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2 years ago

What is the axis of symmetry for f(x) = −3x2 + 18x − 7?

Mathematics

1 answer:

katrin2010 [14]2 years ago

4 0

The axis of symmetry of a parabola like

$y=ax^2+bx+c$

is a vertical line of the form

$x = k$

where k is the x coordinate of the vertex of the parabola.

In particular, the x coordinate of the vertex of the parabola is given by

$x = -\dfrac{b}{2a}$

which in your case becomes

$x = -\dfrac{18}{-6} = 3$

So, the axis of symmetry is the line

$x=3$

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On a coordinate plane, line D F goes through points (negative 1, negative 3) and (2, 3). Point G is at (negative 4, negative 4).

FromTheMoon [43]

Answer:

The line passes through the y-axis at point (0,4).

Step-by-step explanation:

On a coordinate plane, line DF goes through points (-1,-3) and (2,3).

So, the slope of the line DF is $\frac{- 3 - 3}{- 1 - 2} = 2$

Then the straight line which is parallel to DF will be given by

y = 2x + c.

Where, c is any constant and we have to evaluate it if this line passes through the point (-4,-4).

So, - 4 = 2(- 4) + c

⇒ c = 4

So, the straight line which is parallel to DF and passes through the point (-4,-4) is y = 2x + 4.

Now, putting x = 0, we get, y = 4.

Therefore, the line passes through the y-axis at point (0,4). (Answer)

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1 year ago

Read 2 more answers

A movie theater was putting up their posters in the frames they had installed on the wall for upcoming attractions. They have 8

Serjik [45]

Answer:

1680

Step-by-step explanation:

Since there are 4 places (frames) to put up each poster, we think individually:

In the first place they can place ANY OF THE 8 POSTERS

In 2nd place, they can place ANY OF THE REMAINING 7 POSTERS

In 3rd place, they can place ANY OF THE REMAINING 6 posters

and

in last place, they can place ANY OF THE REMAINING 5 posters

The number of ways is the multiplication of them all, so:

8 * 7 * 6 * 5 ways = 1680 ways

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2 years ago

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Trapezoid STUV with vertices S(-3,6),T(0,7),U(1,4),and V(-5,2): (x,y)>(x+7,y-9)

hjlf

Answer:

See below

Step-by-step explanation:

Given points:

S(-3,6),T(0,7),U(1,4),and V(-5,2)

Translation rule:

(x,y) → (x+7,y-9)

New coordinates by applying the rule:

S'(4, -3), T'(7, -2), U'(8, -5), V'(2, -7)

See attached for the graph

The blue trapezoid is STUV and the red one is S'T'U'V'

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1 year ago

Over the past decade, the mean number of hacking attacks experienced by members of the Information Systems Security Association

fredd [130]

Answer:

$P(X>600)=P(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma})=P(Z>\frac{600-510}{14.28})=P(z>6.302)$

And we can find this probability using the complement rule and the normal standard distribution and we got:

$P(z>6.302)=1-P(z$

Step-by-step explanation:

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 number of attacks of a population, and for this case we know the distribution for X is given by:

$X \sim N(510,14.28)$