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Dvinal [7]
3 years ago
11

Identify the parent function that can be used to graph the function f(x)= |4|-3

Mathematics
1 answer:
son4ous [18]3 years ago
7 0

Answer: Option d.

Step-by-step explanation:

 1. The parent function of an absolute value function is shown below:

f(x)=|x| (This is the simplest form). Because from this function we can make transformations that allow us to obtain the function f(x) = 4|x| -3

2. If you take the parent function and make y= f(x)-3/4, then you have:

y= f(x)-3/4=|x|-3/4 (The function is shifted down 3/4 units on the y-axis).

3. Then you if you make y= 4(f(x)-3/4), as following, you obtain:

y = 4(f(x)-3/4))=4|x|-3 (The function is reflected in the y-axis).

4. That is how you obtain the final function. f(x) = 4|x|-\frac{3}{4}

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Line f has a slope of -3. what is the slope of the line that is parallel to line f
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3 years ago
Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work​ together, it takes them 2 hours. How
aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood  = K hrs

So, the per hour rate of Dwight  = (\frac{1}{K})

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood  = (K- 3) hrs

So, the per hour rate of Joe  = (\frac{1}{K-3})

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them  = (\frac{1}{2})

⇒ Per hour rate of ( Dwight  + Joe)  =(\frac{1}{2} )

\implies (\frac{1}{K}) +  (\frac{1}{K-3}) = (\frac{1}{2})

Now, solving for the value of K , we get:

(\frac{1}{K}) +  (\frac{1}{K-3}) = (\frac{1}{2})\\\implies  \frac{(K-3) + K}{K (K-3)}  = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K  + 6=  0\\\implies K^2 - 6K - K  + 6=  0\\\implies K(K-6) -1(K - 6)=  0\\\implies (K-6)(K-1) = 0

Implies either K = 6 Or K = 1

But if K = 1, (K-3)  = 1- 3  = -2 hours would be A CONTRADICTION.

⇒ K  = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

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2 years ago
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