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zzz [600]
3 years ago
13

Perform the requested operation or operations. f(x) = x-5/8 g(x) = 8x + 5 find g(f(x))

Mathematics
2 answers:
sertanlavr [38]3 years ago
6 0
We assume 
f(x)=\dfrac{x-5}{8}
When this is written using plain text, parentheses are required in order to show what the numerator of the fraction is: f(x) = (x-5)/8.

g(f(x)) = g((x-5)/8)
 = 8((x-5)/8) +5
 = (x-5) +5
 = x

g(f(x)) = x
NARA [144]3 years ago
5 0
Just to confirm is it x-5/8 or (x-5)/8
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Suppose that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with th
KatRina [158]

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21 weeks

Step-by-step explanation:

In this question, we are to use proportionality to find the solution to the question.

We were made to know that the time taken to build the highway is varied directly with the length and inversely with the number of workers.

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t = kl/w

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Find out if the 3 positions are on the same line or not (3,2,0) (1, -1,2) (5,5, 2)
sattari [20]

Answer:

The three positions are not on the same line.

Step-by-step explanation:

We have three points: A:(3,2,0),  B:(1,-1,2) and C:(5,5,2).

Let's build a vector that goes from one point to another; that vector will be the director of a line (if we draw a vector that goes from A to B, that vector will be the direction of the line that pass by A and B because it does not change). In order to build that vector, let's subtract B from A:

A-B=(3,2,0)-(1,-1,2)=(2,3,-2)

The equation of a line is:

p=p_0+rt

Where p is every singular point of the line, p_0 is a particular point of the line (any that we are sure that it is on the line), r is the director vector and t is the independent variable.

Now we have the director vector: (2,3,-2), and we can verify that A and B are on the line:

p=p_0+(2,3,-2)t

Because there is a value for t that satisfies both A and B: If we do p_0=(3,2,0) and t=0, we are going to obtain the point p=A; and if we do t=-1, we are going to obtain p=B. Let's see that:

p=(3,2,0)+(2,3,-2)*0=(3,2,0)\\p=A\\p=(3,2,0)+(2,3,-2)*-1=(1,-1,2)\\p=B\\

If C is also in the same line, C must accomplish the equation: p=(3,2,0)+(2,3,-2)t, so:

C=(5,5,2)=(3,2,0)+(2,3,-2)t

Let's simplify the equation writing the parametric equation, which is just to write the equation for each dimension:

5=3+2t\\5=2-3t\\2=-2t\\

You can verify that there is not a value of t that satisfies all three equations, so, the point C is not on the same line as A and B; which means that A, B and C are not on the same line.

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