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
alukav5142 [94]
3 years ago
14

A^2 + b^2 + c^2 = 2(a − b − c) − 3. (1) Calculate the value of 2a − 3b + 4c.

Mathematics
1 answer:
Verdich [7]3 years ago
7 0

Answer:

2a - 3b + 4c = 1

Step-by-step explanation:

Given

a^2 + b^2 + c^2 = 2(a - b - c) - 3

Required

Determine 2a - 3b + 4c

a^2 + b^2 + c^2 = 2(a - b - c) - 3

Open bracket

a^2 + b^2 + c^2 = 2a - 2b - 2c - 3

Equate the equation to 0

a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0

Express 3 as 1 + 1 + 1

a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0

Collect like terms

a^2 - 2a + 1 + b^2 + 2b + 1 + c^2  + 2c + 1 = 0

Group each terms

(a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

Factorize (starting with the first bracket)

(a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

(a(a - 1) -1(a - 1)) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b^2 + 2b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b^2 + b+b + 1) + (c^2  + 2c + 1) = 0

((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2  + 2c + 1) = 0

((a - 1)^2) + ((b + 1)(b + 1)) + (c^2  + 2c + 1) = 0

((a - 1)^2) + ((b + 1)^2) + (c^2  + 2c + 1) = 0

((a - 1)^2) + ((b + 1)^2) + (c^2  + c+c + 1) = 0

((a - 1)^2) + ((b + 1)^2) + (c(c  + 1)+1(c + 1)) = 0

((a - 1)^2) + ((b + 1)^2) + ((c  + 1)(c + 1)) = 0

((a - 1)^2) + ((b + 1)^2) + ((c  + 1)^2) = 0

Express 0 as 0 + 0 + 0

(a - 1)^2 + (b + 1)^2 + (c  + 1)^2 = 0 + 0+ 0

By comparison

(a - 1)^2 = 0

(b + 1)^2 = 0

(c  + 1)^2 = 0

Solving for (a - 1)^2 = 0

Take square root of both sides

a - 1 = 0

Add 1 to both sides

a - 1 + 1 = 0 + 1

a = 1

Solving for (b + 1)^2 = 0

Take square root of both sides

b + 1 = 0

Subtract 1 from both sides

b + 1 - 1 = 0 - 1

b = -1

Solving for (c  + 1)^2 = 0

Take square root of both sides

c + 1 = 0

Subtract 1 from both sides

c + 1 - 1 = 0 - 1

c = -1

Substitute the values of a, b and c in 2a - 3b + 4c

2a - 3b + 4c = 2(1) - 3(-1) + 4(-1)

2a - 3b + 4c = 2 +3  -4

2a - 3b + 4c = 1

You might be interested in
How many twelfths are there in 2/3 of 3/4 more than 1/3 of 3/8 ? I know the answer already, please show how you do it .
maksim [4K]
Ok so what this means is below:
\frac{2}{3}* ( \frac{3}{4}+  \frac{1}{3} * \frac{3}{8} )
Now we need to follow the rules of PEMDAS:
So inside the parentheses we need to do the multiplication first 1/3*3/8=1/8
Now we need to add 3/4 to this 1/8+3/4=7/8
Now do 2/3 of the value of the parenthesis 7/8
This is 14/24 = 7/12
Therefore there are 7 twelfths
7 0
3 years ago
Simplify the following expression 9v^2(v^2+3v-4)
Anvisha [2.4K]

The answer would be 9v ^4 + 27v ^3 - 36v^2

Step-by-step explanation:

You first would multiply each term in the parenthesis by 9v^2

9v^2 (v^2) + 9v^2 (3v) - 9v^2 (4)

After this you combine the like terms

9v^2 * v^2 is 9v^4

9v^2  * 3v is 27v^3

-9v^2 * 4 is -36v^2

Because you can not simplify it any smaller, this is your final answer

3 0
3 years ago
55% of 70 round to the nearest tenth
Verizon [17]
70 * 55/100=38.5

Enjoy
3 0
3 years ago
Read 2 more answers
ASAP 4th GRADE MATHHH<br><br><br> 1.99 + 0.39 - 6.12
Dovator [93]

Answer:

-3.74

Step-by-step explanation:

5 0
3 years ago
What the simplified of 2/3 dived by 2/9
mars1129 [50]

Answer:

3

Step-by-step explanation:

Divide \dfrac{2}{3} by \dfrac{2}{9}:

\dfrac{2}{3}:\dfrac{2}{9}=\dfrac{2}{3}\cdot \dfrac{9}{2}=\dfrac{2\cdot9}{3\cdot 2}=\dfrac{9}{3}=3.

6 0
3 years ago
Other questions:
  • This question is a fair question: “Which do you think is the most common age group of people who like pop music?” true or false
    13·1 answer
  • If you find out that shawns coin landed on heads 62 out of 80 flips.How many times would you expect his coin to land on heads if
    15·1 answer
  • How I would I do number 3
    8·2 answers
  • The two rectangular prisms shown have bases with the same area. the height of Y=6 cm. The height of Z=24. Which statement is tru
    9·2 answers
  • Solve the following log3 34<br> a. 3.3<br> b.3<br> c.3.2098<br> d. 0<br> e.2<br> f. 312
    9·1 answer
  • Explain how each part of the equation 9=3(x+2) is represented for 9
    14·2 answers
  • Y=hx+s solve for the equation for h
    13·2 answers
  • Mateo, a 31-year-old nonsmoker ($5.50), wants to purchase $100,000 in coverage for himself and $75,000 for his spouse, who is fe
    10·1 answer
  • Anyone best gets brainky
    6·2 answers
  • Yes plz help w homework xp​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!