Answer: 7.40
It's too short. Write at least 20 characters to explain it well.
Equation of a parabola is written in the form of f(x)=ax²+bx+c.
The equation passes through points (4,0), (1.2,0) and (0,12), therefore;
replacing the points in the equation y = ax² +bx+c
we get 0 = a(4)²+b(4) +c for (4,0)
0 = a (1.2)²+ b(1.2) +c for (1.2,0)
12 = a(0)² +b(0) +c for (0,12)
simplifying the equations we get
16a + 4b + c = 0
1.44a +1.2b + c = 0
+c = 12
thus the first two equations will be
16a + 4b = -12
1.44 a + 1.2b = -12 solving simultaneously
the value of a = 5/2 and b =-13
Thus, the equation of the parabola will be given by;
y= 5/2x² - 13x + 12 or y = 2.5x² - 13x + 12
The answer is an expression because you can not solve for x.
(5x⁴ - 3x³ + 6x) - (3x³ + 11x² - 8x)<span>
</span>Expand the second bracket by multiplying throughout by -1
5x⁴ - 3x³ + 6x - <span>3x³ - 11x² + 8x
</span>
Group like terms and simplify
5x⁴ - 3x³ - 3x³ - 11x² + 6x <span>+ 8x
</span>5x⁴ <span>- 6x</span>³ - <span>11x² + 14x</span>
To find the slope between two coordinates, you use the formula:
m = y2 - y1/x2 - x1
If coordinate A is (-2, 5) and coordinate B is (3, -4), then:
y2 = -4
y1 = 5
x2 = 3
x1 = -2
So, just substitute the points into the formula.
m = -4 - 5/3 - (-2)
m = -9/5
The slope of the line is -9/5.
