you select a card at random from 50 cards numbered 1-50 what are the possible out comes for the event of choosing a number that
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<h3>Answer: -7 < x < 17</h3>
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Explanation:
Plug in the lower bound of the domain, which is x = -3
f(x) = 3x+2
f(-3) = 3(-3)+2
f(-3) = -9+2
f(-3) = -7
If x = -3, then the output is y = -7. Since f(x) is an increasing function (due to the positive slope), we know that y = -7 is the lower bound of the range.
If you plugged in x = 5, you should find that f(5) = 17 making this the upper bound of the range.
The range of f(x) is -7 < y < 17
Recall that the domain and range swap places when going from the original function f(x) to the inverse
This swap happens because how x and y change places when determining the inverse itself. In other words, you go from y = 3x+2 to x = 3y+2. Solving for y gets us y = (x-2)/3 which is the inverse.
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In short, we found the range of f(x) is -7 < y < 17.
That means the domain of the inverse is -7 < x < 17 since the domain and range swap roles when going from original to inverse.
The equation of the parallel line in slope-intercept form is;
y = x -
Step-by-step explanation:
Let us revise some facts about parallel lines
The equations of two parallel lines have:
- Same slopes
- Different y-intercept
The slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept
The given line has equation 5x - 2y = 10
Put it in the form of y = m x + b to find its slope
∵ 5x - 2y = 10
- Subtract 5x from both sides
∴ -2y = 10 - 5x
- Divide to sides by -2
∴ y = -5 + x
∴ y = x - 5
- The value of m is the coefficient of x
∴ m =
∴ The slope of the given line is
∵ Parallel lines have same slopes
∴ The slope of the parallel line is m =
- Substitute the value of m in the form of the equation
∴ The equation of the parallel line is y = x + b
To find b substitute x and y in the equation by the coordinates of any point lies on the line
∵ The parallel line passes through point (3 , -5)
- Substitute x and y by the coordinates of the point (3 , -5)
∵ x = 3 and y = -5
∴ -5 = (3) + b
∴ -5 = + b
- Subtract from both sides
∴ b =
∴ The equation of the parallel line is y = x +
∴ The equation of the parallel line is y = x -
The equation of the parallel line in slope-intercept form is;
y = x -
Learn more:
You can learn more about the equations of parallel lines in brainly.com/question/8628615
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