Step-by-step explanation:
For a quadratic expression ax²+bx + c = 0
The discriminant D = b²-4ac
Given the following quadratic equation;
x^2 - 6x-27 = 0
a = 1, b = -6, c = -27
D = (-6)²-4(-27)
D = 36+108
D = 144
Hence the discriminant is 144
For the roots;
x = -b±√D/2a
x = 6±√144/2
x = 6±12/2
x = 18/2 and -6/2
x = 9 and -3
For the expression x2 - 25 = 0
a = 1, b = 0 and c = -25
D = (0)²-4(-25)
D = 100
Hence the discriminant is 100
For the roots;
x = 0±√100/2
x = ±10/2
x = ±5
x =-5 and 5
Given the following quadratic equation;
x^2 +10x+25 = 0
a = 1, b = 10, c = 25
D = (10)²-4(25)
D = 100-100
D = 0
Hence the discriminant is 0
For the roots
x = -10±√0/2
x = -10/2
x = -5
Given the following quadratic equation;
2x^2 - 5x+3 = 0
a = 2, b = -5, c = 3
D = (-5)²-4(2)(3)
D = 25-24
D = 1
Hence the discriminant is 1
For the roots;
x = 5±√1/2(2)
x = 5±1/4
x = 5+1/4 and 5-1/4
x = 6/4 and 4/4
x = 3/2 and 1
x = 18/2 and -6/2
x = 9 and -3
(D) 4 shaded for every 2 unshaded! Hope this helps! :)
The kelvin scale is the standard absolute thermodynamic temperature scale.
Therefore, this question is simply asking you to convert the degree fahrenheit into degree kelvin.
The formula used to convert between kelvin and fahrenheit is as follows:
T(K)<span> = (</span>T(°F)<span> + 459.67) × 5/9
</span>
We will substitute in this equation with T(F)=-13 and calculate T(K) as follows:
t(K) = (-13 + 459.67) x 5/9 = 248.15 K
Based on this, the previous sentence can be written using absolute value of the number as follows:
The temperature at night reached 248.15 K.
<span>Q’(0, –4), P’(–7, –6), R’(–1, –2) </span>
If you have a TI-84 graphing calculator, you should type the function in using the y= key and hit 2nd calculate to let the calculator calculate the zeroes for you.
x=-20.30, the rest are imaginary