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juin [17]
3 years ago
5

the sum of three times a number and 2 less than 4 times the same number is 15. which of the following equations could be used to

find the value of the number m, n? explain how you arrived at your choice.
Mathematics
1 answer:
Ulleksa [173]3 years ago
4 0
To solve for a number x,

3x+4x-2=15
7x-2=15
7x=17
x=2 3/7
or x=~2.43

was one of your answer choices either of the first two equations?
You might be interested in
Solve for x 0=3x^2+3x+7​
Aloiza [94]

Answer:

x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i

x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    0-(3*x^2+3*x+7)=0

Step by step solution:

Step  1:

Equation at the end of step  1  :

 0 -  ((-3x^{2} +  3x) +  7)  = 0  

<u>Step  2:</u>

Pulling out like terms:

2.1     Pull out like factors:

  -3x^{2} - 3x - 7  =   -1 • (3x^{2} + 3x + 7)

Trying to factor by splitting the middle term

2.2     Factoring  3x^{2} + 3x + 7

The first term is,  3x^{2}  its coefficient is  3 .

The middle term is,  +3x  its coefficient is  3 .

The last term, "the constant", is  +7

Step-1 : Multiply the coefficient of the first term by the constant   3 • 7 = 21

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   3 .

     -21    +    -1    =    -22

     -7    +    -3    =    -10

     -3    +    -7    =    -10

     -1    +    -21    =    -22

     1    +    21    =    22

     3    +    7    =    10

     7    +    3    =    10

     21    +    1    =    22

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  3  :

 -3x^{2} - 3x - 7  = 0

<u>Step  3:</u>

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = -3x^{2}-3x-7

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -0.5000  

Plugging into the parabola formula  -0.5000  for  x  we can calculate the  y -coordinate :

 y = -3.0 * -0.50 * -0.50 - 3.0 * -0.50 - 7.0

or   y = -6.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = -3x^{2}-3x-7

Axis of Symmetry (dashed)  {x}={-0.50}

Vertex at  {x,y} = {-0.50,-6.25}

Function has no real roots

Solve Quadratic Equation by Completing The Square

3.2     Solving   -3x^{2}-3x-7 = 0 by Completing The Square .

Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:

3x^{2}+3x+7 = 0  Divide both sides of the equation by  3  to have 1 as the coefficient of the first term :

  x^{2}+x+(7/3) = 0

Subtract  7/3  from both side of the equation :

  x^{2}+x = -7/3

Now the clever bit: Take the coefficient of  x , which is  1 , divide by two, giving  1/2 , and finally square it giving  1/4

Add  1/4  to both sides of the equation :

 On the right hand side we have :

  -7/3  +  1/4   The common denominator of the two fractions is  12   Adding  (-28/12)+(3/12)  gives  -25/12

 So adding to both sides we finally get :

  x^{2}+x+(1/4) = -25/12

Adding  1/4  has completed the left hand side into a perfect square :

  x^{2}+x+(1/4)  =

  (x+(1/2)) • (x+(1/2))  =

 (x+(1/2))2

Things which are equal to the same thing are also equal to one another. Since

  x^{2}+x+(1/4) = -25/12 and

  x^{2}+x+(1/4) = (x+(1/2))2

then, according to the law of transitivity,

  (x+(1/2))2 = -25/12

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+(1/2))2   is

  (x+(1/2))2/2 =

 (x+(1/2))1 =

  x+(1/2)

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:

  x+(1/2) = √ -25/12

Subtract  1/2  from both sides to obtain:

  x = -1/2 + √ -25/12

 √ 3   , rounded to 4 decimal digits, is   1.7321

So now we are looking at:

          x  =  ( 3 ± 5 •  1.732 i ) / -6

Two imaginary solutions :

x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i

 or:

x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i

6 0
3 years ago
The length of a ribbon is 8 meters it is cut into 6 equal pieces how long is each piece HELP
Serggg [28]

8 meters divided by 6 is

1.3 meters

4 0
3 years ago
Which one of the following tables is a relation that represents a function?
TiliK225 [7]
C is the correct answer homie
4 0
3 years ago
Read 2 more answers
Eve leaves £400 in the bank for 3 years, it earns 5% compound interest. What is the total amount eve has in the bank at the end
zubka84 [21]
Eve has 420 in the bank.
7 0
3 years ago
The correct and best answer will be marked as brainiest
marta [7]

Answer:

x=10

m=3

Step-by-step explanation:

The angles are the same since the sides are the same length (isosceles triangle)

55 = 5x+5

Subtract 5

55-5 =5x+5-5

50 = 5x

Divide by 5

50/5 = 5x/5

10=x

The altitude is a perpendicular bisector so

5m-3 = 2m+6

Subtract 2m from each side

5m-3-2m = 2m+6-2m

3m-3 = 6

Add 3 to each side

3m-3 +3 =6+3

3m =9

Divide by 3

3m/3 = 9/3

m =3

8 0
3 years ago
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