Write the equation for a parabola with a focus at (2, 2) and a directrix at x = 8.
Answers
Answer:
x = -1/12(y -2)² +5
Step-by-step explanation:
You want the equation of the parabola with focus (2, 2) and directrix x = 8.
VertexThe directrix is a vertical line to the right of the focus. This means the parabola opens to the left. The vertex is halfway between the focus and the directrix, so its coordinates are ...
vertex = ((2 +8)/2, 2) = (5, 2)
Leading coefficientThe leading coefficient will be negative for a parabola that opens to the left. Its magnitude is 1/(4p), where p is the distance from the focus to the vertex. Here, that distance is 5 -2 = 3, so the leading coefficient is ...
-1/(4p) = -1/(4·3) = -1/12
EquationIn vertex form, the equation of the parabola is ...
x = a(y -k)² +h . . . . . . . . . . . vertex (h, k); leading coefficient 'a'
x = -1/12(y -2)² +5
The equation of the parabola is [tex]\( (x-5)^2 = 12y \), with focus (2, 2) and directrix \(x = 8\).[/tex]
The standard equation for a parabola with a vertical axis of symmetry is:
[tex]\[ (x-h)^2 = 4p(y-k) \][/tex]
where (h, k) is the vertex of the parabola and p is the distance between the vertex and the focus (or the vertex and the directrix).
Given that the focus is at (2, 2) and the directrix is at x = 8, we can find the distance between the focus and the vertex, which is p. Since the directrix is a vertical line, the vertex's x-coordinate is the midpoint between the x-coordinate of the focus and the x-coordinate of the directrix:
[tex]\[ h = \frac{{x_f + x_d}}{2} = \frac{{2 + 8}}{2} = 5 \][/tex]
So, the vertex is at (5, k). Since the focus is above the vertex, k > 2.
Now, we find the distance between the focus and the vertex, which is equal to p. The distance formula is:
[tex]\[ p = \sqrt{(x_f - h)^2 + (y_f - k)^2} \]\[ p = \sqrt{(2 - 5)^2 + (2 - k)^2} \]\[ p = \sqrt{9 + (2 - k)^2} \][/tex]
Given that p is the distance from the focus to the vertex, we know that [tex]\(p = 3\).[/tex]
So, the equation of the parabola is:
[tex]\[ (x-5)^2 = 12(y-k) \][/tex]
Now, we need to find the value of k. Since the vertex lies on the parabola, we can substitute the coordinates of the vertex into the equation:
[tex]\[ (5-5)^2 = 12(0-k) \]\[ 0 = -12k \]\[ k = 0 \][/tex]
So, the equation of the parabola is:
[tex]\[ (x-5)^2 = 12y \][/tex]
Related Questions
Which is the most accurate estimate of 27% of 39 ?
A: 13×40
B: 12×40
C: 14×40
D: 23×40
Answers
Answer:
Option D.
Step-by-step explanation:
we know that
The number 39 represent the 100%
so
using proportion
[tex]\frac{39}{100}=\frac{x}{27}[/tex]
solve for x
[tex]100x=39(27)\\x=10.53[/tex]
The following distribution is not a probability distribution because
the probability values are not discrete.
the values of the variable are negative
the probability values are not increasing
the probability values do not add to 1.
Answers
Answer:
Choice 2
Step-by-step explanation:
The following distribution is not a probability distribution because the probability values do not add to 1.
If it were a probability distribution, the sum of all the probability values would be equal to 1.
The sum of the probability values is 0.16 + 0.15 + 0.42 + 0.13 + 0.31,
which is equal to 1.17.
Since the sum is greater than 1, it violates the requirement for a probability distribution.
Hence, the probability values do not add to 1.
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each side of a square plastic tarp is 9 meters long. what is the tarps perimeter
Answers
Answer:
36
Step-by-step explanation:
9 times 4
The perimeter of a square is calculated by 4 times the length of one side. For a square plastic tarp with each side being 9 meters, the perimeter would be 36 meters.
Explanation:The perimeter of a square can be calculated by using the formula: 4 x side length. In this case, the length of the side of the tarp is 9 meters. Therefore, to find the perimeter, you would multiply 4 (the number of sides in a square) by 9 (the lengths of one side). That calculation would look like this: 4 x 9 = 36 meters. So, the perimeter of the square plastic tarp is 36 meters.
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What is (3 - 3i)(-5 - 4) in the form a + bi?
