What is the expanded form of 3x(x+3)^2?

Arabellah earned $20 for babysitting her younger sibling, spent $4 on ice cream, and received a $5 allowance. Which expression r

bearhunter [10]

Answer:

The correct answer is "E"

6 0

4 years ago

What is this pattern going down by 512,128,32,8,2

Juliette [100K]

It is going down by 384

7 0

4 years ago

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A 172 ft. building casts a 444 ft. shadow from the sun. To the nearest tenth of a degree, what is the angle of depression? Help

Simora [160]

Answer:

beesechurger

Step-by-step explanation:

:)

6 0

3 years ago

Sketch the asymptotes and graph the function y=4/(x-1)+5

Brums [2.3K]

orizontal Asymptote:

y

=

0

Vertical Asymptote:

x

=

1

Refer to the graph of

y

=

1

x

when you graph

y

=

4

x

−

1

might help you get some idea of the shape of this function.

graph{4/(x-1) [-10, 10, -5, 5]}

Explanation:

Asymptotes

Find the vertical asymptote of this rational function by setting its denominator to

0

and solving for

x

.

Let

x

−

1

=

0

x

=

1

Which means that there's a vertical asymptote passing through the point

(

1

,

0

)

.

*FYI you can make sure that

x

=

1

does give a vertical asymptote rather than a removable point of discontinuity by evaluating the numerator expression at

x

=

1

. You can confirm the vertical asymptote if the result is a non-zero value. However if you do end up with a zero, you'll need to simplify the function expression, remove the factor in question, for example

(

x

−

1

)

, and repeat those steps. *

You may find the horizontal asymptote (a.k.a "end behavior") by evaluating

lim

x

→

∞

4

x

−

1

and

lim

x

→

−

∞

4

x

−

1

.

If you haven't learned limits yet, you'll still able to find the asymptote by plugging in large values of

x

(e.g., by evaluating the function at

x

=

11

,

x

=

101

, and

x

=

1001

.) You'll likely find that as the value of

x

increase towards positive infinity, the value of

y

getting closer and closer to- but never reaches

0

. So is the case as

x

approaches negative infinity.

By definition , we see that the function has a horizontal asymptote at

y

=

0

Graph

You might have found the expression of

y

=

1

x

, the

x

-reciprocal function similar to that of

y

=

4

x

−

1

. It is possible to graph the latter based on knowledge of the shape of the first one.

Consider what combination of transformations (like stretching and shifting) will convert the first function we are likely familiar with, to the function in question.

We start by converting

y

=

1

x

to

y

=

1

x

−

1

by shifting the graph of the first function to the right by

1

unit. Algebraically, that transformation resembles replacing

x

in the original function with the expression

x

−

1

.

generated with fooplot

Finally we'll vertically stretch the function

y

=

1

x

−

1

by a factor of

4

to obtain the function we're looking for,

y

=

4

x

−

1

. (For rational functions with horizontal asymptotes the stretch would effectively shifts the function outwards.)

generated with footplot

3 0

3 years ago

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an open box is to be made from a piece of metal 16 by 30 inches by cutting out squares of equal size from the corners and bendin

blagie [28]

Let the lengths of the bottom of the box be x and y, and let the length of the squares being cu be z, then
V = xyz . . . (1)
2z + x = 16 => x = 16 - 2z . . . (2)
2z + y = 30 => y = 30 - 2z . . . (3)

Putting (2) and (3) into (1) gives:
V = (16 - 2z)(30 - 2z)z = z(480 - 32z - 60z + 4z^2) = z(480 - 92z + 4z^2) = 480z - 92z^2 + 4z^3
For maximum volume, dV/dz = 0
dV/dz = 480 - 184z + 12z^2 = 0
3z^2 - 46z + 120 = 0
z = 3 1/3 inches

Therefore, for maximum volume, a square of length 3 1/3 (3.33) inches should be cut out from each corner of the cardboard.
The maximum volume is 725 25/27 (725.9) cubic inches.

8 0

3 years ago