Question:
Approximate log base b of x, log_b(x).
Of course x can't be negative, and b > 1.
Answer:
f(x) = (-1/x + 1) / (-1/b + 1)
Step-by-step explanation:
log(1) is zero for any base.
log is strictly increasing.
log_b(b) = 1
As x descends to zero, log(x) diverges to -infinity
Graph of f(x) = (-1/x + 1)/a is reminiscent of log(x), with f(1) = 0.
Find a such that f(b) = 1
1 = f(b) = (-1/b + 1)/a
a = (-1/b + 1)
Substitute for a:
f(x) = (-1/x + 1) / (-1/b + 1)
f(1) = 0
f(b) = (-1/b + 1) / (-1/b + 1) = 1
Answer:
(12, 1)
Step-by-step explanation:
Arbitrarily choose y = 1. Then x - 6y = 6 becomes
x = 6(1) + 6, or x = 12.
Thus, one (of many) point on the graph is (12, 1).
Answer:
E. 2i√5
Step-by-step explanation:
√-20 = (√-1)(√20) = i·(2√5) = 2i√5
Answer:
the last one
Step-by-step explanation:
Two lines will be parallel when their slopes are equal, and two lines will be perpendicular when their slopes are negative reciprocals of each other. Our slopes for these two equations are the coefficient for the x value. Both slopes are equal so these lines are parallel.
Answer:
angle c = <u>83</u> degrees
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral add up to 180 degrees.
According to the rule, <D and <B add up to 180° and same for <A and C.
This means that the sum of (x + 100) and (3x) equal 180.
Therefore (x + 100) + (3x) = 180 →
4x + 100 = 180
–100 –100
4x = 80
÷4 ÷4
x = 20.
Since x = 20, <A = 5x – 3 = 5(20) – 3 = 97.
Since <A + <C = 180.
97 + <C = 180 → 97 + <C = 180
–97 –97
<C = 180 – 97 = 83°
