(f•g)(x) = (2x+1) (<span>x^2-7)
</span>(f•g)(x) = 2x^3 + x^2- 14x - 7
............................................
Vertex form of a parabola
<span>y = a (x - h)^2 + k </span>
<span>where (h, k) is the vertex </span>
Substituting the values of h and k.
we get,
<span>y = a(x + 4)^2 + 2 </span>
<span>substituting in the point (0, -30) for x and y
</span><span>-30 = a (0 + 4)^2 + 2
</span>solve for a,
<span>-30 = 16 a + 2 </span>
<span>-32 = 16 a </span>
<span>-2 = a </span>
<span>y = -2(x + 4)^2 + 2 </span>
<span>Put y = 0 </span>
<span>-2 x^2 - 16 x - 30 = 0 </span>
<span>-2(x^2 + 8 x + 15) = 0 </span>
<span>x^2 + 8 x + 15 = 0 </span>
<span>(x + 3)(x + 5) = 0 </span>
<span>x = -3
x = -5</span>
Answer:
So the slope of this function is 
and the y-intercept is 
Step-by-step explanation:
A first order function has the following format:
In which a is the slope and b is the y-intercept, that is, the value of y when x = 0.
We have the following equation:
We just have to rewrite this equation
Which means that
So the slope of this function is and the y-intercept is
Pq + pr = 80 => p (q+r) = 80
pq + qr = 425 => q (p+r ) = 425
Factorize 80 with having one factor as prime number
80 = 2 * 40 = 5 *16
Factrorize 425 with having one factor as prime number
425 = 5 * 85 = 17 * 25...
Therfore, p has to be 2.
q = 17 and r= 23...
p + q +r = 2 + 17+ 23 = 42
