A red marble is selected at random from a bag containing 2 blues and 9 red marbles and is not replaced.the probability that a se
2 answers:
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If and
have the same sign, then either
or
If and
have opposite sign, then
or
This is to say that the region has boundaries given by these two sets of parallel lines, so we can equivalently describe the region with the set
The area of is given by the double integral
To compute the area, change the variables to
The Jacobian for this transformation is
with determinant . Then the integral transforms to
which is 1/12 the area of a square with side length 12. Hence the integral evaluates to
.
Answer:
slope: -3/5
y-intercept: (0, 4)
slope-intercept form: y = -3/5x + 4
Step-by-step explanation:
<h3><u>Finding the slope</u></h3>To find the slope of this line, you would take two points from the table and substitute their coordinates into the slope formula.
Slope formula:
I'm going to use the points (0, 4) and (5, 1). You can really use any point from the table. Substitute these points into the formula to find the slope.
(0, 4), (5, 1) →
This means the slope of the line is -3/5.
<h3><u>Finding the y-intercept</u></h3>The y-intercept will always have the value of x be 0 (so the point is solely on the y-axis), so by looking at the table we can see that the y-intercept is at (0, 4).
<h3><u>Finding the slope-intercept form</u></h3>Since we have the slope and a point of the line, we must use point-slope form to find the equation of the line in slope-intercept form. Substitute in the point (0, 4) --you could use any point from the table-- and the slope -3/5 into the point-slope form equation.
point-slope form: y - y1 = m(x - x1) --you'll be substituting the point coordinates and slope into y1, x1, and m.
y - (4) = -3/5(x - (0))
Simplify.
y - 4 = -3/5x
Add 4 to both sides.
y = -3/5x + 4 is the equation of the line in slope-intercept form (you have both the slope and the y-intercept in this form).