Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1.
f(x) = −one twelfth(x − 5)2 + 2
f(x) = one twelfth(x − 5)2 + 2
f(x) = −one twelfth(x + 5)2 + 2
f(x) = one twelfth(x + 5)2 + 2
Answer:
The equation of the parabola with a focus at (-5,5) and a directrix of y = -1 is [tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex].
Step-by-step explanation:
From statement we understand that parabola has its axis of symmetry in an axis parallel to y-axis. According to Analytical Geometry, the minimum distance between focus and directrix equals to twice the distance between vertex and any of endpoints.
If endpoints are (-5, 5) and (-5, -1), respectively, then such distance ([tex]r[/tex]), dimensionless, is calculated by means of the Pythagorean Theorem:
[tex]r = \frac{1}{2}\cdot \sqrt{[-5-(-5)]^{2}+[5-(-1)]^{2}}[/tex]
[tex]r = 3[/tex]
And the location of the vertex ([tex]V(x,y)[/tex]), dimensionless, which is below the focus, is:
[tex]V(x,y) = F(x,y)-R(x,y)[/tex] (1)
Where:
[tex]F(x,y)[/tex] - Focus, dimensionless.
[tex]R(x,y)[/tex] - Vector distance, dimensionless.
If we know that [tex]F(x,y) = (-5,5)[/tex] and [tex]R(x,y) = (0,3)[/tex], then the location of the vertex is:
[tex]V(x,y) = (-5,5)-(0,3)[/tex]
[tex]V(x,y) =(-5,2)[/tex]
In addition, we define a parabola by the following expression:
[tex]y-k = \frac{(x-h)^{2}}{4\cdot r}[/tex] (2)
Where:
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, dimensionless.
[tex]r[/tex] - Distance of the focus with respect to vertex, dimensionless.
If we know that [tex]h = -5[/tex], [tex]k = 2[/tex] and [tex]r = 3[/tex], then the equation of the parabola is:
[tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex]
The equation of the parabola with a focus at (-5,5) and a directrix of y = -1 is [tex]y = \frac{1}{12}\cdot (x+5)^{2}+2[/tex].
The data from the U.S. Census Bureau for 1980-2010 shows that the median weekly earnings of full-time
male employees who have at least a bachelor's degree can be modeled by the function
M(x) = 0.009x3 - 0.29x2 + 30.7x + 439.6 where x Is the number of years after 1980 and M(x) Is the
median weekly earnings in dollars. The median weekly earnings of all full-time employees who have at
least a Bachelor's degree can be modeled by the function T(x) = 0.012x3 - 0.46x2 + 56.1x + 732.3 where
x Is the number of years after 1980 and T(x) Is the median weekly earnings in dollars.
Estimate the median weekly earnings of a full-time female employee with at least a Bachelor's degree in
2006. Round to the nearest dollar.
The median weekly earnings of a female employee in 2006 is about
Answer:
890.908
Step-by-step explanation:
Given that :
Median weekly salary for males :
M(x) = 0.009x3 - 0.29x2 + 30.7x + 439.6
x = number of years after 1980
Median weekly salary for all employees :
T(x) = 0.012x3 - 0.46x2 + 56.1x + 732.3
Estimate the median weekly earnings of a full-time female employee with at least a Bachelor's degree in 2006
Estimated median weekly earning for a full time female employee with at least bachelor's degree ; F(x)
F(x) = T(x) - M(x)
F(x) = (0.012x3 - 0.46x2 + 56.1x + 732.3) - (0.009x3 - 0.29x2 + 30.7x + 439.6)
F(x) = (0.012 - 0.009)x3 + (-0.46 + 0.29)x2 + (56.1 - 30.7)x + (732.3 - 439.6)
F(x) = 0.003x³ - 0.17x² + 25.4 + 292.7
x = 2006 - 1980 = 26
F(26) = 0.003x³ - 0.17x² + 25.4x + 292.7
0.003(26)^3 - 0.17(26)^2 + 25.4(26) + 292.7 = 890.908
=
Apply the distributive property to the expression to write an equivalent expression.