Answers
Answer:
Hey
Step-by-step explanation:
Answer:
-27+27i
Step-by-step explanation:
you are trying to simplify this and have to follow pemdas and rearrange it into a+bi form
A playground 96 ft long and 48 ft wide is to be resurfaced at a cost of $4.75 per sq ft. What will the resurfacing cost?
Answers
Answer:
$21888
Step-by-step explanation:
96*48=4608
4608*$4.75=21888
The cost to do the resurfacing of the playground can be found to be $21, 888.
How to find the cost ?To find the cost of resurfacing the playground, you need to calculate the total area of the playground and then multiply it by the cost per square foot.
The playground is 96 feet long and 48 feet wide, so its area is:
Area = Length × Width
Area = 96 ft × 48 ft
Area = 4,608 square feet
Multiply the area by the cost per square foot:
Resurfacing Cost = Area × Cost per square foot
Resurfacing Cost = 4,608 sq ft × $4.75/sq ft
Now, calculate the resurfacing cost:
Resurfacing Cost = $ 21,888
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Can y’all help me please
Answers
Answer: 3 equal sides a 3 vertices
Step-by-step explanation:
In the diagram, the measure of angle 1 is (3x), and the measure of angle 2 is (12x)".
516
87
What is the measure of angle 4?
Answers
Answer:
Angle 4 is 144.
Step-by-step explanation:
Applying the definition of vertical angles, the measure of angle 4 is: 144°.
What are Vertical Angles?Vertical angles are a pair of angles that lie directly opposite each other and are equal in measure to each other.
m∠1 + m∠2 = 180° (linear pair)
Substitute
3x + 12x = 180
15x = 180
x = 12
∠4 and ∠2 are vertical angles, therefore:
m∠4 = m∠2 = 12x
Plug in the value of x
m∠4 = 12(12)
m∠4 = 144°
Therefore, applying the definition of vertical angles, the measure of angle 4 is: 144°.
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The volume of a sphere with a radius of 5 (in terms of pi) is ?
Answers
Answer:
523.6
Volume of Sphere is V=4 /3πr3
A savings account with an initial deposit of $10,000 has an annual interest rate of 3.2%. The interest on the account is compounded monthly. What is the
balance of the account, to the nearest cent, after 6 years?
Answers
Answer:
account balance will be $12113.9 and the interest is $2113.9.
What is the area of of this tile 6 in and 2 in
Answers
Answer:
12 inches squared
Step-by-step explanation:
If it is 6 inches by 2 inches, then you multiply 6 by 2 to get 12 inches squared.
Answer:
12 inches squared
Step-by-step explanation:
6 x 2 = 12
Because it's area, you need to make sure that the units are squared.
What is the equation of the axis of symmetry for the graph?
Answers
Answer:
-b/2a
Step-by-step explanation:
x=y-4 and 2x+4y=10 help me
Answers
Answer:
Step-by-step explanation:
1. x = y-4
0 = y - 4 -x
4 = y - x
2. 2x+4y = 10
x+4y = 5
x+y = 5/4
What is the minimum amount of information you need in
order to calculate the slope of a line?
A. The x and y intercepts of the line.
B. Any two points along the line.
C. The length of the line.
D. The endpoints of the line,
NEED THIS BY TODAY PLZZZZ!!!!! BE SURE OF YOU ANSWER
Answers
To calculate the slope of a line we require any two points along the line.
Explanation:
suppose two points are given that is (x1,y1) (x2, y2) . The equation of a line is y-y1=m(x-x1) , where m is referred to as the slope of the line .
To find m,
m= y2-y1/x2-x1 . Hence this way of finding slope is known as point- slope form. Another form is there known as slope- intercept form
y=mx+c.
But to find a slope , minimum amount of information that we require is points along the line.
Final answer:
To calculate the slope of a line, only two points on the line are needed. Slope is computed as the difference in y-coordinates divided by the difference in x-coordinates of these points.
Explanation:
To calculate the slope of a line, the minimum amount of information needed is any two points along the line. The slope is the rate of change between two points on a line and can be calculated using the formula slope (m) = (Y₂ - Y₁) / (X₂ - X₁), where Y₂ and Y₁ are the y-coordinates and X₂ and X₁ are the x-coordinates of the two points. It is not necessary to know the length of the line, the endpoints specifically, or the x and y intercepts separately.
