Answer:
0.4077
Step-by-step explanation:
It's important to use parenthesis to avoid confusion.
9^(2x) = 6
Use exponent properties:
(9^2)^x = 6
81^x = 6
Take log of both sides
ln(81^x) = ln(6)
Use log properties:
x ln(81) = ln(6)
Solve for x:
x = ln(6) / ln(81)
x ≈ 0.4077
The line that is parallel to this line will have the same slope of this line, as the two will never intersect. They will run side by side. The line y = 2x - 5 is written in slope-intercept form, which is y = mx + b. The value of m represents the slope, and in this equation m = 2. Therefore, the line we are looking for will have a slope of 2 also.
That line should also be in slope-intercept form. We now know the value of m, but we also know the value of x and y. The ordered pair (8, 10) is a point on the line, and every ordered pair is in the form (x, y). Therefore, x = 8 and y = 10. We can plug those values into y = mx + b, along with m = 2. That gives us:
10 = 2(8) + b We need to solve for b.
10 = 16 + b
b = -6
Answer: The greatest number of playlist Katherine can make =8
Each of playlist will have 4 pop songs and 9 rock songs.
Step-by-step explanation:
Given: The number of pop songs Katherine has= 32
The number of rock songs Katherine has= 72
If she want to make playlist such that in each playlist there is equal number of pop and rock songs, we need to find the GCF(greatest common factor) of 32 and 72.
We know that 
We can see the GCF(32,72)=
Hence, the greatest number of playlist Katherine can make =8
The number of pop songs= 
the number of rock songs=
Each of playlist will have 4 pop songs and 9 rock songs.
Answer:3(7)+2=23. 21+2=23
Step-by-step explanation:
Answer:

Step-by-step explanation:

{-84:(-4)=21 and -1764:(-84)=21 and -37044:(-1764)=21}
geometric sequence formula: 