5x + 35
Complete the statements.
Find the GCF of
.
Now, factor out the GCF by dividing each term in the expression by
.
5x divided by the GCF is
, and 35 divided by the GCF is
.
The equivalent expression is
.
SOMEONE PLS HELP I'M. DYING PLS
Answer:
I don't get it everyone is telling the wrong answers am here to tell you guys and girls the right answer. The answer is : D A B B C your welcome
A friend gives you two baseball cards for your birthday. Afterward you begin collecting them. You buy the same number of cards once each week. The equation y=4x +2 describes the number of cards ,y, you have after x weeks.
Answer: x and y have the same absolute value. Also, x is a positive number, and y is a negative number.
Step-by-step explanation:
Answer:
The slope is 2, while the y-intercept is 4. This equation represents starting with 4 cards and adding 2 cards each week.
Step-by-step explanation:
Given the equation which describes the number of cards, y, you have after x weeks: y=2x+4
Comparing this with the slope intercept form of the equation of the line: y=mx+b, where:
m is the slope
b is the y-intercept.
We have that:
Slope, m=2.
A slope of 2 indicates that you buy 2 cards per week.
The y-intercept of the line, b=4.
This is the starting value. In this case, it represents the number of cards you were given by your friend.
The slope is 2, while the y-intercept is 4. This equation represents starting with 4 cards and adding 2 cards each week.
How to reduce 0.35 to the lowest term
please help and I will mark big brain
Answer: 6
Step-by-step explanation:
(41--1)/ (8-1) = 42/7 = 6
Answer:
6
Step-by-step explanation:
I learned this before
Brainliest Answer
(has to be right for brainliest)
Answer:
it is 0.7x0.4=0.28
Step-by-step explanation:
Answer:
3627514
Step-by-step explanation:
Determine if this data is an example
of a function.
(-2,5); (0, 3); (-2, 8); (1, 14)
Relation
Function
Answer:
Step-by-step explanation:
it is not a function because -2 has two y values
On Monday, Erin ran a mile in 7.5 minutes. On Tuesday, she ran a mile in 6.9 minutes. What was the average time for a mile over those two days, expressed as a fraction?
Answer: 14.4/2
Step-by-step explanation: to find the average time, we add both numbers then divide by how many numbers we have, which is two. So 7.5 + 6.9 = 14.4. we then divide by 2, so 14.4/2.
whats is the only solution of 2x2+8x2-16?
Answer:
4
Step-by-step explanation:
Simplify each expression, Help plz
Answer:
I believe that the answer is the second one.
Step-by-step explanation:
y - 2/5 = 1 3/5 (plz show work)
Answer:
y=2
Step-by-step explanation:
that's the answer hope u understand it
Answer:
[tex]y = 2[/tex]
Step-by-step explanation:
Sure.
[tex]y - \frac{2}{5} = 1 \frac{3}{5} \\[/tex]
Convert to improper fraction
[tex]y - \frac{2}{5} = \frac{8}{5}[/tex]
Combine like terms
[tex]y - \frac{2}{5} = \frac{8}{5} \\[/tex]
[tex]+\frac{2}{5}[/tex] from both sides
[tex]y = \frac{8}{5} + \frac{2}{5} \\y = 2[/tex]
Love from Nepal :)
Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.06 and a standard deviation of 1.52. Using the empirical rule, what percentage of American women have shoe sizes that are less than 9.58? Please do not round your answer.
Answer:
84%
Step-by-step explanation:
The Empirical rule formula states that:
68% of data falls within 1 standard deviations from the mean - between μ – σ and μ + σ
95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .
Mean = 8.06
Standard deviation = 1.52
Using the empirical rule, what percentage of American women have shoe sizes that are less than 9.58? Please do not round your answer.
