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].
Kayla drives 144 miles in 3 hrs. Kendra drives 224 miles in 4 hours. How much faster does Kendra drive on an average?
Answer:
12 miles per hour more
Step-by-step explanation:
Answer:
Kendra drives 8 hours more on average.
Step-by-step explanation:
We divide 144/3 to get Kayla's mile to hour.
That is 48 miles.
We divide 224/4 to get Kendra's mile to hour.
That is 56 miles.
56 - 48 = 8.
hope this helped!
2. Joanne's car insurance is reduced by 10% for each year that she has not had an
accident.
The normal cost of her insurance is £420 but she has a 3-years' no claims bonus.
How much is her insurance?
Answer:
220
Step-by-step explanation:
help
Please!!!!!!!!
Will appreciate it :)
Answer:
-5(-6x² + x + 2)
Step-by-step explanation:
-5(-6x² + x + 2)
= (-5)(-6x²) + (-5)(x) + (-5)(2)
= 30x²-5x-10
If I read 4 pages of a book in 5 minutes, how many pages did I read per minute?
Answer:
about a half a page
Step-by-step explanation:
In a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the Roman alphabet.
(a) How many different license plates can the country produce?
(b) How many license plates have no repeated letter? (c) How many license plates have at least one repeated letter?
(d) What is the probability that a license plate has a repeated letter? (Round your answer to the nearest whole percent.)
Answer:
Step-by-step explanation:
From the given information:
The number of different license plate the country can produce is in the form:
=L₁L₂L₃L₄ or L₁L₂L₃L₄L₅ or D₁L₁L₂L₃L₄ or D₁L₁L₂L₃L₄L₅
∴
The Total number of the license plate that can be produced is;
= 26⁴ + 26⁵ + (10 × 26⁴) + (10 × 26⁵)
= 456976 + 11881376 + 4569760 + 118813760
= 135721872
Number of license plate with no repeated letter = P(26,4) + P(26,5) + 10 P(26,4) + 10 P(26,5)
= 11 P(26,4P + 11 P(26,5)
[tex]=11 \times \dfrac{26!}{(26-4)!} + 11 \times \dfrac{26!}{(26-5)!}[/tex]
= 90776400
c) The number of the licensed plate with 1 repeated letter = Total number of the licensed plate - number of the licensed plate with no repeated letter.
= 135721872 - 90776400
= 44945472
d) The probability that a licensed plate has repeated letter is:
[tex]= \dfrac{no(rep \ letter) }{n (total)} \times 100\%[/tex]
[tex]= \dfrac{44945472}{135721872}\times 100\%[/tex]
= 33.12%
A) The country can produce 118,813,760 different licence plates.
B) 78,936,000 license plates have no repeated letter.
C) 39,877,760 license plates have at least one repeated letter.
D) The probability that a license plate has a repeated letter is 33.56%.
Given that in a certain country license plates consist of zero or one digit followed by four or five uppercase letters from the Roman alphabet, to determine (A) how many different license plates can the country produce; (B) how many license plates have no repeated letter; (C) how many license plates have at least one repeated letter; and (D) what is the probability that a license plate has a repeated letter, the following calculations must be performed:
A)
10 x 26 x 26 x 26 x 26 x 26 = X 10 x 11,881,376 = X 118,813,760 = X
B)
10 x 26 x 25 x 24 x 23 x 22 = X 10 x 7,893,600 = X 78,936,000 = X
C)
118,813,760 - 78,936,000 = X 39,877,760 = X
D)
118,813,760 = 100 39,877,760 = X 39,877,760 x 100 / 118,813,760 = X 33.56 = XLearn more about quantities in https://brainly.com/question/12161780
a = 65 – 100n
Find a
39
Rods car takes 14 gallon to fill up and gets 35 miles per gallon rod drives 17.5 miles a day can rod go a whole month with out filling up
Answer:
No
Step-by-step explanation:
Rod would have to fill his care up 7 times to drive a whole month, cause a month would be 225 miles and his car holds 35 miles worth of gas.
Calculate the present value PV of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time. 7 years, at 3% per year, compounded annually.
Answer:
PV= $813.09
Step-by-step explanation:
Giving the following information:
Future Value (FV)= $1,000
Number of periods (n)= 7 years
Interest rate (i)= 3% compounded annually
To calculate the present value (PV), we need to use the following formula:
PV= FV/(1+i)^n
PV= 1,000 / (1.03^7)
PV= $813.09
How many is 3+7??staijsvsvsgsusidvsvsuoshsgsusisishsbvsss
Answer:
10
Step-by-step explanation:
Solve 8x - 2(x + 1) = 7x + 8.
The answer is
X = -10
Apologies though, I am not good at explaining.
Four less than 6 times a number is the same as the number plus 11.
Complete the equation
Answer:
×=3
Step-by-step explanation:
6x-4 = x+11
6x-x = 11+4
5x = 15
x = 3
What is the domain of the function for this situation?
Answer:
There is no problem. If you put the problem then i'll help
Step-by-step explanation:
In testing the validity of a multiple regression model in which there are four independent variables, the null hypothesis is:_________.
Answer: H0 : β1 = β2 = β3 = β4 = 0
Step-by-step explanation:
The null hypothesis refers to a hypotheses that simply states that no relationship exists between two phenomenons that are being tested.
In testing the validity of a multiple regression model in which there are four independent variables, the null hypothesis is H0 : β1 = β2 = β3 = β4 = 0.
