Answer:
1 2 real
2. No real
3. 2 Real
4. One real Multiplicity 2.
Step-by-step explanation:
Find the value of the discriminant D (b^2 - 4ac) :-
1 . D = (1)^1 -4 * -3 * 12 = 1 + 144 = 145
D is positive so there re 2 real solutions.
2. D = (-6)^2 - 4*2*5 = 36 - 40 = -4
D is negative so there are NO real solutions.
3. D = (7)^2 - 4 * 1 * -11 = 49 + 44 = 93
2 real
solutions
4. D = (-8)^2 - 4* -1 * -16 = 64 - 64
1 solution. Multiplicity 2.
Answer:
exponential function f(x) is
Answer:
a) 250
b) 27405
c) 10098
Step-by-step explanation:
a) 12 * 7 * 6 * 5 = 250 committees
b) committees
c) Number of ways to select seniors ->
Number of ways to select remaining members ->
66 * 153 = 10098
Theorem: If a function y = f(x) has a real root of b, then (x – b) is a factor of f(x).
As given in the problem, there are two roots: –2 and 1/2. The multiplicity of 1/2 is 2 meaning that the root 1/2 repeats twice. So the function f(x) can be written like this.
f(x) = k• (x – (–2))(x – 1/2)^2 = k•(x + 2)(x – 1/2)^2
We're supposed to find the coefficient k to complete the function.
Given that f(–3) = 5, we can plug –3 in for x and 5 in for f(x).
So 5 = k •(–3 + 2)(–3 – 1/2)^2
5 = k(–1)(–7/2)^2
5 = -k•49/4
Then 5 • 4/49 = -k
Or k = –20/49
So the function with the least degree is
f(x) = –20/49 (x + 2)(x – 1/2)^2.
Both slopes are going to be the same, as parallel lines have the same slopes but different y-intercepts. To find the slope of this line (if you haven’t already), you need to isolate y.
4x - 5y= -1
-5y= -4x - 1 (or -1 - 4x)
-y= (-4/-5)x - 1/5
Canceling out the negatives,
y= (4/5)x + 1/5.
Therefore, the slope of both the listed line and any line parallel to it is 4/5.