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2 years ago

Consider the equation One-fourth(x – 5) = (y – 2)2. What is the equation of the directrix?

Mathematics

1 answer:

jeka57 [31]2 years ago

6 0

Considering the parabolic equation, the equation for the directrix is given by x = 4.9375.

<h3>What is the equation of a parabola given it’s vertex?</h3>

The equation of a horizontal quadratic function, of vertex (h,k), is given by:

(y - k)^2 = 4p(x - h)

The directrix is given by:

x = h - p.

In this problem, the equation is given by:

(y - 2)² = 0.25(x - 5).

Hence h = 5, p = 0.25/4 = 0.0625, hence the directrix is:

x = h - p = 5 - 0.0625 = 4.9375.

More can be learned about parabolic equations at brainly.com/question/24737967

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(09.02 HC)

Vesna [10]

We factor the equation to get:

-(x-25)^2+361

In the form a(x-h)^2+k, the vertex is (h, k), so the vertex is (25, 361). This means that the studio makes the most profit from selling 25 memberships, and thus makes 361 dollars.

B. The x-intercepts are the values of x for which f(x) is 0. This equation can be factored as (-a+6)(a-44)=0, with solutions 6 and 44. Therefore, by selling either 6 memberships or 44 memberships, the studio breaks even, neither making nor losing money.

4 0

2 years ago

Will give brainliest! please answer!

Montano1993 [528]

Answer:

Step-by-step explanation:

933 + the cost <=1500

933+ c <=1500

3 0

2 years ago

Read 2 more answers

If the filling equipment is functioning properly what is the probability that the volume of oil in a randomly selected barrel wi

Sophie [7]

Answer:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

$P(Z>0.8)=1-P(Z\leq 0.8)$

$P(Z>0.8)=1-0.788=0.212$

Step-by-step explanation:

Assuming this previous info : "Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly, the actual volume of oil loaded into each barrel by the filling equipment at the port is approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5 gallons. If the mean is greater than 55.4 gallons, the filling mechanism is overfilling."

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the amount filling of a population, and for this case we know the distribution for X is given by:

$X \sim N(55,0.5)$

Where $\mu=55$ and $\sigma=0.5$

We are interested on this probability

$P(X>55.4)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

And we can find this probability using the complement rule:

$P(Z>0.8)=1-P(Z\leq 0.8)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(Z>0.8)=1-0.788=0.212$

8 0

2 years ago

Whic

andreyandreev [35.5K]

Figure A which has two rays connected at a vertex is an angle in this scenario.

<h3>What is an Angle?</h3>

This is formed when two rays share a common endpoint with there being different types of angles.

The common endpoint shared forms a vertex which is why Figure A was chosen as the most appropriate choice.

Read more about Angle here brainly.com/question/25770607

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5 0

1 year ago

Ned walks 6 tenths of a mile to school.Fred walks 9 tenths of a mile to school.who walks farther?.Explain

FromTheMoon [43]

Fred. .9 is larger than .6 therefore, Fred walked a longer distance.

8 0

2 years ago

Read 2 more answers