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Stella [2.4K]
2 years ago
7

What is the function g(x) created from f(x) = x2 by moving the graph left 2 units, adding vertical compression by a factor of 1/

4
shifting the graph up 3 units?
Mathematics
1 answer:
Naily [24]2 years ago
7 0

Answer:

Step-by-step explanation:

g(x)= 1/4x^2(x+2)+3

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A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s
yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2}  = \frac{1 \pm 9 }{-0.4}

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0
2 years ago
Which is greater 34.653 or 3.4653?
Charra [1.4K]
34 is larger than 3, so 34.653
4 0
3 years ago
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Which statement best explains why this expression is equal to 9.4? A)Any expression multiplied by 0 equals 0. B)Any number divid
tigry1 [53]

Answer: A.

Step-by-step explanation:

yeet

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2 years ago
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Given g(x)=8x+3 find the following g(-1) and g(2a+1)
Degger [83]

Answer:

g(-1) = -5

g(2a+1) = 16a+11

Step-by-step explanation:

Substitute the given value into the function and evaluate.

So for g(x) = 8x+3

You substitute g(-1)

So g(-1) = 8(-1)+3

That is how you get -5

Then g(2a+1)

So g(2a+1) = 8(2a+1)+3

Thats how you get 16a+11

Hope this helps. Mark as brainlist

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2 years ago
Evaluate <br><br>2³ + 4 • 2 - 7<br><br>I need help fast its a test ;-;​
djverab [1.8K]

Answer:

5

Step-by-step explanation:

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