Consider the parabola with a focus at the point (0, 7) and directrix y = 1. Which two equations can be used to correctly relate the distances from the focus and the directrix to any point (x, y) on the parabola?
Answers
Step-by-step explanation:
The equation that relates the distance from the focus and directrix to any point is
\((y - k) {}^{2} = 4p(x - h)\)
or
\((x - h) {}^{2} = 4p(y - k)\)
Since the directrix is a horizontal line, we will use the second equation.
The vertex lies halfway between the focus and directrix.
Since y=1, is perpendicular to the axis of symmetry, we are going to use the point (0,1) to represent the directrix.
Next, using the y values the number that lies between 7 and 1 is 4 so our vertex is
\((0,4)\)
Our h is 0 and. k is 4.
\((x - 0) {}^{2} = 4p(y - 4)\)
\( {x}^{2} = 4p(y - 4)\)
To find p, the equation of the focus is
\((h,k + p)\)
\((0,4 + p)\)
\(4 + p = 7\)
\(p = 3\)
So we have
\( {x}^{2} = 4(3)(y - 4)\)
\( {x}^{2} = 12(y - 4)\)
or
\( \frac{ {x}^{2} }{12} + 4 = y\)
Related Questions
Find f(0) for the
piece-wise function.
f(x) =
if x ≤ 0
x+1 if x>0
X
f(0) = [?]
![Find f(0) for thepiece-wise function.f(x) =if x 0x+1 if x>0Xf(0) = [?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/8HyXqTd671WFovbAMChnJ9OC5eDW3MYT.png)
Answers
\(f(x)=x\) for \(x\leq0\), therfore \(f(0)=0\).
the first domain is true for f(0) so we substitute value of x in the first function
\(f(x) = x \\ f(0) = 0\)
Use this rule to fill in the table.
Rule: Add 3 to the input to get the output.
Add 3
?
Input
Output
1
0
6
11
Answers
Answer:
Input --- Output
1 ------------ 4
6 ------------9
8--------------11
Step-by-step explanation:
Given
Rule:
Output = Input + 3
Required
Complete the table
Represent the input with x and the output, y
So, the rule becomes
\(y = x + 3\)
When Input = 1
\(x = 1\)
\(y = x + 3\)
\(y = 1 + 3\)
\(y = 4\)
This means:
Output = 4
When Input = 6
\(x = 6\)
\(y = x + 3\)
\(y = 6+3\)
\(y = 9\)
This means:
Output = 6
When output = 11
\(y = 11\)
\(y = x + 3\)
\(11 = x + 3\)
\(x = 11 -3\)
\(x = 8\)
This means
Input = 8
So, the complete table is:
Input --- Output
1 ------------ 4
6 ------------9
8--------------11
What is the measure of
m
∠
A
?
Answers
Answer:
I think it would be 22
Step-by-step explanation:
Please help I’m stuck and keep getting the wrong answer
Answers
The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42
A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.
The six o'clock position on the Ferris wheel is level with the loading platform.
The wheel completes 1 full revolution in 2 minutes.
We have to find how many minutes of the ride are spent higher than 26 meters above the ground.
So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters
So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)
Also, the height of a person at the lowest point = 4 - 15 = -11 meters
Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.
So, the total distance travelled will be = 19 + 11 = 30 meters.
Also, we are given that the wheel completes 1 full revolution in 2 minutes.
We need to calculate the time spent higher than 26 meters above the ground.
So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.
This angle can be calculated as follows:
Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees
Angle = 30 / (pi * 30) * 360 degrees
Angle = 360 degrees / pi
= 114.59 degrees
So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.
Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.
This can be calculated as follows:
Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken
Time = (180 - 114.59) / 360 * 2 minutes
Time = 0.42 minutes
For more related questions on time spent:
https://brainly.com/question/28263820
#SPJ8
A toothpaste advertises that 30% of stains are removed after 1 week. As Alexa is brushing her teeth, she thinks "after 2 weeks, 60% of stains will be gone, and 90% after three weeks".
Using this reasoning, what percent of stains will be gone after four weeks? Does this result make sense? Why or why not?
Answers
Answer:
120%. doesn't make sense because there's nothing above 100%
What additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria?
