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olga nikolaevna [1]
3 years ago
7

A. 2 • (3(5 + 2) - 1)

Mathematics
1 answer:
tankabanditka [31]3 years ago
5 0

Step-by-step explanation:

2(3(7)-1)

= 2(21-1)

=2(20)

=40

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If f ( 4 ) = − 2 , write an ordered pair that must be on the graph of y = f ( x + 4 ) + 1
AlekseyPX

We have been given that

y = f ( x + 4 ) + 1\\
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f(4)=-2

Now, we need to find an ordered pair that must be on the graph of

y = f ( x + 4 ) + 1

On substituting x=0 in the above equation, we get

y = f ( 0 + 4 ) + 1\\
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y=f(4)+1\\
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\text{On substituting the value of f(4)= -2, we get}\\
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y=-2+1\\
y=-1

Therefore, the required ordered pair is given by (0,-1)

4 0
3 years ago
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

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viktelen [127]

Answer:

Step-by-step explanation:

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