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3 years ago

D) 12x^3 - 4x^2 Factorise fully

Mathematics

1 answer:

Vinvika [58]3 years ago

8 0

Answer:

The answer for the equation is $4x^2 (3x - 1)$ .

Step-by-step explanation:

Solve:

$12^3 - 4x^2$

-Factor out the $4$ :

$12^3 - 4x^2$

$4(3x^3 - x^2)$

-Factor out the $x^2$ :

$4(3x^3 - x^2)$

$x^2 (3x - 1)$

-Then, you rewrite the complete factored expression:

$x^2 (3x - 1)$

$4x^2 (3x - 1)$

So, the answer is $4x^2(3x - 1)$ .

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Based on Pythagorean identities, which equation is true? A. Sin^2 theta -1= cos^2 theta B. Sec^2 theta-tan^2 theta= -1 C. -cos^2

Arturiano [62]

Answer:

Step-by-step explanation:

our basic Pythagorean identity is cos²(x) + sin²(x) = 1

we can derive the 2 other using the listed above.

1. (cos²(x) + sin²(x))/cos²(x) = 1/cos²(x)

1 + tan²(x) = sec²(x)

2.(cos²(x) + sin²(x))/sin²(x) = 1/sin²(x)

cot²(x) + 1 = csc²(x)

A. sin^2 theta -1= cos^2 theta

this is false

cos²(x) + sin²(x) = 1

isolating cos²(x)

cos²(x) = 1-sin²(x), not equal to sin²(x)-1

B. Sec^2 theta-tan^2 theta= -1

1 + tan²(x) = sec²(x)

sec²(x)-tan(x) = 1, not -1

false

C. -cos^2 theta-1= sin^2

cos²(x) + sin²(x) = 1

sin²(x) = 1-cos²(x), our 1 is positive not negative, so false

D. Cot^2 theta - csc^2 theta=-1

cot²(x) + 1 = csc²(x)

isolating 1

1 = csc²(x) - cot²(x)

multiplying both sides by -1

-1 = cot²(x) - csc²(x)

TRUE

3 0

3 years ago

Unit 3 homework 6 Gina Wilson

Sonja [21]

Answer:

5) The equation of the straight line is 2 x - y + 1 =0

6) The equation of the straight line is x + y -5 =0

7) The equation of the straight line is 5 x + 6 y - 24 =0

8) The equation of the straight line is x - 4 y -4 =0

9) The equation of the parallel line is 3x + y -19 =0

Step-by-step explanation:

The equation of the straight line is

$y - y_{1} = m ( x - x_{1} )$

Slope of the line

$m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Given points are (1,3) , ( -3,-5)

$m = \frac{-5-3 }{-3-1 } = \frac{-8}{-4} = 2$

The equation of the straight line is

$y - y_{1} = m ( x - x_{1} )$

$y - 3 = 2 ( x - 1 )$

y = 2x - 2 +3

2 x - y + 1 =0

The equation of the straight line is 2 x - y + 1 =0

The equation of the straight line is

$y - y_{1} = m ( x - x_{1} )$

Slope of the line

$m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Given points are (1,4) , ( 6,-1)

$m = \frac{-1-(4) }{6-1 } = \frac{-5}{5} = -1$

The equation of the straight line is

$y - y_{1} = m ( x - x_{1} )$

$y - 1 = -1 ( x - 4 )$

y - 1 = - x +4

The equation of the straight line is x + y -5 =0

The equation of the straight line is

$y - y_{1} = m ( x - x_{1} )$

Slope of the line

$m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Given points are (-12 , 14) , ( 6,-1)

$m = \frac{-1-(14) }{6+12 } = \frac{-15}{18} = \frac{-5}{6}$

$y - 14 = \frac{-5}{6} ( x - (-12) )$

6( y - 14 ) = - 5 ( x +12 )

6 y - 84 = - 5x -60

5 x + 6 y -84 + 60 =0

5 x + 6 y - 24 =0

The equation of the straight line is

$y - y_{1} = m ( x - x_{1} )$

Slope of the line

$m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Given points are (-4 , -2) , ( 4 , 0)

$m = \frac{0+2}{4 +4} = \frac{2}{8} = \frac{1}{4}$

$y - (-2) =\frac{1}{4} ( x - (-4) )$

4 ( y + 2) = x + 4

x - 4 y -4 =0

The equation of the line y = 3x + 6 is parallel to the line

3x + y + k =0 is passes through the point ( 4,7 )

⇒ 3x + y + k =0

⇒ 12 + 7 + k =0

⇒ k = -19

The equation of the parallel line is 3x + y -19 =0

4 0

3 years ago

What is the determinant of k =[ 6 8]

Sergeeva-Olga [200]

That would be 6 *3 - 8*0 = 18

Its D

5 0

3 years ago

An alloy of tin is 15% tin and weights 20 pounds. A second allow is 10% tin. How many pounds of the second alloy must be added t

Fofino [41]

Let x represent the amount to be added. The total amount of tin will be
15%·20 + 10%·x = 12%·(20+x)
(15%-12%)·20 = (12%-10%)·x
3%·20/2% = x
30 = x

30 pounds of 10% tin must be added to get a 12% mixture.

8 0

3 years ago

Find the cube root.

nignag [31]

9514 1404 393

Answer:

(d) 5a²

Step-by-step explanation:

$\displaystyle\sqrt[3]{125a^6}=\sqrt[3]{5^3a^6}=\sqrt[3]{(5a^2)^3}=\boxed{5a^2}$

The applicable rules of exponents are ...

(a^b)^c = a^(bc)

∛a = a^(1/3)

4 0

3 years ago