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gregori [183]
3 years ago
8

Show all your work to find the axis of symmetry of f(x) = −2(x − 4)^2 + 2.

Mathematics
1 answer:
Naya [18.7K]3 years ago
6 0

Answer:

-2(x^2+15)

Step-by-step explanation:

f(x) = −2(x − 4)^2 + 2.

Expanding (x-4)^2

(x-4)(x+4)

x(x+4)-4(x+4)

x^2+4x-4x-16

x^2-16

F(x) = -2(x^2-16)+2

-2x^2-32+2

-2x^2-30

-2(x^2+15)

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4 0
3 years ago
Read 2 more answers
PLZ SHOW ALL WORK
lara31 [8.8K]

Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width:  w = 12 - 2x
length: l = 18 - 2x
height: h = x

Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x

Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6

Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160

Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224

And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
3 0
3 years ago
Can there be more than one coefficient in a expression?
Lorico [155]

Answer:

yes

Step-by-step explanation:

take for example

in the expression: 3x²+5x+2=0,

the coefficients here are +3 and +5 while +2 is a constant. +3 and +5 are coefficients of the variables x² and x respectively

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3 years ago
I do not get this question
postnew [5]
Hello!

When you put money into the bank you make a deposit

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