1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
netineya [11]
3 years ago
5

If the vertex of a parabola is (-4, 6) and another point on the curve is (-3, 14), what is the coefficient of the squared expres

sion in the parabola's equation?
Mathematics
1 answer:
Luda [366]3 years ago
8 0
\bf \qquad \textit{parabola vertex form}\\\\\begin{array}{llll}
\boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\
x=a(y-{{ k}})^2+{{ h}}
\end{array}\qquad\qquad  vertex\ ({{ h}},{{ k}})\\\\
-------------------------------\\\\
vertex\ (-4,6)\qquad 
\begin{cases}
h=-4\\
k=6
\end{cases}\implies y=a(x-(-4))^2+6
\\\\\\
y=a(x+4)^2+6
\\\\\\
\textit{we also know that }
\begin{cases}
x=-3\\
y=14
\end{cases}\implies 14=a(-3+4)^2+6

solve for "a"
You might be interested in
Suppose you are given two quadrilaterals, ABCD EFGH. If the similarity ratio of ABCD to EFGH is 4:3, and if EH = 60, find AD.
Sophie [7]
4/3 = AD/EH (similarity)

hence, AD= EH*4/3=60*4/3=80

so, 80
4 0
3 years ago
How to write 9,009,009 in word form
DaniilM [7]
Nine million nine thousand and nine
7 0
3 years ago
Read 2 more answers
Birds arrive at a birdfeeder according to a Poisson process at a rate of six per hour.
m_a_m_a [10]

Answer:

a) time=10 \frac{1}{6}=\frac{10}{6}=1.67 hours

b) P(T\geq 0.25h)=e^{-(6)0.25}=0.22313

c) P(T\leq 0.0833)=1-e^{-(6)0.0833}=0.39347

Step-by-step explanation:

Definitions and concepts

The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:

P(X=x) =\lambda^x \frac{e^{-\lambda}}{x!}

And the parameter \lambda represent the average ocurrence rate per unit of time.

The exponential distribution is useful when we want to describ the waiting time between Poisson occurrences. If we assume that the random variable T represent the waiting time btween two consecutive event, we can define the probability that 0 events occurs between the start and a time t, like this:

P(T>t)= e^{-\lambda t}

a. What is the expected time you would have to wait to see ten birds arrive?

The original rate for the Poisson process is given by the problem "rate of six per hour" and on this case since we want the expected waiting time for 10 birds we have this:

time=10 \frac{1}{6}=\frac{10}{6}=1.67 hours

b. What is the probability that the elapsed time between the second and third birds exceeds fifteen minutes?

Assuming that the time between the arrival of two birds consecutive follows th exponential distribution and we need that this time exceeds fifteen minutes. If we convert the 15 minutes to hours we have 15(1/60)=0.25 hours. And we want to find this probability:

P(T\geq 0.25h)

And we can use the result obtained from the definitions and we have this:

P(T\geq 0.25h)=e^{-(6)0.25}=0.22313

c. If you have already waited five minutes for the first bird to arrive, what is the probability that the bird will arrive within the next five minutes?

First we need to convert the 5 minutes to hours and we got 5(1/60)=0.0833h. And on this case we want a conditional probability. And for this case is good to remember the "Markovian property of the Exponential distribution", given by :

P(T \leq a +t |T>t)=P(T\leq a)

Since we have a waiting time for the first bird of 5 min = 0.0833h and we want that the next bird will arrive within 5 minutes=0.0833h, we can express on this way the probability of interest:

P(T\leq 0.0833+0.0833| T>0.0833)

P(T\leq 0.1667| T>0.0833)

And using the Markovian property we have this:

P(T\leq 0.0833)=1-e^{-(6)0.0833}=0.39347

3 0
3 years ago
if the radius of a sphere is tripled, the surface area of a sphere will increasea) by a factor of 3b) by a factor of 4c)by a fac
Vlad1618 [11]

Answer:

D

Step-by-step explanation:

The area and the radius of a sphere are related by the formula:

A=4πr^2

Let’s say this is A1 and r1

Now the radius is tripled. This means r2 = 3r1

The new area thus becomes: A = 4 * (3r)^2 * π = 36πr^2

Comparing A1 and A2 , we can see that A2 = 9A1

4 0
3 years ago
What is the answer show work -15 + n = -27
tangare [24]
<span>-15 + n = -27
Add 15 to both sides so that the only thing remaining on one side is the variable n.
Final Answer: n= -12</span>
8 0
3 years ago
Read 2 more answers
Other questions:
  • Tai used a coupon and bought a sweater for $32. The full retail price of the sweater was $40. What percent did Tai save with her
    8·1 answer
  • Graph the exponential model y = 3(6)x .Which point lies on the graph?
    11·1 answer
  • Write a linear equation from a slope and a point
    12·1 answer
  • I need help with this question
    8·1 answer
  • Point Y is the midpoint of segment XZ. If XY = 2(3x +1) and YZ = 5x + 22, find the value of x. x = 20 x = 24 x = 18 x =11
    12·1 answer
  • Im going to give 20 points for this question please answer it please
    9·2 answers
  • 1)A bag contains seven red marbles and seven
    12·1 answer
  • The ratio of dogs to cats in a veterinarian's office is 9:7. What is the ratio of the number of dogs
    9·1 answer
  • Find the height of a cone with a diameter of 12 m whose volume is 264 m
    11·2 answers
  • The product of 12, x and y. Translate the following phrase into an algebraic expression. Do Not simplify.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!