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iragen [17]
3 years ago
15

HELP!!! (x+3)²+8=72 (quadratic equation)

Mathematics
2 answers:
svet-max [94.6K]3 years ago
4 0

Answer:

x = 5 or x = -11

Step-by-step explanation:

(x+3)²+8=72

x² + 6x + 9 + 8 = 72

x² + 6x -55 = 0

(x - 5) (x + 11) = 0

x = 5 or x = -11

777dan777 [17]3 years ago
4 0

Answer:

x = 5 and x= -11

Step-by-step explanation:

This equation is a quadratic equation because the variable x is raised to the power of 2 so, there will be two values for x.

Also, a quadratic equation is the product of two linear functions and each functions are equated to zero as seen in the solution below.

(x +3)^2 +8 = 72

Expand the bracket

(x + 3)(x + 3) + 8 =72

x^2 +3x + 3x + 9 +8 =72

x^2 + 6x + 17 = 72

Subtract 72 from both sides

x^2 + 6x + 17 -72 = 72- 72

x^2 + 6x - 55 = 0

Now let's solve for both values of x

The two numbers that when multiplied gives -55 and when summed gives 6 are...

...Yes! 11 and 5

x^2 + 11x - 5x -55 = 0

x(x + 11)-5 (x + 11) =0

(x - 5) (x + 11) = 0

x - 5 = 0

x = 5

x + 11 = 0

x = -11

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A cylinder has a helght of 16 cm and a radius of 5 cm. A cone has a helght of 12 cm and a radius of 4 cm. If the cone is placed
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Answer:

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Step-by-step explanation:

Given that,

Height of a cylinder, h = 16 cm

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The radius of a cone, r' = 4 cm

The volume of the cylinder will be :

V=\pi r^2 h\\\\=3.14\times 5^2\times 16\\\\=1256\ cm^3

The volume of a cone is given by :

V'=\dfrac{1}{3}\pi r^2 h\\\\=\dfrac{1}{3}\times 3.14\times (4)^2\times 12\\\\=200.96\ cm^3

Volume of the air surrounding the cone Inside the cylinder = 1256 - 200.96 = 1055.04 cm³

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3 0
2 years ago
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Step-by-step explanation:

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3 years ago
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Answer:

41 units

Step-by-step explanation:

Rectangles have right angles, so we can use Pythagorean theorem to find the diagonal.

c² = a² + b²

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Step-by-step explanation:

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