Question 5 options:
A)
||
B)
≅
C)
≅
D)
∠F ≅ ∠H
Answers
The additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria is
EJ ≅ GJ. Option A
How to prove the statementWe need to know the properties of a parallelogram, we have;
Opposite sides are parallel.Opposite sides are congruent.Opposite angles are congruent.Same-Side interior angles (consecutive angles) are supplementary.We know that FJ ≅ JH, it's given by the marks, now if it were to happen that EJ ≅ GJ, that would mean that the diagonals on that quadrilateral are bisecting each other, and if that's so, then the quadrilateral it's indeed a parallelogram.
Learn more about quadrilaterals at: https://brainly.com/question/23935806
#SPJ1
The complete question:
What additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria?
A)
ej ≅ gj
B)
ej || gj
C)
fg || eh
D)
ef ≅ hg
PLEAS EHELP FAST ILL GOVE YOU AS MUCH POINTS AS YOU WANT WHAT IS THE ANSWER FOR THIS MULTIPLE CHOICE
Answers
Answer:
B
Step-by-step explanation:
when u do elimination u want to get the same number as the top. so 10 divided by 2 is 5.
Answer:
B. divide the bottom by 2
Step-by-step explanation:
you want one of the variables to have the same coeficient. Dividing it by 2 will make both equations have the same coefficient for x.
Which of the following quantities is a variable?
A. Number of minutes in an hour.
B. Number of inches in a foot.
C. Length of a person's arm.
D. Length of the Brooklyn Bridge
Answers
Answer:
Length of a Brooklyn Bridge
Step-by-step explanation:
A variable is an unfixed pattern that is liable to change at any time
hello I'd like to know what\(7 {x}^{2} - 5x + 3\)minus\((2 {x}^{2} + 7x - 4)\)equals to
Answers
Distribute the negative to the second trinomial and simplify by adding like terms. We get the following:
\(\begin{gathered} 7x^{2}-5x+3-(2x^{2}+7x-4) \\ =7x^2-5x+3-2x^2-7x+4 \\ =7x^2-2x^2-5x-7x+3+4 \\ =5x^2-12x+7 \\ \\ \text{Therefore,} \\ 7x^2-5x+3-(2x^2+7x-4)=5x^2-12x+7 \end{gathered}\)HELP a which one is it!!!!
Answers
Answer:
I think it's C
Step-by-step explanation:
On the other ones there is multiple outputs for one input.
can anyone help me with this?
Answers
Answer:
The surface area is 65.94 ft
What is the sin B?
/21
B
5
2
sin (B) =
[?]
![What is the sin B?/21B52sin (B) =[?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/bJqEBQdNtkeNzRPqszdQkxPqXUYlMPak.png)
Answers
Answer:
Step-by-step explanation:
sin (B) = \(\frac{2}{5}\)
Answer the question with an algebraic expression.
The perimeter of a square is m meters. How long, in centimeters, is each side of the square?
Answers
The length of the square in centimetres in algebraic expression is 25m
How to find the side length of a square?The perimeter of a square is m meters.
The length of the each side of the square in centimetres can be represented in an algebraic expression as follows:
Therefore,
perimeter of a square = 4l
where
l = side lengthTherefore,
m = 4l
where
m = perimeter of the squarel = m / 4 meters.
Therefore, the side length of the square in centimetres is as follows:
1 meters = 100 cm
m / 4 meters = ?
cross multiply
length of the square in meters = m / 4 × 100
length of the square in meters = 100m / 4
length of the square in meters = 25m
learn more on square here: https://brainly.com/question/13379880
#SPJ1
There are 26 students in Jenna’s class. Jenna brought in 14 cupcakes. Which equation can be used to find the number of cupcakes the class still needs (n) so that everyone will get one?
Answers
Answer:
Equation: 26-14=(n)
Step-by-step explanation:
If you rest 14 from 26 that is the number of people that still need one.
(The answer is 12)
evaluate the numerical expression 3 + 8 x(7-4)
Answers
Answer:
3+24x
Step-by-step explanation:
3 + 8x(7-4)
= 3 + 56x -32x
= 3+24x
AABC is dilated by a factor of į to produce AA'B'C!
