Only one triangle can be drawn that fits this description.
No two triangle's can have all three matching sides
Answer:
$100 increase
Step-by-step explanation:
500 x 20%
= $100 increase
Answer:
<h3> 1.)
![x_1=\dfrac{7+\sqrt{13}}{2}\,,\qquad x_2=\dfrac{7-\sqrt{13}}{2}](https://tex.z-dn.net/?f=x_1%3D%5Cdfrac%7B7%2B%5Csqrt%7B13%7D%7D%7B2%7D%5C%2C%2C%5Cqquad%20x_2%3D%5Cdfrac%7B7-%5Csqrt%7B13%7D%7D%7B2%7D)
</h3><h3> 2.)
![x_1=-\dfrac13\,,\qquad x_2=-3](https://tex.z-dn.net/?f=x_1%3D-%5Cdfrac13%5C%2C%2C%5Cqquad%20x_2%3D-3)
</h3>
Step-by-step explanation:
1.)
![x^2 - 7x + 9 = 0\quad\implies\quad a=1\,,\ b=-7\,,\ c = 9\\\\\\x=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{7\pm\sqrt{(-7)^2-4\cdot1\cdot9}}{2\cdot1}=\dfrac{7\pm\sqrt{49-36}}{2}\\\\x_1=\dfrac{7+\sqrt{13}}{2}\,,\qquad x_2=\dfrac{7-\sqrt{13}}{2}](https://tex.z-dn.net/?f=x%5E2%20-%207x%20%2B%209%20%3D%200%5Cquad%5Cimplies%5Cquad%20a%3D1%5C%2C%2C%5C%20b%3D-7%5C%2C%2C%5C%20c%20%3D%209%5C%5C%5C%5C%5C%5Cx%3D%5Cdfrac%7B-b-%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B7%5Cpm%5Csqrt%7B%28-7%29%5E2-4%5Ccdot1%5Ccdot9%7D%7D%7B2%5Ccdot1%7D%3D%5Cdfrac%7B7%5Cpm%5Csqrt%7B49-36%7D%7D%7B2%7D%5C%5C%5C%5Cx_1%3D%5Cdfrac%7B7%2B%5Csqrt%7B13%7D%7D%7B2%7D%5C%2C%2C%5Cqquad%20x_2%3D%5Cdfrac%7B7-%5Csqrt%7B13%7D%7D%7B2%7D)
2.)
![3x^2 + 10x = -3\\\\3x^2+10x+3=0\quad\implies\quad a=3\,,\ b=10\,,\ c = 3\\\\\\x=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-10\pm\sqrt{10^2-4\cdot3\cdot3}}{2\cdot3}=\dfrac{-10\pm\sqrt{100-36}}{6}=\dfrac{-10\pm\sqrt{64}}{6}\\\\x_1=\dfrac{-10+8}{6}=\dfrac{-2}6=-\dfrac13\,,\qquad x_2=\dfrac{-10-8}{6}=\dfrac{-18}{6}=-3](https://tex.z-dn.net/?f=3x%5E2%20%2B%2010x%20%3D%20-3%5C%5C%5C%5C3x%5E2%2B10x%2B3%3D0%5Cquad%5Cimplies%5Cquad%20a%3D3%5C%2C%2C%5C%20b%3D10%5C%2C%2C%5C%20c%20%3D%203%5C%5C%5C%5C%5C%5Cx%3D%5Cdfrac%7B-b-%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-10%5Cpm%5Csqrt%7B10%5E2-4%5Ccdot3%5Ccdot3%7D%7D%7B2%5Ccdot3%7D%3D%5Cdfrac%7B-10%5Cpm%5Csqrt%7B100-36%7D%7D%7B6%7D%3D%5Cdfrac%7B-10%5Cpm%5Csqrt%7B64%7D%7D%7B6%7D%5C%5C%5C%5Cx_1%3D%5Cdfrac%7B-10%2B8%7D%7B6%7D%3D%5Cdfrac%7B-2%7D6%3D-%5Cdfrac13%5C%2C%2C%5Cqquad%20x_2%3D%5Cdfrac%7B-10-8%7D%7B6%7D%3D%5Cdfrac%7B-18%7D%7B6%7D%3D-3)
Answer:
99% confidence interval for the population average examination score is between a lower limit of 69.2872 and an upper limit of 82.7128.
Step-by-step explanation:
Confidence interval = mean +/- margin of error (E)
mean = 76
variance = 144
sd = sqrt(variance) = sqrt(144) = 12
n = 25
degree of freedom (df) = n - 1 = 25 - 1 = 24
confidence level (C) = 99% = 0.99
significance level = 1 - C = 1 - 0.99 = 0.01 = 1%
t-value corresponding to 24 df and 1% significance level is 2.797
E = t×sd/√n = 2.797×12/√25 = 6.7128
Lower limit = mean - E = 76 - 6.7128 = 69.2872
Upper limit = mean + E = 76 + 6.7128 = 82.7128
99% confidence interval is (69.2872, 82.7128)