The slope-intercept form of a linear equation, y = mx + b, shows that m is the slope and b is the y-intercept. Here, the y-intercept is simply the point where the line crosses the y-axis, but it is not required for calculating the slope when you have two points on the line.
is y=1-x a linear equation
Answers
Answer:
Yes
Step-by-step explanation:
It can be rewritten as y = -x + 1.
The slope is -1 and the y-intercept is (0,1)
Final answer:
The equation y=1-x is indeed a linear equation, fitting the general form y = a + bx with a slope of -1 and y-intercept of 1.
Explanation:
Yes, y=1-x is a linear equation. In general, a linear equation can be written in the form y = a + bx, where a is the y-intercept and b is the slope. In this case, the equation y=1-x can be rewritten as y = (-1)x + 1, which clearly fits the form of a linear equation with a slope of -1 and a y-intercept of 1.
The graph of a linear equation is a straight line, and the equation y=1-x represents a straight line with a downward slope. Unlike nonlinear equations, such as y=xb where b is a power, linear equations represent a direct proportionality between y and x.
what is the domain for y=3
Answers
Answer:
The domain is all real numbers
Step-by-step explanation:
The domain is the input values
y= 3 is a horizontal line across all x
The domain is all real numbers
The domain is all real numbers.
The domain is the possible values for x that result in a valid equation, no dividing by zero or any of that stuff. Here there's no x in the formula, y=3 is a horizontal line, f(x)=3 for all x. No x in the formula means it works for all x; nothing to go wrong.
Find the value of x and y in the diagram below 9 30 degrees
Answers
Answer:
not enough information.
Step-by-step explanation:
Answer: D!!
Step-by-step explanation:
For a standard normal distribution, find the approximate value of P(z≤0.42). Use the portion of the standard normal table below to help answer the question.
0.00
0.22
0.32
0.42
0.44
0.64
0.84
1.00
Probability
0.5000
0.5871
0.6255
0.6628
0.6700
0.7389
0.7995
0.8413
O
A. 16%
B. 34%
C. 66%
D. 84%
Answers
We have been given that a z-score table and corresponding probability to each z-score. We are asked to find the probability of a getting a z-score less than or equal to 0.42 that is [tex]P(z\leq0.42)[/tex].
z-score Probability
0.00 0.5000
0.22 0.5871
0.32 0.6255
0.42 0.6628
0.44 0.6700
0.64 0.7389
0.84 0.7995
1.00 0.8413
Upon looking at our given table, we can see that the probability corresponding to z-score of 0.42 is 0.6628.
[tex]P(z\leq0.42)=0.6628[/tex]
Now, we will convert [tex]0.6628[/tex] into percent as:
[tex]0.6628\times 100\%=66.28\%[/tex]
Upon rounding to nearest percent, we will get:
[tex]66.28\%\approx 66\%[/tex]
Therefore, the approximate value of [tex]P(z\leq0.42)[/tex] is [tex]66\%[/tex] and option C is the correct choice.
Answer:
C
Step-by-step explanation:
graph the line that has an x intercept (-3,0) and y intercept (0,-5)
Answers
Answer:
Step-by-step explanation:
Plot points at the given points and connect with a line.
Explain to me the strategy that you use to order a group of numbers that may be written in different forms, for example percentages, decimals, and fractions.
Answers
Answer:
Convert fractions, decimals, and percents to the same form to compare the values. Convert Percent to Decimal or Fraction. Convert Decimal to Percent or Fraction. Convert Fraction to Decimal or Percent. Then figure out which is greater or lesser. Use this information to write a set of numbers or quantities in order from least to greatest or from greatest to least.
Step-by-step explanation:
Ordering numbers mean plan of numbers either from little to enormous or from huge to little. At the point when the numbers are orchestrated in an expanding order, it is known as Ascending Order, and when the numbers are organized in a diminishing order, and afterward they are known as Descending Order. For ascending, check the most modest number from the given rundown and spot it first and afterward put the numbers as indicated by the expanding order. For descending check the greatest number from the given rundown and spot it first and afterward put the numbers as per the diminishing order.
A percentage is a part of an entire communicated as a number somewhere in the range of 0 and 100 instead of as a portion. All of something is 100 percent, half of it is 50%, none of something is zero percent.
A decimal is a part written in an extraordinary structure. Rather than composing 1/2, for instance, you can communicate the division as the decimal 0.5, where the zero is during the ones spot and the five is in the tenths spot.