Using the first rule if Empirical formula
68% of data falls within 1 standard deviations from the mean - between μ – σ and μ + σ
μ + σ
= 8.06 + 1.52 = 9.58
This satisfies one side of the distribution, hence:
100 - 68%
= 32%
P(x >9.58) = 32%/2 = 16%
Hence,the percentage of American women have shoe sizes that are less than 9.58 is
P(x < 9.58) = 100 - 16%
= 84 %
answer in percent 20/80 = x/100
Michael bought 4 types of fruit to make a fruit salad. He paid $3.00 per pound of apples, $2.00 per pound for bananas, $2.50 per pound for grapes, and $3.50 per pound for blackberries.
He bought the same number of pounds of each fruit. Let the number of pounds be represented by the variable x.
Michael figured out the total amount of money that he spent on fruit can be shown using the expression 3x+2x+2.50x+3.50x
Which expression shows how Michael’s expression can be written in an equivalent single term?
A. (2+2.50)(3+3.50)x
B. (2+3+2.50+3.50)x
C. (2) (3) (2.50) (3.50)x
D. (2) (3)x+(2.50) (3.50)x
Answer:
C
Step-by-step explanation:
you can add like terms so C is the correct answer
Answer:
hi how are you doing today Jasmine
You are given the explicit formula below. Identify if will produce an arithmetic or geometric sequence. Also identify the common difference or common ratio
f(n) = 25(4)^n-1
1. Geometric, common ratio of 1/4
2. Geometric, common ratio of 4
3. Arithmetic, common ratio of 25
4. Arithmetic, common ratio of 4
Answer:
2. Geometric, common ratio of 4Step-by-step explanation:
Given is the exponential function which is a geometric sequence
It has common ratio of 4
Correct answer option:
2. Geometric, common ratio of 43x = 8
3x + y = 15
???
ucjvlvjcyxgxjglhlchzfzhckcj
Answer:
Huhuhuhhuh?!!!
Step-by-step explanation:
LOL.. What's that?
Answer: approximately oihfviauegfvyabgfiubaqvuoa
Step-by-step explanation:
first you gotta ohgnvailuerfhivlugehiuvlh the fepoghvapirugv93hrv9igp
then once thats done you edjfahuilurevh the p8eufhavipuhgfv8i7uh to the rfugvhligauerhgiuvlwhreaoiuvh
finally, you ifujevhoaiug the iujhfliauerhgifu with the oifuhewiuasrhfi and uirjewg it to the iudfhvailkvkaebrfvilhjb, and you get your answer
Among all pairs of numbers whose sum is 12 , find a pair whose product is as large as possible. What is the maximum product? Show steps.
Answer:
We can only take positive number , Because negative is always smaller than positive.
We can take ,
6 + 6 = 12 .
6 x 6 = 36.
Where both are largest numbers possible.
Thus, the answer is 36.
The required pair of values which gives a sum of 12 and the largest product is 12
For a pair of numbers that sums of to 12 to ba as large as possible, then only positive integers would be considers.
11 and 1 = (11 × 1) = 11
10 and 2 = (10 × 2) 20
9 and 3 = (9 × 3) = 27
8 and 4 = (8 × 4) = 32
7 and 5 = (7 × 5) = 35
6 and 6 = (6 × 6) = 36
From the list, the highest product obtained is a value of 36. Hence, the number are 6 and 6.
Learn more : https://brainly.com/question/10905928
What is the perimeter of the figure?
A. 22.0 yd2
B. 21.1 yd
C. 22.0 yd
D. 21.1 yd2
Answer:
B. 21.1 yd
Step-by-step explanation:
The perimeter of the figure is the sum of all its three sides.
Take note that the dotted line is not a side length of the figure.
The side lengths are 9 yd, 5 yd, and 7.1 yd.
Therefore, the perimeter of the figure = 9 + 5 + 7.1
Perimeter = 21.1 yd.
