HELPPP will brainlist 35 points!!!!
1 answer:
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Answer:
Base = 10 cm
Height = 60 cm
Step-by-step explanation:
The formula for the area of a triangle is , where <em>b</em> is the length of the base of the triangle, and <em>h</em> is the length of the height of the triangle.
We know the area is 300, and since the height of the triangle is 6 times its base, we know that . We can plug in these values into our formula for the area of a triangle, which gives us the following equation to solve:
The base of the triangle is 10 centimeters.
Now that we know the base of the triangle, we can plug its value in to the original formula to solve for the height of the triangle, which gives us the following equation:
The height of the triangle is 60 centimeters.
Your calculator's cubic regression function can tell you the equation is
... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)
The x-intercepts are -4, 0, +1.5.
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If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as
... f(x) = ax³ + bx² + cx
Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.
... -a +b -c = 15 . . . . . for x=-1
... a + b + c = -5 . . . . for x=1
... 8a +4b +2c = 12 . . for x=2
adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to
... a + c = -10
... 4a +c = -4
Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).
Then your equation is
... f(x) = x(2x² +5x -12)
Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.
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Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have
... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above
