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Dominik [7]
3 years ago
6

Solve 4x + 3 = 9 for x using the change of base formula log base b of y equals log y over log b.

Mathematics
1 answer:
Aleks04 [339]3 years ago
4 0

Answer:

-1.415

Step-by-step explanation:

log4 ^9 = x + 3

log9 / log4 = x + 3

0.95424425 / 0.6020599 = x + 3

1.584962725 -3 = x + 3 - 3

x = -1.415037275

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2 years ago
The function below shows the number of car owners f(t), in thousands, in a city in different years t: f(t) = 0.25t2 − 0.5t + 3.5
N76 [4]
We solve this by the definition of slope in analytical geometry. The definition of slope is the rise over run. In equation, that would be

m = Δy/Δx = (y₂-y₁)/(x₂-x₁)

The x-coordinates here are the t values, while the y-coordinates are the f(t) values. So, let's find the y values of the boundaries.

At t=2: f(t)= 0.25(2)²<span> − 0.5(2) + 3.5 = 3.5
Point 1 is (2, 3.5)
At t=6: </span>f(t)= 0.25(6)² − 0.5(6) + 3.5 = 9.5
Point 2 is (6, 9.5)

The slope would then be

m = (9.5-3.5)/(6-2)
m = 1.5

Hence, the slope is 1.5. Interpreting the data, the rate of change between t=2 and t=6 is 1.5 thousands per year.
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3 years ago
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