Find the inverse function. f(x) = 3x – 1 f-1(x) = x + [?]
1 answer:
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Step 1: Read and understand the problem statement.
You are given (time, depth) pairs of (20 s, 8 cm) and (40 s, 0 cm) and asked to write an equation that describes the relationship of depth (y) to time (x).
The rate of change is (0 cm -8 cm)/(40 s -20 s) = -8 cm/(20 s) = -2/5 cm/s. Then in point-slope form using the second point, the linear function rule is
y = (-2/5)(x -40) +0
You can expand this to
y = (-2/5)x +16
y = -0.4x +16 . . . . . . using a decimal number for the slope
_____
If the bathtubs in your "draining race" start with the same level, the one with the steepest slope (-0.5 cm/s) will win.
You are given (time, depth) pairs of (20 s, 8 cm) and (40 s, 0 cm) and asked to write an equation that describes the relationship of depth (y) to time (x).
The rate of change is (0 cm -8 cm)/(40 s -20 s) = -8 cm/(20 s) = -2/5 cm/s. Then in point-slope form using the second point, the linear function rule is
y = (-2/5)(x -40) +0
You can expand this to
y = (-2/5)x +16
y = -0.4x +16 . . . . . . using a decimal number for the slope
_____
If the bathtubs in your "draining race" start with the same level, the one with the steepest slope (-0.5 cm/s) will win.
<h2> Miranda's rate is 12 hours per mies.</h2>
Step-by-step explanation:
Given by question,
Miranda began her ride from home merely that she was 50 miles away from home after 4 hours of riding.
To find, Miranda's rate = ?
2 hours later she was 974 miles from home.
∴ 2 hours she rode = 74 miles - 50 miles
Miranda rides 24 miles in 2 hours.
∴ Miranda rides in 1 hour =
=
Thus, Miranda's rate is 12 hours per mies.
<h2>Answer: y = - ¹/₂ x + 5
</h2><h3>Step-by-step explanation:
</h3>
<u>Find the slope of the perpendicular line</u>
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.
⇒ if the slope of this line = 2 (y = 2x + 2)
then the slope of the perpendicular line (m) = - ¹/₂
<u>Determine the equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 3 = - ¹/₂ (x - 4)
We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:
since y - 3 = - ¹/₂ (x - 4)
y = - ¹/₂ x + 5 (in slope-intercept form)