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
mina [271]
2 years ago
7

et f(x) = x + |2x − 3|. Find all solutions to the equation f(x) = 12. (Enter your answers as a comma-separated list. If an answe

r does not exist, enter DNE.) x = $$5,−9 (b) Let g(x) = 5x − 3 + |x + 4|. Find all values of a which satisfy the equation g(a) = 4a + 9. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) a = $$4 (c) Let h(x) = |x| − 2x + 5. Find all solutions to the equation h(x − 1) = x − 3. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) x = $$ 9 2​
Mathematics
1 answer:
Alinara [238K]2 years ago
8 0

Answer:

1. {5,-9}

2.{4}

3.{9/2}

Step-by-step explanation:

The equation f(x)=x+\lvert 2x-3 \rvert=12 can be solved as follows:

x+\lvert 2x-3 \rvert =12\,\,\,\text{(given equation)}

\lvert 2x-3 \rvert =12-x

2x-3=12-x\,\,\text{or}\,\,2x-3=-(12-x)

3x=15\,\,\text{or}\,\,\x=-9

Then, the solutions of the equation are x=5, x=-9.

Now, if g(x)=5x-3+\lvert x+4\rvert, we can solve the equation g(a)=4a+9 as follows:

5a-3+\lvert a+4 \rvert =4a+9

\lvert a+4\rvert =4a+9-5a+3

a+4 =-a+12\,\,\text{or}\,\,a+4=-(-a+12)

2a=8\,\,\text{or}\,\,4=12

So, the unique solution of this last equation is a=4

The last equation is h(x-1)=x-3, where h(x)=\lvert x \rvert -2x+5.. To solve this equation we can proceed as follows:

h(x-1)=x-3

\lvert x-1\rvert -2(x-1)+5=x-3

\lvert x-1 \rvert -2x+2+5=x-3

\lvert x-1\rvert =3x-10

x-1=3x-10\,\,\text{or}\,\,x-1=-(3x-10)

-2x=-9\,\,\text{or}\,\,4x=11

x=9/2\,\,\text{or}\,\,x=11/4

But, x=11/4 is not a solution of this equation. So the unique solution is x=9/2.

You might be interested in
What is the probability of getting eiather getting blue or green spinner that is 3/10 green and 1/3 blue
inysia [295]
The probability is 50% or half or 1/2
8 0
3 years ago
120-2x=30, what’s x?
KiRa [710]

Step-by-step explanation:

-2x=30-120

-2x = -90

=x = -90/-2

=x = +45

4 0
3 years ago
The ratio of two numbers is 2/3. The sum of the numbers is 105. What are the two numbers?
Pepsi [2]
A) x/y = 2/3
B) x + y = 105
Solving Equation A for y
A) y = 1.5x
Substituting A into B
B) x + 1.5x = 105
2.5x = 105
x = 42
y = 63


8 0
3 years ago
Simplify the expression: 2(x+h)^2 - 2x^2 over (x+h) - x
Karolina [17]

Answer:

4x

Step-by-step explanation:


4 0
3 years ago
Given 100 grams of bacteria that decreases at the rate of 1/2 per year. What would be an appropriate range after 4 years
Brilliant_brown [7]

Answer: B 0

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • If​ P(E) = 0.25​, what are the odds against​ E?
    7·1 answer
  • Use the substitution method to solve the system of equations choose the correct ordered pair
    9·1 answer
  • Mass of a spherical grape is 8.4 grams and
    15·2 answers
  • Multiply (2x^2-3x+1)*(x^2-4x-3)
    9·1 answer
  • Solve the following equation for x.<br> 0.1(x + 250) = 5,000<br> h
    12·2 answers
  • Which is the net for this rectangular prism?
    13·2 answers
  • Please I need someone to help my assignment​
    9·1 answer
  • 8+4+9y+10-8x+12xy-3y <br> please help me
    5·1 answer
  • Heather's graduation picnic will cost $62 if it has 31 attendees. If there are 137 attendees, how much will Heather's graduation
    6·2 answers
  • What is the value of p
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!