Use the quadratic formula to find the exact solutions of x2 - 5x - 2 = 0.

Mathematics

1 answer:

Fudgin [204]3 years ago

6 0

Step-by-step explanation:

${x}^{2} - 5x - 2 = 0 \\ a = 1 \: and \: b = - 5 \: and \: c = - 2 \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 5)± \sqrt{ {( - 5)}^{2} - (4 \times 1 \times - 2)} }{(2 \times 1)} \\ x = \frac{5± \sqrt{33} }{2} \\ either : x = \frac{5 + \sqrt{33} }{2} \: or \: \frac{5 - \sqrt{33} }{2} \\ x = 5.4 \: or \: - 0.4$

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3y2+y3−5)+(4y2−4y+2y3+8)

jeka57 [31]

Answer: 3y3+7y2+−4y+3

Step-by-step explanation:

3y2+y3+−5+4y2+−4y+2y3+8

Combine Like Terms:

=3y2+y3+−5+4y2+−4y+2y3+8

=(y3+2y3)+(3y2+4y2)+(−4y)+(−5+8)

=3y3+7y2+−4y+3

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3 years ago

A piece of wire measuring 20 feet is attached to a telephone pole as a guy wire. The distance along the ground from the bottom o

dem82 [27]

Answer: Height at which the wire is attached to the pole is 12 feet.

Explanation:

Since we have given that

Length of the wire = 20 feet

Let the height at which wire is attached to the pole be h

and distance along the ground from the bottom of the pole to the end of the wire be x+4

Now, it forms a right angle triangle so, we can apply "Pythagorus theorem".

$H^2=B^2+P^2\\\\20^2=x^2+(x+4)^2\\\\400=x^2+x^2+8x+16\\\\400=2x^2+8x+16\\\\400=2(x^2+4x+8)\\\\200=x^2+4x+8\\\\x^2+4x-192=0\\\\x^2+16x-12x-192=0\\\\x(x+16)-12(x+16)=0\\\\(x+16)(x-12)=0\\\\x=-16\ and\ 12$