37
12
15
53
9
с
What is AC, the length of AC after the dilation? What is the measure of ZA?
A. A'C' = 5, m ZA= 12
O B. A'C' = 5, mZA'= 37°
O C. A'C' = 45, m A'= 37°
D. A'C' = 4, mZA'= 53°
Answers
Answer:
A'C = 45, m A' = 37
Step-by-step explanation:
You find the 45 by multiplying 15, the length of A'C by 3 to find the original size.
round 525,600 to the nearest ten thousand
Answers
Answer:530,000
Step-by-step explanation: ten thousand is the 2 so you would round the number to the right up or down and it is 5 so you round up
Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $5,000, annual interest: 9%, interest periods: 4, number of years: 18
After 18 years, the investment compounded periodically will be worth $? more than the investment compounded annually.
(Round to two decimal places as needed.)
Answers
After 18 years, the investment compounded periodically (quarterly) will be worth $1,230.23 more than the investment compounded annually.
What is compounded interest?Compounded interest refers to the interest system that charges interest on both principal and accumulated interest.
The period of compounding in a year determines the worth of the future value.
The future value can be ascertained using an online finance calculator as follows:
Interest periods: = 4 times yearly (Quarterly)
Principal = $5,000
Annual interest rate = 9%
Number of years: 18
N (# of periods) = 72 quarters (18 years x 4)
I/Y (Interest per year) = 9%
PV (Present Value) = $5,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $24,815.83
Total Interest = $19,815.83
Interest periods: = Annually
N (# of periods) = 18 years
I/Y (Interest per year) = 9%
PV (Present Value) = $5,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $23,585.60
Total Interest = $18,585.60
Difference in Future Values $1,230.23 ($24,815.83 - $23,585.60)
Thus, an investment compounded periodically earns more than an investment compounded annually.
Learn more about compounded interest at https://brainly.com/question/28020457.
#SPJ1
19
Select the correct answer.
You work for a carpet company. You sell carpets at these prices: 100 square feet for $67, 200 square feet for $130, 400 square feet for $240, and 800 square feet for $504.
What is the best deal for buying carpet?
A.
B.
C.
D.
100 square feet of carpet for $67
200 square feet of carpet for $130
400 square feet of carpet for $240
800 square feet of carpet for $504
Answers
400 square feet of carpet area for $240 is the best deal among the given option.
What is Area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).
Detailed explanation:The carpets were sold for the following prices:
1) $67 for 100 square feet.
2) $130 for 200 square feet.
3) $240 for 400 square feet
4) $504 for 800 square feet.
Calculation:
For each of them, we would calculate the unit cost per square foot. It develops
1) The price per square foot is 67÷100 = $0.67
2) The price per square foot is 130÷200 = $0.65.
3) The price per square foot is 240÷400 = $0.6.
4) The price per square foot is 504÷800 = $0.63.
Comparing the unit costs per square foot the best deal costs $0.6 per square foot per unit, which is 400 square feet of carpet for $240.
400 square feet of carpet area for $240 is the best deal among the given option.
To know more about areas, visit:
https://brainly.com/question/25292087
#SPJ1
The ratio of the measures of the sides of a
triangle is 3:4:6 and its perimeter is 91 inches.
What is the length of the longest side?
Answers
The perimeter of the ratio triangle is 6+4+3=13
Divide that into the actual triangle perimeter to get the scale 91/13=7
Multiply that scale times the longest side of the ratio (6)
7x6 = 42
To check do the other two as well
7x3=21 and 7x4=28
Add them up to check the perimeter
42+21+28=91
And 42 was the longest side
QUESTION : find the measure of angle A
Hint : solve for x then replace in angle A
please help !
Answers
Angle A should be 40 since x=10
Answer:
X=10°
Step-by-step explanation:
on the picture
if it's helpful ❤❤❤❤
THANK YOU.
The Value of 1/2 + 3/5
Answers
Answer: 1 1/10 or 11/10
Step-by-step explanation: 1/2 x 5/5 = 5/10 and 3/5 x 2/2 = 6/10 so 5/10 + 6/10 = 11/10.
Ann had $500 at the beginning of the year. If she had $360 left, what percent of her money did she spend?