Carmen spent 88.00 at the mall the money she spent was 25% of the total amount she had in her wallet how much money did Carmen have in her money
Answer:
$352
Step-by-step explanation:
x = total money she had
spent 25% of x = 88
solve for x
x = 88/0.25
x = $352
the length of a rectangle is increased by 15% while its perpendicular height is decreased by 15%. determine, if any, the percentage change in its area.
No change in area if sides of rectangle are equal.
Hope this helps.
Which expression is equivalent to 2(m − 5) + 6?
2m − 1
2m + 22
2m − 4
2m + 16
Answer:
The answer is c
Step-by-step explanation:
Which linear function is represented by the graph?
O f(x) = -2x + 1
O f(x) = -1/2x + 1
O f(x) = 1/2x + 1
O f(x) = 2x + 1
Answer:
The answer is B
Step-by-step explanation:
Using reasoning, determine the number of marbles that you would expect to fit if you doubled the diameter
Original diameter was 8cm, could fit 40 marbles. New diameter is 16cm. How many marbles would I fit?
Answer:
80 marbles
Step-by-step explanation:
8 times 2=16
40 times 2=80
What is the x-intercept of the line?
(-38,40)
(-23,30)
(-8,20)
The answer fam is.......... 22
PLEASE HELP I HAVE 8 min left
Answer:
I would help but I can't see the picture... sorry good luck
Step-by-step explanation:
PLEASE HELP!
Identify the y-intercept and zeros of
y = x^4 - 9x^2 - 36
Algebraically
Answer:
Our y-intercept is (0, -36).
Our real zeros are: (-2√3, 0) and (2√3, 0)
And our imaginary zeros are: (i√3, 0) and (-i√3, 0)
Step-by-step explanation:
We have the function:
[tex]y=x^4-9x^2-36[/tex]
Let's identify the y- and x-intercepts.
Y-Intercept:
To determine the y-intercept, we will substitute 0 for x and solve for y. So:
[tex]y=(0)^4-9(0)^2-36[/tex]
Evaluate:
[tex]y=-36[/tex]
Therefore, our y-intercept is at (0, -36).
X-Intercepts:
To determine our x-intercepts, we need to substitute 0 for y and solve for x. So:
[tex]0=x^4-9x^2-36[/tex]
Now, we can factor. Before doing so, we can make the factored easier to see by converting this into quadratic form. Let's let u=x². Then:
[tex]0=(u^2)^2-9(x^2)-36[/tex]
Substitute:
[tex]0=u^2-9u-36[/tex]
Now, let's factor. We can use -12 and 3. So:
[tex]0=u^2+3u-12u-36 \\ 0=(u(u+3)-12(u+3)) \\ 0=(u-12)(u+3)[/tex]
Now, we can substitute back u:
[tex]0=(x^2-12)(x^2+3)[/tex]
Zero Product Property:
[tex]x^2-12=0\text{ or } x^2+3=0[/tex]
Solve for x in each case:
[tex]x^2=12 \text{ or } x^2=-3[/tex]
Take the square root of both sides. Since we're taking an even root, we will need plus/minus. Therefore:
[tex]x=\pm\sqrt{12}=\pm2\sqrt{3}\text{ or } x=\pm\sqrt{-3}=\pm i\sqrt{3}[/tex]
Therefore, our zeros (both real and imaginary) are: (2√3, 0), (-2√3, 0), (i√3, 0), and (-i√3, 0)
I NEED HELP WITH THIS MATH PROBLEM!!
Which equation has infinitely many solutions?
does anyone like 4freakshow if so start a convo in comments 11-16 pleasee
Answer:
mhm
Step-by-step explanation:
Answer:
Bet
Step-by-step explanation:
9. A company's quality control department found and average of 1.6 defective
models for every 1000 models that were checked. If the company produced
160,000 models in a year, how many of them would be expected to be
defective?
(a) 356
(b) 256
(c) 476 (d) 856
7 apples cost $2.10. How many apples can I buy for $6.30
Answer:
21
Step-by-step explanation
If 7 apples are 2.10 then for 4.20 its 14 apples. And 3 apples is 90 cents. 1 apple is 0.30. So the amount you can buy is 21 because 6.30/0.3 is 21
Answer:
21
Explanation:
If 7 apples cost y cents, how many can you buy for x dollars?
As y cents buy 7 apples, y dollars will buy 7×100 apples.
Hence one dollar will buy 7×100y=700y apples and,
x dollars will buy 700y × x apples or 700x y apples.
Hence 7 apples multiplied by $6.30 divided by $2.10 will get you 21 apples.
Have a beautiful day! v(⌒o⌒)v♪
what is 40/17 rounded to the nearrst hundreth as a decimal
Answer:
★ 40 over 17 is roughly 2.35294, which can be rounded to the nearest hundredth as 2.35
Step-by-step explanation:
Hope you have a great day :)
A pizzeria charges $4 per slice of pizza, plus an additional $0.50 per topping. If Erica has at most $13.50 to spend on her pizza, how many toppings could she get on ONE slice of pizza? Write an inequality expression that represents the situation and solve! Explain your reasoning
Answer:
19 topings
t=(13.5-4)/.5
Step-by-step explanation:
13.5-4
=9.5
9.5/.5
=19
1. (01.02)
Given that f(x) = 6x + 2 and g(x)
2x + 4/5
solve for g(f(1)). (5 points)
1
3
4
8
Answer:4
Step-by-step explanation:
f(1)=6(1)+2
=8
g(f(1))=2(8)+4/5
=20/5
=4
algebra 2. pls help:(