A fraction just discloses to us what number of parts of an entire we have. You can perceive a fraction by the slice that is composed between the two numbers. We have a top number, the numerator, and a base number, the denominator. For instance, 1/2 is a fraction. You can compose it with an inclined slice like we have or you can compose the 1 on the 2 with the slice between the two numbers. The 1 is the numerator, and the 2 is the denominator.
Need help..................
Answers
Answer:
(4-7x)(4+7x)
Step-by-step explanation:
This is a difference of squares. (16 is the square of 4, 49x^2 is the square of 7x.)
The formula for difference of squares is a^2 - b^2 = (a-b)(a+b)
16 - 49^2 = (4-7x)(4+7x)
!!!!20 POINTS PLZ HELP!!!
A scale drawing of a rectangular garden has a length of 5 inches and a width of 3.5 inches. If the scale is 1-inch colon 3 feet, what is the area of the actual garden?
Answer options with 5 options
A.10.5 square feet
B.15 square feet
C.17.5 square feet
D.52.5 square feet
E.157.5 square feet
Answers
Answer:
E
Step-by-step explanation:
map scale: actual scale
= 1 inch: 3 feet
Area scale
= (1 in)²: (3 ft)²
= 1 in²: 9 ft²
This means that 1 in² of the drawing represents an actual area of 9 ft².
Area of garden in the drawing
= 5(3.5)
= 17.5 in²
Area of actual garden
= 17.5 ×9
= 157.5 ft²
Thus, the answer is E.
ne
Which set of line segments could create a right triangle? (4)
24,30.35
12. 18.30
18. 24.30
18. 24.35
Answers
Answer:
Hi There the correct answer 18. 24.30
Step-by-step explanation:
because there is a special triangle triple (it only works on right triangles.) it is the ration 3:4:5. If you multiply 6 to all of them you get 18:24:30 which is your answer.
Based on the scale drawing, what is the length, in feet, of the actual parking lot?
Answers
Answer:
No one can help
Step-by-step explanation:
You did not provide the scale drawing
Have a Sibling Only Child
Have Chores 7 9
Do Not Have Chores 8 6
The table represents the results of a class survey. What is the relative frequency that someone will have chores, given that they have a sibling?
A) 0.21
B) 0.44
C) 0.47
D) 0.53
Answers
Answer: 0.47
Step-by-step explanation:
Answer:
C) 0.47
Step-by-step explanation:
Which graph represents the function f(x)=2/x-1+4
Answers
Answer:
Step-by-step explanation:
What is the solution to the equation 4x-6= 10x-3?
Answers
Answer:
To solve this equation we need to get x by itself.
4x-6=10x-3, (the first step would be adding 6 to both sides.)
4x=10x+3 (the next step is the subtract ten from both sides.)
-6x=3 (Last step is the divide both sides by -6.)
x=-1/2
Hope this helps ;)
X= -1/2
A segment XD is drawn in rectangle QUAD as shown
below.
What are the measures of ZXDQ and ZUXD ?
mZ XDQ=
mZ UXD =
–
–
–
–
–
–
–
–
Answers
Answer:
41 and 139
Step-by-step explanation:
the answers are 41 and 139
What will be the total area of the garden and the walkway?
A. 504 ft^2
B. 594 ft^2
C. 638 ft^2
D. 648 ft^2
E. 696 ft^2
Answers
Rebecca is making bracelets to sell at a charity event. Each bracelet takes 1 1/4 of a foot of embroidery floss to make.If Rebecca has five yards of embroidery floss,how many bracelets can she make?
Answers
Answer:
12
Step-by-step explanation:
She has 15 feet of floss. 15/1.25 is 12.
Hope this helps!!
Answer:
15
Step-by-step explanation:
She has 15 feet of floss
By how many factors of 10 did you multiply 0.008? Why?
Answers
Answer: 3
Step-by-step explanation:
Move the decimal back to its point of origin
To multiply a number by a power of 10, you move the decimal point to the right by the number of zeros in the power of 10.
Explanation:When multiplying a number by a power of 10, you can count the number of zeros in the power of 10 and move the decimal point that same number of places to the right.
In the case of multiplying 0.008 by 10, the power of 10 is 1, so you would move the decimal point one place to the right, resulting in 0.08.
Therefore, you multiply 0.008 by 10 to get 0.08.
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