In the first few steps for deriving the quadratic formula left side of the equation due to the distributive property for balancing the equation.
<h3>What is quadratic equation?</h3>
A quadratic equation is the equation in which the highest power of the variable is two.
Here, The first few steps in deriving the quadratic formula are shown in the table.
Use the substitution property of equality to solve it further,
-c=-ax² +bx
Now factor out the term a, to solve further as,
- c = a (x² + b/a x)
for half of the b value and square it to determine the constant of the perfect square trinomial as,
(b/2a)² = b²/4a²
Now the distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.
-c + b²/4a² = a(x² + b/a x + b²/4a² )
Thus, the distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.
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(2x + 3)(x + 4)
Extra characters.
The rate of change of a linear equation (first degree) is equivalent to the slope of a line. Slope is described as the vertical movement (rise) of the line over its horizontal counterpart (run). In determining the rate of change or slope (m) given 1 data point (x',y'), point-slope form is applicable. Point-slope form is: (y-y') = m (x-x'). Substitute the given point (-5,-1) in the equation. By substitution, [y-(-1)] = m [x-(-5)]. Re-arranging the equation, the rate of change or slope is, m = (y+1)/(x+5).
The airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Let a represent the rate of the airplane with no wind. and b the rate of the wind, hence:
(a - b)3.2 = 640
a - b = 200 (1)
Also:
(a + b)2 = 640
a + b = 320 (2)
The solution to equation 1 and 2 is:
a = 260, b = 60
The airplane flies at 260 mi/h with no wind, while the rate of the wind is 60 mi/h.
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