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allsm [11]
3 years ago
11

Joseph has started completing the square on the equation 3x2 - 7x + 12 = 0. He has worked to the point where he has the expressi

on x2 - 7/4x = -4. Use complete sentences describe Joseph’s steps up to this point and whether or not his work is accurate.
Mathematics
2 answers:
blondinia [14]3 years ago
7 0

Answer:

His work is not accurate.

Step-by-step explanation:

Since, when we solve a quadratic equation by completing the square method,

Then, we follow the following steps,

Step 1 : Move the constant term to the right side of the equation,

Step 2 : Make 1 as the coefficient of x^2

Step 3 : Add the square of the half of the coefficient of the x in both sides.

Here, the given equation is,

3x^2-7x+12=0

Step 1 :  3x^2-7x=-12

Step 2 : x^2-\frac{7}{3}x=-4

Since, in the Joseph's work the above expression is x^2-\frac{7}{4}x=-4

Hence, his work is not accurate because he divide the second term of the left side of equation by 4 instead of 3.

tresset_1 [31]3 years ago
5 0
3x^2 - 7x + 12 = 0 ....subtract 12 from both sides
3x^2 - 7x = -12 ....divide both sides by 3 to get x^2 by itself
x^2 - 7/3x = -4

His work is not accurate because he divided the second term by 4 instead of 3.
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4 years ago
Which of the following expressions is equivalent to a3 + b3?
lubasha [3.4K]
ANSWER
{a}^{3}  + {b}^{3} = (a + b)( {a}^{2 }  - ab +  {b}^{2} )


EXPLANATION

To find the expression that is equivalent to
{a}^{3}  + {b}^{3}
we must first expand
{(a + b)}^{3}
Then we rearrange to find the required expression.


So let's get started.


{(a + b)}^{3}  = (a + b) {(a + b)}^{2}

We expand the parenthesis on the right hand side to get,



{(a + b)}^{3}  = (a + b) ( {a}^{2} + 2ab +  {b}^{2}  )



We expand again to obtain,

{(a + b)}^{3}  =  {a}^{3}  + 3 {a}^{2}b + 3a {b}^{2}   +  {b}^{3}


Let us group the cubed terms on the right hand side to get,

{(a + b)}^{3}  =  {a}^{3}   +  {b}^{3}  + 3 {a}^{2}b + 3a {b}^{2}




{(a + b)}^{3}  =  {a}^{3}   +  {b}^{3}  + 3ab (a+ b)





We make the cubed terms the subject,

{(a + b)}^{3}  - 3ab (a+ b) =  {a}^{3}   +  {b}^{3}

We factor to get,


(a + b)({(a + b)}^{2}  - 3ab ) =  {a}^{3}   +  {b}^{3}


We expand the bracket on the left hand side to get,

(a + b)( {a}^{2}  + 2ab +  {b}^{2}   - 3ab ) =  {a}^{3}   +  {b}^{3}


We finally simplify to get,

(a + b)( {a}^{2}   - ab +  {b}^{2}  ) =  {a}^{3}   +  {b}^{3}
5 0
3 years ago
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Step-by-step explanation:

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2 years ago
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9514 1404 393

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