1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ioda
2 years ago
15

|1/2b-8|=|1/4b-1| b=____ and ____

Mathematics
1 answer:
Deffense [45]2 years ago
4 0

Answer:

  b = 12 and 28

Step-by-step explanation:

The absolute value equation |1/2b-8| = |1/4b-1| resolves to a piecewise linear function with three pieces. There are two solutions.

<h3>Domains</h3>

The absolute value function on the left has a turning point where its value is zero:

  1/2b -8 = 0

  b -16 = 0

  b = 16

The absolute value function on the right has a turning point where its value is zero:

  1/4b -1 = 0

  b -4 = 0

  b = 4

For b > 16, both absolute value functions are identity functions. In this domain, the equation is ...

  1/2b -8 = 1/4b -1

For 4 < b < 16, the function on the left negates its argument, so the equation in this domain is ...

  -(1/2b -8) = 1/4b -1

For b < 4, both functions negate their arguments, so the equation in this domain is ...

  -(1/2b -8) = -(1/4b -1)

For the purpose of finding the value of b, this is effectively identical to the equation for b > 16. (The value of b does not change if we multiply both sides of the equation by -1.)

<h3>Solutions</h3>

<u>Domain b < 4 ∪ 16 < b</u>

  1/2b -8 = 1/4b -1

  2b -32 = b -4 . . . . . . . . multiply by 4

  b = 28 . . . . . . . . . . . . add 32-b to both sides

This solution is in the domain of the equation, so is one of the solutions to the original equation.

<u>Domain 4 < b < 16</u>

  -(1/2b -8) = 1/4b -1 . . . . equation in this domain

  -2b +32 = b -4 . . . . . . multiply by 4

  36 = 3b . . . . . . . . . . . add 2b+4 to both sides

  12 = b . . . . . . . . . . . . divide by 3

This solution is in the domain of the equation, so is the other solution to the original equation.

<h3>Graph</h3>

For the purposes of the graph, we have define the function g(b) to be the difference of the two absolute value functions. The solutions are found where g(x) = 0, the x-intercepts. The graph shows those to be ...

  b = 12  and  b = 28

__

<em>Additional comment</em>

Defining g(b) = |1/2b-8| -|1/4b-1|, we can rewrite it as ...

  g(b)=\begin{cases}7-\dfrac{1}{4}b&\text{for }b < 4\\-\dfrac{3}{4}b+9&\text{for }4\le b < 16\\\dfrac{1}{4}b-7&\text{for }16\le b\end{cases}

Then the solutions are the values of b that make g(b) = 0.

You might be interested in
Complete the function table and write the function rule.
Vedmedyk [2.9K]
Y = x but what is pi

3 0
3 years ago
What is the value of x in the equation 1/2x - 3/4 = 3/8 - 5/8
Kitty [74]

The answer

x = 1

step by step

\frac{1}{2} x -  \frac{3}{4}  = \frac{3}{8}  -  \frac{5}{8} \\  \frac{1}{2} x = \frac{3}{8}  -  \frac{5}{8} +  \frac{3}{4}  \\  \frac{1}{2} x = \frac{3}{8}  -  \frac{5}{8} +  \frac{6}{8}  \\  \frac{1}{2}x =   \frac{4}{8}  \\  \frac{1}{2} x =  \frac{1}{2}  \\ x = 1

5 0
3 years ago
What is i + 6i simplified?​
kkurt [141]

Answer:

7i..........................

3 0
3 years ago
Answer....... (-1)^3×(-1)^2
8090 [49]
Hello there!

(-1)^3 * (-1)^2

Use the distributive property

= (-1)(-1)(-1)* (-1)(-1)

= (-1)^5

= -1


I hope this helps!
3 0
3 years ago
.A bacteria culture grows at a rate of 20%
Zolol [24]

The number of the specimens would be in the culture after 5 minutes will be 7,962.62.

<h3>What is an exponent?</h3>

Consider the function:

y = a (1 + r) ˣ

Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.

A bacteria culture grows at a rate of 20% per minute.

If the culture initially has 3,200 bacteria specimens.

Then the equation will be

y = 3200 (1 + 0.2) ˣ

y = 3200 (1.20) ˣ

Then the number of the specimens would be in the culture after 5 minutes will be

y = 3200 (1.20)⁵

y = 7962.62

More about the exponent link is given below.

brainly.com/question/5497425

#SPJ1

5 0
2 years ago
Other questions:
  • How many pennies is $100
    6·2 answers
  • 15 points IF ANY1 HELPS ASAP PLZ
    8·1 answer
  • |-3 + 15| what is the sum (answer) ? I think it is 12 but my friend thinks it is 18. Who is right?
    10·2 answers
  • What's the perimeter of rectangle DEFG, shown? A) 17 B) 28 C) 40 D) 34
    11·2 answers
  • In 4 years, a mother will be 5 times as old as her daughter. At present, the mother is 9 times as old as the daughter. How old a
    13·2 answers
  • A construction team gives an estimate of three months to repave a large stretch of a very busy road with their core crew of 9 pe
    10·1 answer
  • What are the roots of the equation? <br> 2x^2+x=6
    15·2 answers
  • PLEASE HELP ITS DUE RIGHT NOW
    5·1 answer
  • 6 is subtracted from a number. The result is divided by 4. This result is added to 10 to give 30. What is the number?
    11·1 answer
  • If one piece of furniture was sold every 3/4 hour, how many pieces of furniture are sold in 3 hours
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!