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Olin [163]
3 years ago
9

Determine the axis of symmetry for the function f(x)= -2(x + 3)2 - 5.

Mathematics
2 answers:
ehidna [41]3 years ago
5 0

Answer:-2.125

Step-by-step explanation:

1. simplify the function

-2(x+3)2-5

(-2x-6)2-5

(-4x-12)-5

-4x-17

2. formula for axis of symmetry: -b/2a

a=-4 b=-17

-(-17)/2(-4)=17/-8=-2.125

ivolga24 [154]3 years ago
3 0

Answer:

The axis of symmetry for the function f(x) is x=-3.

Step-by-step explanation:

The vertex form of a quadratic function is

y=a(x-h)^2+k                 .... (1)

Where, (h,k) is vertex and x=h is the axis of symmetry.

The given function is

f(x)=-2(x+3)^2-5           .... (2)

From (1) and (2), we get

a=-2,h=-3,k=-5

The axis of symmetry is

x=h

Substitute h=-3 in the above equation.

x=-3

Therefore the axis of symmetry for the function f(x) is x=-3.

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Write the sentence as an absolute value inequality, then solve the inequality: A number “n” is more than 9 units from 3
Helga [31]

Answer:

absolute vlaue inequality: |x-3| > 9; solved: x<-6 and x>12

Step-by-step explanation:

I’m going to start this off by saying I learned all this right now by just searching up how to solve an absolute inequality equation and watching one video, so this might not be an accurate explanation. (I’m pretty sure the answer’s right though)

So an absolute value inequality must be written like this:  

| x - a | *inequality* b

a is going to be the number that the inequality is centered around, in this case, 3. b will be how far you can deviate from that number, which in this case is 9.  

Now, you will have this:

|x - 3| *inequality* 9

Now, to find the inequality, you need to understand the wording. If it says “more than” as it does here, then you would have the greater-than symbol (>). If you have “less than” then you’d have the less-than symbol (<). If the problem says “at least b away” then it would be greater-than-or-equal to (≥), and likewise, if it says “at most b away” then it would be less-than-or-equal-to (≤).

So now we're at:

|x - 3| > 9

To solve the equation, you just need to subtract 9(b) from 3(a) and add 9(a) to 3(b) to get -6 and 12. Since x must be more than 9 units away, you would get:

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Hope this is helpful!

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3 years ago
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Alex17521 [72]
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the area of a rectangle is 42.15 square meters. if the length is 21 meters, what is perimeters of the rectangle?
Vsevolod [243]

Answer:

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Step-by-step explanation:

Given that:

Length (l) = 21 m

Area of rectangle(A) = 42.15 meter-square

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Perimater of Rectangle=p=?

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As we know that Area of rectangle=A=l*w

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