Answer:
1 ± i(1/2)√2
Step-by-step explanation:
Write this quadratic in standard form: subtract 3 from both sides. This results in 2x^2 - 4x - 3 = 0. Let's apply the quadratic formula. The coefficients of the x terms are 2, -4 and -3, so the discriminant is (-4)^2 - 4(2)(-3), or 16 - 24 = -8.
Following the format of the quadratic formula, we get
-(-4) ±i2√8 4 ±i2√2
x = ----------------- = --------------- = 1 ± i(1/2)√2
4 4
Answer:
X = 30
Step-by-step explanation:
20^2 + 23^2 = x^2
400 + 529 = x^2
929 = x^2
√929 = √x^2
X = √929
X = 30.48
1) To create an equation with r isolated, you divide both sides by π and square root both (it is given that all variables are positive). The equation is √A/π = r.
2) Plugging in the numbers give us <em>√54/(22/7) = r</em>.
√54(22/7) can be rewritten as √54*7/22, which is √378/22, which can be simplified to √189/11, or about 17.18.
True/false questions grant a 50% chance for each question. If there are 6 questions, the probability of getting 3 right is 50%. You can find the answer by multiplying the percentages for each outcome.
50% × 50% = 25%
The student ultimately has a 25% chance of getting 3 of the 6 true/false questions correct.
![\left[\begin{array}{ccc}1&3&7\\1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%267%5C%5C1%261%261%5Cend%7Barray%7D%5Cright%5D%20)
multiply 2nd row by -1 and add to first row
![\left[\begin{array}{ccc}0&2&6\\1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%262%266%5C%5C1%261%261%5Cend%7Barray%7D%5Cright%5D%20)
divide the 1st row by 2
![\left[\begin{array}{ccc}0&1&3\\1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%263%5C%5C1%261%261%5Cend%7Barray%7D%5Cright%5D%20)
multiply the first row by -1 and add to 2nd row
![\left[\begin{array}{ccc}0&1&3\\1&0&-2\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%263%5C%5C1%260%26-2%5Cend%7Barray%7D%5Cright%5D%20)
now we know
y+3=0
x-2=0
therefor
y=-3
x=2
