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german
3 years ago
9

Solve quadratic equation by factoring x^2-6x+9=0

Mathematics
1 answer:
Ray Of Light [21]3 years ago
7 0
What you have to find is what numbers add to -6 and multiply to 9. these numbers would be -3 and -3 (-3+-3=-6, -3*-3=9). substitute these in for -6x as x^2-3x-3x+9=0. then factor out c and three to get x(x-3)-3(x-3)=0. x-3=0 in both cases, so x is three.
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What is 4.735 rounded to the nearest one
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A company is designing a new cylindrical water bottle. The volume of the bottle will be 156156 cmcubed3. The height of the water
DaniilM [7]

Answer: the radius is 2.61 cm

Step-by-step explanation:

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Volume = πr²h

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

From the information given,

Volume = 156 cm³

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Find the roots of h(t) = (139kt)^2 − 69t + 80
Sonbull [250]

Answer:

The positive value of k will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80, roots are those values of t so that h(t) = 0. That is:

19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0 (1)

Roots are determined analytically by the Quadratic Formula:

t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}

t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }

The smaller root is t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }, and the larger root is t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }.

h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80 has one real root when \frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0. Then, we solve the discriminant for k:

\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}

k \approx \pm 0.028

The positive value of k will result in exactly one real root is approximately 0.028.

7 0
2 years ago
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