) = x³ - 5x² + 6x + x² - 5x + 6
⇒ f(x) = x³ - 4x² + x + 6
Hence, this is the polynomial with least degree having rational coefficients and with leading coefficient of 1 and the zeroes -1, 2, 3. (Answer)
At a competition with 6 runners, 2 medals are awarded for first and second
place
Each medal is different. How many ways are there to award the medals?
Answers
Answer:
30 ways
Step-by-step explanation:
The first medal can be awarded in 6 different ways since any of the runners could have it. Once the first medal is awarded, the second medal can only be given to any of the 5 runners available.
So there are 6x5=30 different ways to award the medals
There are 30 ways to award the medals to the winners
How to determine the number of ways?The given parameters are:
Runners = 6
Medals = 2
The first position can be awarded to any of the 6 runners, while the second position can be awarded to any of the remaining 5 runners
So, the number of ways is:
Ways = 6 * 5
Evaluate
Ways = 30
Hence, there are 30 ways to award the medals
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The telephone company offers two billing plans for local calls. Plan 1 charges $29 per month for unlimited calls and Plan 2 charges $19 per month plus $0.04 per call. If you have Plan 1 for 4 months, how much will your total be?
Answers
Answer:
$116 for four months
Step-by-step explanation:
$29 • 4 = 116
Which of the following expressions are equivalent to (9 7/8 + 2 4/5) - 1/2
Answers
Answer:
A and B
Step-by-step explanation:
C) 9 7/8 - (- 2 4/5) - (- 1/2) =
= 9 7/8 + 2 4/5 + 1/2 (F)
D) - (- 9 7/8 + 2 4/5) - 1/2) =
= 9 7/8 - 2 4/5 - 1/2 (F)
E) 9 7/8 - (- 2 4/5 - 1/2) =
= - 7/8 + 2 4/5 + 1/2 (F)
Answer:
Step-by-step explanation:
Bc bhh
Find the derivative of f(x).
f(x)=x3
Write your answer as a constant times a power of x.
Answers
Answer:
3x²
Step-by-step explanation:
[tex]\frac{d}{dx}[/tex](x³)
Apply the power rule: [tex]\frac{d}{dx}[/tex](x^a) = a * x^(a - 1):
3 * x^(3 - 1)
Simplify:
3x²
Sin(cosx) = 1 solve for x
Answers
Answer:
There is no solution for x.
Step-by-step explanation:
We are given that [tex]\sin (\cos x) = 1[/tex] and we have to solve for x.
Let us assume that [tex]\cos x = \theta[/tex] then [tex]\sin \theta = 1[/tex] ........ (1)
Now, we know that for any value of x the value of cos x lies between 1 to - 1.
Hence, [tex]1 \geq \cos x \geq - 1[/tex] for all x.
⇒ [tex]1 \geq \theta \geq - 1[/tex]
Now, for [tex]1 \geq \theta \geq - 1[/tex], the value of [tex]\sin \theta[/tex] can never be equal to 1.
Hence, there is no solution for x. (Answer)
What is the reciprical of 200 and 450
Answers
Answer:
Part a) [tex]\frac{1}{200}[/tex]
Part b) [tex]\frac{1}{450}[/tex]
Step-by-step explanation:
we know that
A reciprocal of a rational number [tex]\frac{p}{q}[/tex] is obtained by changing the numerator and denominator, so the numerator becomes the denominator and the denominator becomes the numerator obtaining [tex]\frac{q}{p}[/tex]
Part a) we have
200
we know that
the given number can be expressed as [tex]\frac{200}{1}[/tex]
so
changing the numerator and denominator
The reciprocal is equal to [tex]\frac{1}{200}[/tex]
Part b) we have
450
we know that
the given number can be expressed as [tex]\frac{450}{1}[/tex]
so
changing the numerator and denominator
The reciprocal is equal to [tex]\frac{1}{450}[/tex]
Combine like terms to simplify the expression: 9 + 3b − 1 + 7b − 2 =
Answers
Answer:
6+10b
Step-by-step explanation:
Which graph shows the solution to the system of linear inequalities? y > Two-thirdsx + 3 y ≤ Negative one-thirdx + 2
Answers
Answer:
The solution in the attached figure
Step-by-step explanation:
we have
[tex]y > \frac{2}{3}x+3[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the dashed line [tex]y=\frac{2}{3}x+3[/tex]
The slope of the dashed line is positive
The y-intercept of the dashed line A is (0,3)
The x-intercept of the dashed line A is (-4.5,0)
[tex]y\leq -\frac{1}{3}x+2[/tex] ----> inequality B
The solution of the inequality B is the shaded area below the solid line [tex]y=-\frac{1}{3}x+2[/tex]
The slope of the solid line is negative
The y-intercept of the solid line B is (0,2)
The x-intercept of the solid line B is (6,0)
The solution of the system of inequalities is the shaded area between the shaded line and the solid line
using a graphing tool
see the attached figure
Answer:
B
Step-by-step explanation:
On edge 2021
Find all numbers whose absolute value is -9.
Answers
Answer:
None
Step-by-step explanation:
A number's absolute value will always be positive
|9| = 9
|-9| = 9
Answer:
Step-by-step explanation:
none
Which of the following are equivalent ratios?
A: 12 : 16
B: 3 : 5
C: 2 : 3
D: 6 : 8
Answers
The equivalent ratios are A and D.
Here's an explanation:
When you look at D, you see that 12 is a multiple of 6, and 16 is a multiple of 8. So you know that it looks like they're equivalent. Then you test it out, 12/2=6. 16/2=8. so 12:16 = 6:8. Eyeballing it first can save time sometimes.
-1.5,-1,?,0 what is the missing ? HELP PLZ
Answers
Answer:
-0.5
Step-by-step explanation:
It looks like it's increasing by 0.5
Answer:-0.5
Step-by-step explanation:Say you were doing it in postive form half of 1 is 0.50 meaning you just add a negative sign
which of the followibg expressions is equivalent to the expression a^2/3
Answers
Answer:
C. I can’t really enter square roots
Step-by-step explanation:
a^2/3 = a^2*a^1/3
Which is the cube root of a squared