Answer:
The coordinates of the focus are [tex]F(x,y) = (-1,0)[/tex] anf the equation of the directrix is [tex]x = 1[/tex], respectively.
Step-by-step explanation:
Let be [tex]y^{2} = -4\cdot x[/tex], which represents a parabola with a horizontal axis of symmetry. To find the location of the focus and to determine the equation of the directrix we must find the distance between focus and vertex ([tex]p[/tex]), dimensionless, a value than can be extracted from the following definition:
[tex](y-k)^{2} = 4\cdot p \cdot (x-h)[/tex] (Eq. 1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]h[/tex], [tex]k[/tex] - Coordinates of the vertex, dimensionless.
By direct comparison, we get the following coincidences:
[tex]h = 0[/tex]
[tex]k = 0[/tex]
[tex]4\cdot p = -4[/tex] (Eq. 2)
From (Eq. 2) we get that distance between focus and vertex is:
[tex]p = -1[/tex]
Which is consistent with the fact parabola has an absolute maximum.
Now, the location of the focus is:
[tex]F(x,y) = (h+p, k)[/tex] (Eq. 3)
If know that [tex]h = 0[/tex], [tex]k = 0[/tex] and [tex]p = -1[/tex], coordinates of the focus is:
[tex]F(x, y) = (0-1, 0)[/tex]
[tex]F(x,y) = (-1,0)[/tex]
And the equation of the directrix is represented by:
[tex]x = -p[/tex] (Eq. 4)
([tex]p = -1[/tex])
[tex]x = 1[/tex]
The coordinates of the focus are [tex]F(x,y) = (-1,0)[/tex] anf the equation of the directrix is [tex]x = 1[/tex], respectively.
Answer:
The general formula for this parabola is y2 = 4px.
Therefore, the value of p is
✔ –1
.
The coordinates of the focus are
✔ (–1,0)
.
The equation of the directrix is
✔ x = 1
.
Step-by-step explanation:
Solve for x: 1 over 3 (2x − 8) = 4.
2
6
10
Answer:
the answer is x= 10
Step-by-step explanation:
Juan And his little brother had a pizza divided into eight slices of equal size juan ate 5 slices and his little brother ate the rest what fractional part did each person eat? juan ate 5 of 8 slices or his brother ate of 8 slices pieces or?
Answer:
Juan ate 5/8 his little brother ate 3/8
Step-by-step explanation:
Answer:
juan = 5/8
brother = 3/8
please help fast and expalin.
Answer: 10,000
Step-by-step explanation:Hope this helps!
Triangle ABC is translated 5 units to the right and 4 units up to create triangle A'B'C'.
What is the measure of B?
The measure of the angle B is 74 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Triangle ABC is translated 5 units to the right and 4 units up to create triangle A'B'C'.
If triangle ABC is translated 2 units up and 2 units right, that means that all the vertices of the triangle are translated by the same units 2 up and 2 right.
The angle sum property of a triangle;
80 + 26 + B = 180
B = 180 - 106
B = 74
Therefore, the size and shape of the triangle wouldn't change.
The triangle A'B'C' will still have the same size and shape, and all the sides will have the same length.
Hence, the measure of the angle B is 74 degrees.
Learn more about the triangles;
https://brainly.com/question/2773823
#SPJ2
guys hurry i have a starter
idk what the answer
Answer:
The letter E
HOPE THIS HELPS YOU Do mark as brainliestFind |x| when x = – 15.
HELP ME PLEASEE
Answer: 15
Step-by-step explanation: | | means the absolute value the absolute value of -15 is 15 because it is 15 units away from 0.
The average number of seeds in a package of cucumber seed is 95. The numb
of seeds in the package can vary by eight. What are the maximum and
minimum number of seeds that could be in a package?
Select the correct equation and solutions that match this situation.
Answer:
103 at most and 87 at least
Step-by-step explanation:
95-8=87 seeds
95+8=103 seeds
Answer with step-by-step explanation:
Max: 25 + 3 = 28
Min: 25 - 3 = 22
Hope this helped!
