Solve: 3/x-4 >0 A.x -4 C.x>4 D.x<-4
1 answer:
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Answer:
20 units²
Step-by-step explanation:
The x-intercepts are symmetrically located around the x-coordinate of the vertex, so are at
1.5 ± 5/2 = {-1, 4}
Using one of these we can find the unknown parameter "a" in the parabola's equation (in vertex form) ...
0 = a(4 -1.5)² +12.5
0 = 6.25a +12.5 . . . . . simplify
0 = a +2 . . . . . . . . . . . divide by 6.25
-2 = a
Then the standard-form equation of the parabola is ...
y = -2(x -1.5)² +12.5 = -2(x² -3x +2.25) +12.5
y = -2x² +6x +8
This tells us the y-intercept is 8. Then the relevant triangle has a base of 5 units and a height of 8. Its area is given by the formula ...
A = (1/2)bh = (1/2)(5)(8) = 20 . . . . units²
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).