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]
3 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]3 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
2x² + 166 +30
Darya [45]

Answer:

c....................

5 0
3 years ago
What is the answer for this​
jek_recluse [69]

Answer:

Step-by-step explanation:

.72x+3=0.3(2.4+15)

.72x+3=0.72+4.5=0.72+4.50

.72 x=5.22

x=\frac{5.22}{0.72} =\frac{522}{72} =\frac{29}{4} =7\frac{1}{4}

4 0
3 years ago
5×23×2 plzz halppppp
Vikentia [17]

230

because 5x23 is 115 x 2 which is 230

6 0
3 years ago
Read 2 more answers
I need help with this
erik [133]

Answer:

Female: 11

Male: 16

Total:

(1) 34

(2) 25

(3) 100

Step-by-step explanation:

Female:

45 - 18 - 16 = 11

Male:

55 - 25 - 14 = 16

Total:

(1) 18 + 16

(2) 14 + 11 = 25

(3) 45 + 55 =

8 0
2 years ago
Read 2 more answers
7/10, 3/20, 22/25, 2/5 in order from least to greatest
swat32
3/20, 2/5, 7/10 & 22/25
7 0
3 years ago
Other questions:
  • Jada is making a circular birthday invitation for her friends . The diameter of the circle is 12 cm. She bought 180 cm of ribbon
    13·1 answer
  • HELP! Plz! I dont know how to do this anymore
    6·2 answers
  • Workers need to know the area of a park to determine how much grass
    13·1 answer
  • PLEASE HELP MEEE!! 10 points
    8·1 answer
  • Is 3pi/4pi a rational number?
    14·1 answer
  • How much is 12,986.64 Swiss francs in US dollars?
    15·1 answer
  • James has a bank account with $500 that collects 3% interest annually. How much will be in James account after 24 months if no t
    9·1 answer
  • Did i get almost an entire lesson on math done in a day? <br> Yes<br> Was it hard?<br> N o p e
    9·2 answers
  • Solve 3x+2y=5 and 7x+2y=9
    6·1 answer
  • Trig how do you do I do not know
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!