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Nesterboy [21]
3 years ago
11

If you apply the changes below to the absolute value parent function, f(x) = |Xl,

Mathematics
1 answer:
TiliK225 [7]3 years ago
7 0

Answer:

• Shift 5 units to the left  >>>  f(x) = |x+5|

• Shift 4 units down >>>  f(x) = |x| - 4

Step-by-step explanation:

If we have the parent function:

f(x) = |x|

<u>For horizontal translations:</u>

  • |x-a| means horizontally translated a units right
  • |x+a| means horizontally translated a units left

<u>For Vertical translation:</u>

  • |x| + b means vertically translated b units up
  • |x| - b means vertically translated b units down

From the translation rules, we can say:

Shift 5 units left would be:

|x+5|

and

Shift 4 units down would be:

|x| - 4

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3 years ago
The area of a rectangle has decreased by 2%.
MissTica

Answer:

The other side was decreased to approximately .89 times its original size, meaning it was reduced by approximately 11%

Step-by-step explanation:

We can start with the basic equation for the area of a rectangle:

l × w = a

And now express the changes described above as an equation, using "p" as the amount that the width is changed:

(l × 1.1) × (w × p) = a × .98

Now let's rearrange both of those equations to solve for a / l.  Starting with the first and easiest:

w = a/l

now the second one:

1.1l × wp = 0.98a

wp = 0.98a / 1.1l

1.1 wp / 0.98 = a/l

Now with both of those equalling a/l, we can equate them:

1.1 wp / 0.98 =  w

We can then divide both sides by w, eliminating it

1.1wp / 0.98w = w/w

1.1p / 0.98 = 1

And solve for p

1.1p = 0.98

p = 0.98 / 1.1

p ≈ 0.89

So the width is scaled by approximately 89%

We can double check that too.  Let's multiply that by the scaled length and see if we get the two percent decrease:

.89 × 1.1 = 0.979

That should be 0.98, and we're close enough.  That difference of 1/1000 is due to rounding the 0.98 / 1.1 to .89.  The actual result of that fraction is 0.89090909...  if we multiply that by 1.1, we get exactly .98.

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2 years ago
Can somebody please explain and answer this for me? I really don't get it.
Tcecarenko [31]

Answer:

Results can be (-\frac{1}{3} )^5

Step-by-step explanation:

-The solution for this question:

(-\frac{1}{3} )^5 is equal to  (-\frac{1}{3}) × (-\frac{1}{3}) × (-\frac{1}{3}) × (-\frac{1}{3}) × (-\frac{1}{3})

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(-\frac{1}{3} )^5 = -\frac{1}{243}

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Answer:

4y

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How may pound is 1 ton
SVETLANKA909090 [29]
2,000 IBs (pounds) are in a ton.
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