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3 years ago

1.Solve the equation. Check for extraneous solutions.

1 answer:

7 0

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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sdas [7]

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5 0

3 years ago

How many solutions does this linear system have? Y= -1/2x + 4 x + 2y=-8

kkurt [141]

Answer:

No solutions

Step-by-step explanation:

$y=-\dfrac{1}{2}x+4 \\\\x+2y=-8$

Substitute:

$x+2(-\dfrac{1}{2}x+4)=-8\\\\x-x+8=-8\\\\8=-8$

This system has no solutions.

Hope this helps!

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3 years ago

Explain which situation will give you the best price: a discount of 15% and then 10% off that amount, a discount of 10% and then

Katarina [22]

Answer:

Step-by-step explanation:

Let X be the initial price and P be the final price.

#Given a discount of 15% then 10% of that amount:

$P_1=(1-o)[X(1-d)}\\\\=(1-0.15)[X(1-0.10)]\\\\=0.765X$

Hence, the finial price is 76.5% of the initial price.

#Given a discount of 10% then 15% of that amount:

$P_1=(1-o)[X(1-d)}\\\\=(1-0.15)[X(1-0.1)]\\\\=0.765X$

Hence, the finial price is 76.5% of the initial price.

#Given a discount of 25%

$P_1=(1-d)X\\\\=(1-0.25)X\\\\=0.75X$

Hence, the finial price is 75.0% of the initial price. It therefore give's the best price due to it's 25% price reduction.

7 0

3 years ago

HELP ME GRAPH THIS PLEASE IM DUMB I KNOW

cupoosta [38]

Answer:

You should graph the lines (0, 0) to (2, 120), (2, 120) to (2.5, 120), and (2.5, 120) to (3.5, 150).

Step-by-step explanation:

If we see, for the first part, she drive 60 miles an hour and drives for 2 hours. This means that after 2 hours, she has driven 60 * 2 = 120 miles in 2 hours. Then she spends 30 minutes, or half an hour, no moving forward as she changes the tire. Finally, she drives at 30 miles an hour for an hour. This means she has driven 120 + 30 = 150 miles in total after 3 and a half hours.

Our first line goes from (0, 0) to (2, 120), as thats how far we drove in 2 hours. The next line goes from (2, 120) to (2.5, 120), as she was changing a tire and made no progress. Finally, the last line goes from (2.5, 120) to (3.5, 150), as she drives for another hour at 30 miles an hour.

4 0

3 years ago

On apiece of paper graph this system of equations y=x-8 y=x^2-2x-3 then determine which answer choice matches the graph you drew

katen-ka-za [31]

Answer:

No solution.

Step-by-step explanation:

y = x - 8

y = x² - 2x - 3

Let's find the point where the lines meet;

x - 8 = x² - 2x - 3

x² - 2x + x - 3 + 8 = 0

x² - x + 5 = 0

Applying the quadratic formula method we get,

It will give the value of "x" a complex number hence that graph does not have a solution.

6 0

3 years ago