Also, take note of the unit of the perimeter. Unit of the perimeter would not be squared. Only area has a unit that is squarred.
oredr -3/4, 3/8, -1 1/8, - 1/2 from least to greatest.
Answer: -1 1/8 -3/4 -1/2 3/8
Can you do this for me?
Answer:
10, 20, 30, 40
2.5, 5, 7.5, 10
120.8, 60.4, 30.2, 15.1
3624, 1812, 906, 453
hope this helps!
I WILL GIVE BRAINLIEST
Rewrite 12x + 3y = 6 in slope-intercept form. Give the slope and y-intercept.
y =
m =
b =
Answer:
12x + 3y = 6 in slope-intercept form.y = -4x+2m = -4b =(0,2)There are 36 doughnuts in 3 boxes.
How many doughnuts are in 7 boxes?
Answer:
x=84
Step-by-step explanation:
[tex]\frac{36}{3}=\frac{x}{7}[/tex]
(cross multiply)
252=3x
(divide both sides by 3)
x=84
need help on this 1 its really hard but i stilll can get it please help
Answer:
A.
92%
Step-by-step explanation:
Someone please help I’ve been spamming on this and no one has helped yet so please
Answer:
The value of x would 12.2.
Step-by-step explanation:
You have to use the pythagorean theorem to solve this.
a = 5.85 (11.7/2)
b = what we are trying to find
c = 13.5
[tex]\sqrt{13.5^{2} - 5.85^{2} }[/tex] = 12.1666 which rounds to 12.2
I hope this helps, I apologize if it isn't right.
true or false , the best way to represent all the solutions to a linear inequality is to graph a single line through the x intercept and y intercept where neither side of the line is shaded
A charity sells tickets for a fundraising dinner. Each adult's ticket cost $10 and each child's ticket cost $5. A total of $1050 was raised by selling 130 tickets. How many adult and child tickets were sold? Let x represent the number of adult tickets and y represent the number of child tickets.
Number of Adult Tickets Sold =
Number of Child Tickets Sold =
Answer:43
Step-by-step explanation:
3(x+5) +2(2x+3)=0 solveeeeeeeeeeeedddddddddedddddd
Step-by-step explanation:
[tex]{:}\longrightarrow[/tex][tex]\sf 3 (x+5)+2 (2x+3)=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3x+15+4x+6=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3x+4x+15+6=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 7x+21=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 7x=-21 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {-21}{7}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=-3 [/tex]
[tex]\maltese{\underline{\boxed{\bf {x=-3}}}}[/tex]
Which of the following statement(s) is/are true about rectangles? i. The diagonals are congruent. ii. All sides are congruent. iii. Both pairs of opposite sides are parallel. iv. The diagonals are perpendicular bisectors of each other.
Answer:
i. The diagonals are congruent.
iii. Both pairs of opposite sides are parallel.
iv. The diagonals are perpendicular bisectors of each other.
Step-by-step explanation:
Plan quadrilateral, which has four right angles; surface bounded by this quadrilateral. (A parallelogram is a rectangle if it has a right angle or if its diagonals [segments] have the same length. The perpendicular bisectors of two consecutive sides of a rectangle are its axes of symmetry.)
The length of a rectangle is the larger of its two dimensions, the smaller being its width. For measurement purposes, we sometimes distinguish the base b and the height h of a rectangle: Either side of the rectangle can be used as the base; the adjacent side will then be the corresponding height.
Note: A rectangle, therefore, has all the properties of a parallelogram:
Parallel opposite sides
Same length for opposite sides
The intersection of diagonals in the middle
A rectangle possesses two axes of symmetry, which are the perpendicular bisectors of its sides.
A rectangle has a center of symmetry, which is the point of intersection of its diagonals.
Answer:
The diagonals are congruent.
Both pairs of opposite sides are parallel.
The diagonals are perpendicular bisectors of each other.