Which statement is modeled by 2p + 5 < 11
Group of answer choices
The sum of 5 and 2 times p is at least 11
5 added to the product of 2 and p is less than 11
2 times p plus 1 is at most 11
the product of 2 and p added to 5 is 11
what are the solutions of the equation below
(x-2)(x+9)=0
Answer: {2, -9}
Step-by-step explanation: Think of these two binomials, x -2 and x + 9,
as two numbers that are multiplying together to equal zero.
In order for two numbers to multiply together to equal zero,
either one number or the other number must equal zero.
So for two binomials to multiply together to equal zero,
either one binomial or the other binomial must equal zero.
So we can split this problem up into two parts.
If (x - 2)(x + 9) = 0, then either x - 2 = 0 or x + 9 = 0.
On the left, add 2 to both sides and we have x = 2.
On the right, subtract 9 from both sides and we have x = -9.
For our final answer we use set notation.
So our answer is {2, -9}.
Answer:
2 and -9
Step-by-step explanation:
x-2=0
x=2
x+9=0
x=-9
On a spelling test, Lucy got 4 out of 5 correct. If Lucy got
20 questions correct, then how many quesitons did she
miss?
Answer:
4
Step-by-step explanation:
Answer:
She missed 4 questions
Step-by-step explanation:
4/5=8/10=16/20
if MrBeast has 2,000 subscribers, and on the next 2 weeks he has now 44,000 subs. what was his subs during those two weeks?
Answer:
He got 42,000 subs in the 2 weeks.
Step-by-step explanation:
ANSWER:
42,000
SOLUTION:
44,000
- 2,000
42,000
I have ti find the two solutions to this equation. This problem deals with imaginary numbers i
[tex] {3x}^{2} - x + 4 = 0[/tex]
Answer:
[tex] x = \dfrac{1}{6} + \dfrac{i\sqrt{47}}{6} [/tex] or [tex] x = \dfrac{1}{6} - \dfrac{i\sqrt{47}}{6} [/tex]
Step-by-step explanation:
Use the quadratic formula.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4(3)(4)}}{2(3)} [/tex]
[tex] x = \dfrac{1 \pm \sqrt{1 - 48}}{6} [/tex]
[tex] x = \dfrac{1 \pm \sqrt{-47}}{6} [/tex]
[tex] x = \dfrac{1}{6} \pm \dfrac{i\sqrt{47}}{6} [/tex]
[tex] x = \dfrac{1}{6} + \dfrac{i\sqrt{47}}{6} [/tex] or [tex] x = \dfrac{1}{6} - \dfrac{i\sqrt{47}}{6} [/tex]
What is (7.8 x 10) • (1.0 x 10)
780 is the answer. Hope this helps :)
The lifetime in months of a transistor in a certain application is random with probability density function:
f(x) = {0.4e^-0.4x, x>0 0, x<0
a. Compute the mean lifetime.
b. Compute the standard deviation of the lifetimes.
c. Compute the cumulative distribution function of the lifetime.
d. Compute the probability that the lifetime will be less than 6 months.
e. Compute the 60^th percentile of the lifetime.
Answer:
Explained below.
Step-by-step explanation:
The probability density function of lifetime in months of a transistor in a certain application is:
[tex]f(x)=0.4\cdot e^{-0.4x};x>0[/tex]
The probability density function suggests that the random variable X follows a exponential function with parameter λ = 0.4.
(a)
Compute the mean lifetime as follows:
[tex]\mu=\frac{1}{\lambda}=\frac{1}{0.40}=2.5[/tex]
Thus, the mean lifetime is 2.5 months.
(b)
Compute the standard deviation of the lifetimes as follows:
[tex]\sigma=\sqrt{\frac{1}{\lambda^{2}}}=\sqrt{\frac{1}{0.40^{2}}}=2.5[/tex]
Thus, the standard deviation of the lifetimes is 2.5 months.
(c)
The cumulative distribution function of the lifetime is:
[tex]CDF=1-e^{-0.40x}[/tex]
(d)
Compute the probability that the lifetime will be less than 6 months as follows:
[tex]P(X<6)=\int\limits^{6}_{0} {0.40\cdot e^{-0.40x}} \, dx[/tex]
[tex]=0.40\times [\frac{e^{-0.40x}}{-0.40}]^{6}_{0}\\\\=-1\times [e^{-0.40\times6}-e^{-0.40\times0}]\\\\=-0.090718+1\\\\=0.909282\\\\\approx 0.9093[/tex]
Thus, the probability that the lifetime will be less than 6 months is 0.9093.
