Answer:
5p-q = 5. (-6) - 5 = -30 - 5 = -35
5pq= 5. (-6) . 5 = -30 . 5 = -150
Step-by-step explanation:
Answer:
q = -8, k = 2.
r = -6.
Step-by-step explanation:
f(x) = (x - p)^2 + q
This is the vertex form of a quadratic where the vertex is at the point (p, q).
Now the x intercepts are at -6 and 2 and the curve is symmetrical about the line x = p.
The value of p is the midpoint of -6 and 2 which is (-6+2) / 2 = -2.
So we have:
f(x) = 1/2(x - -2)^2 + q
f(x) = 1/2(x + 2)^2 + q
Now the graph passes through the point (2, 0) , where it intersects the x axis, therefore, substituting x = 2 and f(x) = 0:
0 = 1/2(2 + 2)^2 + q
0 = 1/2*16 + q
0 = 8 + q
q = -8.
Now convert this to standard form to find k:
f(x) = 1/2(x + 2)^2 - 8
f(x) = 1/2(x^2 + 4x + 4) - 8
f(x) = 1/2x^2 + 2x + 2 - 8
f(x) = 1/2x^2 + 2x - 6
So k = 2.
The r is the y coordinate when x = 0.
so r = 1/2(0+2)^2 - 8
= -6.
Let, Jason = J and M = Megan
M = J(1 + 1/4)
So putting 6 where J is and solving:
<em>M = 6(1 + 1/4)
</em><em>M= 7.5</em>
When Jason runs 6 miles Megan runs 7.5
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Answer: y = -3.5x - 4.5
suppose: the equation of the line is y = ax + b ( a ≠ 0 )
because the line passes through (-2;2.5) => 2.5 = -2a + b
the line passes though (0;-4.5) => -4.5 = b
=> b = -4.5
2.5 = -2a + b
=> a = -3.5
b = -4.5
=> the equation of the line is y = -3.5x - 4.5
Step-by-step explanation:
5n-4 = 6 gives the equation for 5 times #Nathan rode less 4 miles which solves to n = 2
Nathan rode 2 miles. (5*2)-4 = 6 10-4=6 so 2 miles is right
