What is the discriminant in the quadratic equation x2 + 11x + 121 = x + 96

1 answer:

5 0

Discriminant is the value b^2 -4*a*c once the quadratic is in standard form
x^2 + 11x + 121 = x + 96
subtract x from both sides
x^2 + 10x + 121 = 96
subtract 96 from both sides
x^2 + 10x + 25 = 0
10^2 - 4 * 1 * 25
100 - 100 = 0
Discriminant is 0

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A 2-column table with 6 rows. The first column is labeled miles driven with entries 27, 65, 83, 109, 142, 175. The second column

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Answer:

1) The linear regression model is y = -0.0348·x + 13.989

2) The correlation coefficient is -0.0725

3) The strength of the model is strong - association

Step-by-step explanation:

X Y XY X²

27 13 351 729

65 12 780 4225

83 11 913 6889

109 10 1090 11881

142 9 1278 20164

175 8 1400 30625

∑ 601 63 5812 74513

From y = ax + b, we have

$a = \frac{n\sum xy - \sum x\sum y }{n\sum x^{2}-\left (\sum x \right )^{2}} = \frac{6 \times 5812 - 601 \times 63}{6 \times 74513-601^{2}} = - 0.0348$

b = 1/n(∑y -a∑x) = 1/6(63 - (0.0348)×601) = 13.989

Therefore, the linear regression model is y = -0.0348·x + 13.989

$r = \frac{n\sum xy - \sum x\sum y }{\sqrt{[n\sum x^{2}-\left (\sum x \right )^{2}] [n\sum y^{2}-\left (\sum y \right )^{2}]}} = \frac{6 \times 5812 - 601 \times 63}{\sqrt{[6 \times 74513-601^{2}] [6 \times 3969 - 63^2]} } = - 0.0725$