Mathematics
29.01.2021 01:25
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A^3=4a^2+21a need help please

A^3=4a^2+21a
need help please
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imbadatmath56
imbadatmath56
4,8(59 marks)

Hello!

\large\boxed{a = 0, -3, 7}

a³ = 4a² + 21a

Move all "a" to one side:

0 = -a³ + 4a² + 21a

Factor out "-a" from the equation:

0 = -a(a² - 4a - 21)

Solve for a by factoring:

0 = -a(a - 7)(a + 3)

Solve for the roots by setting each factor equal to 0:

-a = 0

a = 0

a - 7 = 0

a = 7

a + 3 = 0

a = -3

Solutions: a = 0, -3, 7

anyone5382
anyone5382
4,8(49 marks)

A = (\frac{80}{3},9)

B = (5,2.5)

The slope is 0.3

Step-by-step explanation:

Given

y = 0.3x + 1

A = (-,9)

B = (5,-)

Required:

Fill in the gap and calculate the slope

In A = (-,9)

y = 9 and x is ??

Substitute 9 for y in y = 0.3x + 1

9 = 0.3x + 1

Collect Like Terms

0.3x = 9 - 1

0.3x = 8

x = \frac{8}{0.3}

x = \frac{80}{3}

So:

A = (-,9)

A = (\frac{80}{3},9)

In B = (5,-)

x = 5 and y is ??

Substitute 5 for x in y = 0.3x + 1

y = 0.3 * 5 + 1

y = 1.5 + 1

y = 2.5

So:

B = (5,-)

B = (5,2.5)

Calculating the slope (m)

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{2.5-9}{5 - \frac{80}{3}}

m = \frac{-6.5}{\frac{15- 80}{3}}

m = \frac{-6.5}{\frac{-65}{3}}

m = \frac{-6.5*3}{-65}

m = \frac{-19.5}{-65}

m = 0.3

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