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saveliy_v [14]
3 years ago
6

Factor the algebraic expression 12a + 21

Mathematics
2 answers:
Elza [17]3 years ago
8 0
You have to take out the GCF: 3(4a+7)
mixer [17]3 years ago
3 0
It would be impossible to completely factor -12a2+20a-21 into the product of real numbers. The expression would be considered prime in that case. This is probably the answer you are looking for.

 

However, factoring would be possible if complex linear factors are allowed. It would require using the definition i = √(-1) and the quadratic formula:

 

a = (-B ± √(B2-4AC))/2A

 

My first step would be to factor out -1/3, turning A into a positive square number:

 

-12a2+20a-21 = -1/3(36a2-60a+63)

 

From there, I would use the quadratic formula with A=36, B=-60 and C=63:

 

a = (-(-60) ± √((-60)2-4(36)(63)))/(2(36))

= (60 ± √(3600-9072))/72                   [Simplifying]

= (60 ± √(-5472))/72                          [Subtracting]

= (60 ± 12i√(38))/72                           [Simplifying the radical]

= 12(5 ± i√(38))/72                            [Factoring the numerator]   

= (5 ± i√(38))/6                                 [Reducing]

 

With a bit of rewriting this would give a factorization of:

 

-1/3(6a - 5 + i√(38))(6a - 5 - i√(38)) = -1/3(-6i a + √(38) + 5i)(6i a + √(38) - 5i)

 

Bonus:

 

It is also possible to complete the square using the expression -12a2+20a-21:

 

-12a2+20a-21 = -12(a2-5/3a)-21                               [Rewriting]

= -12(a2-5/3a + 25/36)-21 + 25/3     [Completing the square]

= -12(a-5/6)2-63/3+25/3                  [Rewriting]

= -12(a-5/6)2-38/3                           [Simplifying]

 

This form is important, primarily because it shows that at a = 5/6 the expression reaches a maximum value of -38/3.

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the best would be 1.75

Step-by-step explanation:

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5 0
3 years ago
Find the dimensions of a rectangle with a perimeter of 52cm if it’s length is 4cm more than its width
Zina [86]
So the perimeter(P) of a rectangle would be:
P= 2L+2W
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The problem says the length is 4cm more than the width, so L= 4+W.
So if we substitute L with 4+W, we get:
P= 2(4+W) + 2W
Use the Distributive Property
P= 8+2W+2W
Combine like terms
P=8+4W
Since we're given the perimeter, we could replace P with 52. So:
52=8+4W
Subtract 8 to both sides
44=4W
Divide 4 to both sides
11=W
Therefore, the width is 11cm
And since the length is 4cm more than the width, we could add 4cm to 11cm to find that the length is 15cm
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Find the slope of the tangent to y= -7Sin(x)+2cos(x) at x= 3π/4
BaLLatris [955]
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zavuch27 [327]
I believe that X would be -2.47619.
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