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3 years ago

Help Asap!!!!!! Brainliest!

Mathematics

1 answer:

Nastasia [14]3 years ago

6 0

Answer:

f(-2.75)=-1

Step-by-step explanation:

Here we are given a Greatest Integer Function . The characteristic of this function is that it when operated , gives you the greatest integer it has near to it.

Hence if we have any greatest integer function f(x)=[x] , for x = -2.75

[-2.75]=-2 , as -the greatest integer near to -2.75 is -2 as -3<-2

Now coming back to our problem, our function is

f(x)=[x]+1

Hence for x=-2.75

f(x)=[-2.75]+1

as we discussed above [-2.75]=-2

Hence

f(-2.75)=-2+1

f(-2.75)=-1

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2 years ago

1.Solve the equation. Check for extraneous solutions.

elena55 [62]

Okay so I did the math.

1. Two solutions were found :
z=-1
z=2/3
Step 1 :Rearrange this Absolute Value Equation

Absolute value equalitiy entered
|2z-3| = 4z-1

Step 2 :Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2z-3|

For the Negative case we'll use -(2z-3)

For the Positive case we'll use (2z-3)

Step 3 :Solve the Negative Case

      -(2z-3) = 4z-1

     Multiply
      -2z+3 = 4z-1

     Rearrange and Add up
      -6z = -4

     Divide both sides by 6
      -z = -(2/3)

     Multiply both sides by (-1)
      z = (2/3)
     Which is the solution for the Negative Case

Step 4 :Solve the Positive Case

      (2z-3) = 4z-1

     Rearrange and Add up
      -2z = 2

     Divide both sides by 2
      -z = 1

     Multiply both sides by (-1)
      z = -1
     Which is the solution for the Positive Case
Step  5  :Wrap up the solution

z=2/3
 z=-1

2. -6 < x < 26/3

Step 1 :Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
|3x-4|+5 < 27

Another term is moved / added to the right hand side.

|3x-4| < 22

Step 2 :Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |3x-4|

For the Negative case we'll use -(3x-4)

For the Positive case we'll use (3x-4)

Step 3 :Solve the Negative Case

-(3x-4) < 22

 Multiply
 -3x+4 < 22

 Rearrange and Add up
 -3x < 18

 Divide both sides by 3
 -x < 6

 Multiply both sides by (-1)
 Remember to flip the inequality sign
 x > -6
 Which is the solution for the Negative Case

Step 4 :Solve the Positive Case

(3x-4) < 22

 Rearrange and Add up
 3x < 26

 Divide both sides by 3
 x < (26/3)

 Which is the solution for the Positive Case

Step 5 :Wrap up the solution

-6 < x < 26/3

Solution in Interval Notation

(-6,26/3)

HOPE THIS HELPS :D

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3 years ago