(e)
Compute the 60th percentile of the lifetime as follows:
[tex]P(X<x)=0.60\\\\\int\limits^{x}_{0} {0.40\cdot e^{-0.40x}} \, dx=0.60\\\\0.40\times [\frac{e^{-0.40x}}{-0.40}]^{x}_{0}=0.60\\\\-1\times [e^{-0.40\times x}-e^{-0.40\times0}]=0.60\\\\1-e^{-0.40x}=0.60\\\\e^{-0.40x}=0.40\\\\-0.40x=\ln(0.40)\\\\-0.40x=-0.916291\\\\x=2.2907275\\\\x\approx 2.3[/tex]
Thus, the 60th percentile of the lifetime is 2.3 months.
which expression is equivalent to -10 (-40) + (-90) ?
A. 10 + 40 + 90
B. -(10-40) + (-90)
C. -10 - (40 - 90)
D. -10 + (-90) + (-40)
PLS HELP
Answer:B
Step-by-step explanation:-10 times -40 is -400 times -1 is 400.
The median of a set of consecutive odd integers is 138. If the greatest integer in the set is 145, what is the least integer in the set?
Answer:
131
Step-by-step explanation:
Given that:
Median of a consecutive odd integers = 138
Greatest integer In dataset = 145
Least integer in dataset =
Since the integers are consecutive ;
Number of integers to greatest integer value : Greatest integer - median value = 145 - 138 = 7
Hence, 7 integers before the median value should give us the least integer value ;
138 - 7 = 131
CHECK:
131,132,133,134,135,136,137,138,139,140,141,142,143,144,145
Median = (n+1)/2 th term
Median = (15+1)/2 = 8th term = 138
Highest = 145
Least = 131
Answer:
131
Explanation:
It was in a Mathcounts competition
(6 - 4) × 9
sjjdcnjcbdc
Answer:
18
Step-by-step explanation:
(2) x 9
18
That's it
Byeeeee
what 3+6+9
answer 4 pointss
ayo the answer is 18.
Answer:
3+6+9
9+9= 18
Therefore 3+6+9=18
HURRY, PLEASE HELP!!!
Answer:
Equilateral, Isosceles, and Scalene triangles all have at least one pair of equal angles.
The angles must have the same degree and most of the time come when connected by or adjoined by 2 equal side lengths.
Helppppp please !!!!!
Answer:
The answer is A) 1/8^2
Step-by-step explanation:
Both of the equations simplified equal 1/64.
State whether the data described below are discrete or? continuous, and explain why. The volumes left parenthesis in cubic feet right parenthesis of different rooms Choose the correct answer below. A. The data are discrete because the data can take on any value in an interval. B. The data are discrete because the data can only take on specific values. C. The data are continuous because the data can take on any value in an interval. D. The data are continuous because the data can only take on specific values.
Answer:
The correct answer is:
The data are continuous because the data can take on any value in an interval. (C)
Step-by-step explanation:
Discrete data are data that can take on certain limited values. There is a limit to what values can be assigned to such data. For example, the number of children in a school will just be whole numbers, either 20 or 50 or 55 or 108, etc, you cannot have 100.5 children. This makes it limited to the values it can take on, hence it is discrete
Continuous data, on the other hand, are data that can take on any value within a scale. The possibility of assigning a value is unlimited. for example height. The height can be 3m, 3.8m, 4.57m, etc, there's no limit to the possibility that a height can take. Other examples are; temperature, weight, acceleration, volume etc. In this example the volume of a room in cubic feet can be 30ft³, 50.6ft³, etc. The possibilities are endless, hence it is a continuous data.
Tommy is purchasing items from an online store. The store charges $6 shipping and handling for each package. Write an expression to represent the total shipping costs. How much will Tommy pay in shipping and handling for 2 packages? (use x as the variable) When entering your answers use only numbers a lower case x and No spaces The equation that represents this scenario is The shipping and handling for 2 packages would be dollars. (only put the number please)
Answer:
The expression to represent the total shipping costs for x package is 6x.
