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1 year ago

True or false: The equation for the axis of symmetry for the function, y = 2x^2 - 8x + 3 is x = 2.

Mathematics

1 answer:

SCORPION-xisa [38]1 year ago

7 0

ANSWER

True

EXPLANATION

We want to find the equation of the axis of symmetry of the given function:

$y=2x^2-8x+3$

The axis of symmetry of the function is given by:

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

where b = coefficient of x

a = coefficient of x²

From the given function:

$\begin{gathered} a=2 \\ \\ b=-8 \end{gathered}$

Therefore, the equation for the axis of symmetry of the function is:

$\begin{gathered} x=-\frac{-8}{2(2)} \\ \\ x=-\frac{-8}{4}=-(-2) \\ \\ x=2 \end{gathered}$

Therefore, it is true.

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I need to learn how to solve this problem

Sonbull [250]

Answer:

x = 7/2, so every side equals 15.

Step-by-step explanation:

The first thing you want to notice about this problem is that keyword "equilateral." That means every one of the sides are equal, and that means you can play around with the algebra to get your answer.

In an equilateral triangle, if you have two sides 4x + 1 and 6x - 6, these sides must be equal. To solve for x, simply set these two equations equal to each other. Note that you can pick any pairing of the three sides and get the same answer; I only chose these because they look easier.

4x + 1 = 6x - 6 ... subtract 4x from both sides

1 = 2x - 6 ... add 6 to both sides

7 = 2x ... solve for x

x = 7/2

You get the same answer if you try 8x - 13 = 4x + 1, and if you do 8x - 13 = 6x - 6. Now that you have the value of x, take that and plug it into ANY of the sides to get the length. (It would be good to plug 7/2 into all of them to check your work!)

4(7/2) + 1 = 15

So the lengths are all 15 feet each.

3 0

3 years ago

A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing are use

Rashid [163]

Answer:

$A = L W= 9*\frac{9}{2}=\frac{81}{2} m^2$

Step-by-step explanation:

For this case we assume that the total perimeter is 18 ft, we have a wall and the two sides perpendicular to the wall measure x units each one so then the side above measure P-2x= 18-2x.

And we are interested about the maximum area.

For this case since we have a recatangular area we know that the area is given by:

$A= LW$

Where L is the length and W the width, if we replace from the values on the figure we got:

$A(x)= x *(18-2x) = 18x -2x^2$

And as we can see we have a quadratic function for the area, in order to maximize this function we can use derivates.

If we find the first derivate respect to x we got:

$\frac{dA}{dx} = 18-4x=0$

We set this equal to 0 in order to find the critical points and for this case we got:

$18-4x=0$

And if we solve for x we got:

$x=\frac{18}{4}=\frac{9}{2} m$

We can calculate the second derivate for A(x) and we got:

$\frac{d^2 A}{dx^2}= -4$

And since the second derivate is negative then the value for x would represent a maximum.

Then since we have the value for x we can solve for the other side like this:

$L= 18-2x = 18-2 \frac{9}{2}= 18-9 =9m$

And then since we have the two values we can find the maximum area like this:

$A = L W= 9*\frac{9}{2}=\frac{81}{2} m^2$

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3 years ago

What number is in the blank to complete the factorization of 3x + 24?

Lubov Fominskaja [6]

Answer:

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Step-by-step explanation:

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3 years ago

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levacccp [35]

Answer: Its right.

Step-by-step explanation:

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3 years ago

Which expression is equivalent to 27+15

Rom4ik [11]

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3 years ago