Answers
Explanation: 500 x .28 = $360
well, she spent $140, because 500 - 360 = 140.
now, if we take 500 to be the 100%, what is 140 off of it in percentage?
\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 500 & 100\\ 140& x \end{array} \implies \cfrac{500}{140}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{25}{7}=\cfrac{100}{x}\implies 25x=700\implies x=\cfrac{700}{25}\implies x=28\)
is it correct ?
the question is :
(2/5 ÷ 3/8) ÷ (-3/5)
solution : =
2/5 × 8/3 = 16/15. 16/15 × -3/5 = -39 / 80
if its not correct please tell how to do it.
Answers
Answer:
Step-by-step explanation:
It is correct till 16/15
But after that it is 16/15 × 5/-3 = 80/-45
simplify it to 16/-9
Your friend estimated that it would take 5 hours to finish an art project. It actually took him 16 hours to finish the project. The amount of time it took to finish the project was % of the estimated time Use pencil and paper. What does it mean to have more than 100% of something? Give at least two examples The amount of time it took to finish the project was % of the estimated time (Type an integer or a decimal.)
Answers
Answer:
320%
To have over 100% of something means that you have more than the original number you had.
Step-by-step explanation:
Step-by-step explanation:
To find what percent a first number is of second number, divide the first number by the second number and multiply by 100%.
To find what percent 16 is of 5, divide 16 by 5 and multiply by 100%.
16/5 * 100% = 3.2 * 100% = 320%
"Percent" literally means "per 100."
100% means 100 out of 100, and means an entire amount.
More than 100% percent means more than the entire amount.
5 hours was the estimated time. 100% of 5 hours is 5 hours, the entire amount. More than 100% is more than the entire amount, so it is more than 5 hours. 16 hours is certainly much more than 5 hours, and it is 320% of 5 hours.
Which choice is equivalent to the expression below? √-12
A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i
PLEASE DON’T GUESS
Answers
Answer:
D. 2i√3
Step-by-step explanation:
You have the expression √-12. You can divide the number in the radical sign into the numbers that make up the expression. After you do this, you will be able to take numbers out of the radical sign
√(-12)
√(-1 × 4 × 3)
√-1 = i
√4 = 2
√3 = √3
2i√3
The answer is D.
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation.
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths.
What is OB'?
1.5 units
3 units
4.5 units
6 units
Mark this and return
Answers
Answer:
(b) 3 units
Step-by-step explanation:
You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.
DilationThe dilation factor multiplies every length.
If OB is 3/4, then OB' is 4(3/4) = 3.
The length of OB' is 3 units.
<95141404393>
Which point would be a solution to the system of linear inequalities shown below?
Answers
The coordinates in the solution to the systems of inequalities is (12, 1)
Solving the systems of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
y > -4x + 6
y > 1/3x - 7
Next, we plot the graph of the system of the inequalities
See attachment for the graph
From the graph, we have solution to the system to be the shaded region
The coordinates in the solution to the systems of inequalities graphically is (12, 1)
Read more about inequalities at
brainly.com/question/30977554
#SPJ1
HELP PLEASE! WILL GIVE 50 points!
A box contains 5 plain pencils and 7 pens. A second box contains 3 color pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected? Write your answer as a fraction in simplest form.
Answers
41.66% chance for ONLY a plain pencil to be selected, 50% that ONLY a color pencil will be selected, and a 44% chance for BOTH items to be selected.
Explanation:
In box A, there are 12 items total, and in box B, there are 6 items total.
Since 5/12 items in box A are plain pencils, there is a 5/12 or 41.66% chance it will be that (for ONLY box A).
There is a 3/6 or 50% chance it will be a color pencil (for ONLY box B)
Now to find the probability that BOTH will be selected, total all items. 12 = 6 = 18, so in total there are 18 items. Then, add all plain pencils and color pencils, 5 + 3 = 8. 8/18 chance that both will be selected, or 44.44% chance.
Solve the system of equation using elimination
Answers
Answer:
To Solve a System of Equations by Elimination
Write both equations in standard form. ...
Make the coefficients of one variable opposites. ...
Add the equations resulting from Step 2 to eliminate one variable.
Solve for the remaining variable.
Substitute the solution from Step 4 into one of the original equations.
here! ( happy hoildays!)