Tommy will pay $ 12 in shipping and handling for 2 packages.
Step-by-step explanation:
Given that the shipping and handling charge for 1 package = $ 6
So, by using the elementary method, the shipping and handling charge for x package is $ 6x.
Hence, the required expression to represent the total shipping costs for x package is 6x.
For 2 package, x=2
So, the shipping and handling charge for 2 package
=6x2
=12.
So, Tommy will pay $ 12 in shipping and handling for 2 packages.
6 : 4 is equivalent to
Answer:
12 : 8, 18 : 12, 24 : 16, 30 : 20
Step-by-step explanation:
These are the four after 6:4. I didn't know which you needed.
Answer:
3:2
Step-by-step explanation:
If you want to simplify 6:4, it also makes an equivalent equation. To simplify this, we divide by the greatest number that both numbers can be evenly divided by. 6 and 4 can both be divided by 2, which is the biggest number we can divide both numbers by.
6/2=3
4/2=2
The ratio is now simplified/equivalent to 3:2.
I hope this helps...have an amazing day c:
Slove 4(5x-2)= 2(9x+3)
Answer:
x=7
Step-by-step explanation:
divide both sides by two. distribute on the left side. minus 9x on both sides. add 4 on both sides, and you get 7.
Answer:
x = 7
Step-by-step explanation:
Firstly, use the distributive property to distribute the 4 and the 2 respectively.
[tex]4(5x-2) = 2(9x+3)[/tex]
[tex]20x-8=18x+6[/tex]
Then, isolate the variable. Start by subtracting 18x from both sides.
[tex]2x - 8 = 6[/tex]
Add 8 to both sides.
[tex]2x = 14[/tex]
Divide both sides by 2.
[tex]x=7[/tex]
Lemonade was on sale last week ;it cost $12 for every 4 packs of lemonade.How much do 2 packs of lemonade cost
Answer:
$6
Step-by-step explanation:
Each pack is $3
So therefore if you multiply 2($3) it is $6 for two packs
Michael earns $8 an hour to baby sit the Jackson family. How many hours does he have to 1 point
baby sit to earn $56?
Answer:
7 hours
Step-by-step explanation:
56/8=7
Stephen collected data from a travel website. The data included a hotel's distance from Times Square in
Manhattan and the cost of a room for one weekend night in August. A table containing these data appears below.
0
1
1
3
4
7.
19
Distance From
Times Square
(city blocks) (x)
Cost of a Room
(dollars) (y)
293 263
244
224
185
170
219
153
136
111
Stephen calculated the linear regression equation to be y = -7.8x + 246.3. Using this equation, find the cost of a
room 5 city blocks away from Time Square.
1) $195
2) $207
3) $238
4) $285
What’s the answer?
Answer:
$207
Step-by-step explanation:
Given the following :
Data:
X : Distance From Times Square (city blocks)
Y: Cost of a Room (dollars) (y)
The linear regression model generated for the data :
y = -7.8x + 246.3
y = predicted variable ; - 7. 8 = slope of model ; x = predictor variable ; 246.3 = intercept
Using the model:
The cost of a Room 5 block away :
x = 5
y = -7.8(5) + 246.3
y = - 39 + 246.3
y = $207.3
0.75 (6+d)=12 step by steP
Answer:
Step-by-step explanation:
step 1: 0.75 x 6 = 4.5
step 2: 0.75 x d = 0.75d
step 3: 4.5 + 0.75d = 5.25d
It's correct answer
Write an equivalent expression to the following: 1/2 (-6x + 8) – 7
Answer:
-3x -3
If this is not the answer you are looking for plz let me know!!!
Answer:
-6x+8=14
Step-by-step explanation:
1/2*(-6x+8)-7 |+7
1/2*(-6x+8)=7 | ÷1/2
-6x+8=14
You mean sth like this?
3(-4/7) I don’t know how to get the answer
Answer:
Step-by-step explanation:
if its 3 - 4/7 then it = 2 3/7
if its 3*-4/7 then it = -12/7 = - 1 5/7