What is the area of each semicircle of the following composite figure?

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If

PSYCHO15rus [73]

The length will be 3 because of the altitude

7 0

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

7 0

2 years ago

How many times does 19 go into 115

laila [671]

It goes in six times

3 0

3 years ago

Read 2 more answers

A l-meter steel rod is bent into a rectangle so that its length exceeds quadruple its width

Dmitry_Shevchenko [17]

Answer:

The dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.

Step-by-step explanation:

Given,

A 1 meter steel rod is bent into a rectangle.

That means the perimeter of the rectangle is 1 meter.

So, Perimeter = $1\ m=100\ cm$

Let the width of the rectangle be 'x'.

Now According to question, length exceeds quadruple its width by 5 cm.

Hence framing the above sentence in equation form, we get;

$Length=4x+5$

Now we use the formula of perimeter of rectangle,

$Perimeter=2(Length+width)$

On substituting the values, we get;

$2(4x+5+x)=100\\\\(5x+5)=\frac{100}{2}\\\\5x+5=50\\\\5x=50-5\\\\5x=45\\\\x=\frac{45}{5}=9$

Now, we substitute the value of x to get the value of length;

$Length=4x+5=4\times9+5=36+5=41\ cm$

Thus, Width=9 cm Length=41 cm

Hence the dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.

6 0

2 years ago

Write the ratio in fractional notation in lowest terms. 28 inches to 42 inches

ivolga24 [154]

28 to 42 means 28/42

We now reduce 28/42 to lowest terms.

28 ÷ 7 = 4

42 ÷ 7 = 6

We now have 4/6.

We now reduce 4/6.

4 ÷ 2 = 2

6 ÷ 2 = 3

Final answer: 2/3

7 0

2 years ago