Answer:
f(x) has a minimum value of -10.
Step-by-step explanation:
It will have a minimum value because the coefficient of x^2 is positive.
To find its value we convert to vertex form:
f(x) = 4x^2 - 16x + 6
= 4(x^2 - 4x) + 6
= 4[(x - 2)^2 - 4] + 6
= 4(x - 2)^2 - 16 + 6
= 4(x - 2)^2 - 10.
So the minimum value is -10.
Answer:
x=36
Step-by-step explanation:
if PQR is isosceles then
PRQ will also equal 69 degrees
straight line = 180 degrees
so if PRQ is 69, then
PRS = 180-69
= 111 degrees
now to find x , since we have two angles within that triangle
180 - 111 - 33 = 36 degrees
Answer:
x ≥ 7
Step-by-step explanation:
|x - 7| = x - 7
A. For each absolute, find the intervals
x - 7 ≥ 0 x - 7 < 0
x ≥ 7 x < 7
If x ≥ 7, |x - 7| = x - 7 > 0.
If x < 7, |x - 7| = x - 7 < 0. No solution.
B. Solve for x < 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
-x + 14 = x
14 = 2x
x = 7
7 ≮7. No solution
C. Solve for x ≥ 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
True for all x.
D. Merge overlapping intervals
No solution or x ≥ 7
⇒ x ≥ 7
The diagram below shows that the graphs of y = |x - 7| (blue) and of y = x - 7 (dashed red) coincide only when x ≥ 7.