Zx = 5g(2x - c) Apply the Distributive Property
zx = 10gx - 5cg Subtract 10gx from each side
zx - 10gx = -5cg Factor x out
x (z - 10g) = -5cg Divide by (z - 10g)
x = 
Positioning a 45-foot ladder against a building that is 36 feet tall, how far from the base of the building will the bottom of the ladder rest?
Answer: y = 2/5 --> y = 0.4
Step-by-step explanation:
The equation 5y = 2 represents a horizontal line at y = 2/5.
This means that the y-coordinate holds the value of 2/5 = 0.4 for any x-coordinate.
In certain cases, a function necessitates multiple formulas to achieve the desired outcome. An example is the absolute value function \displaystyle f\left(x\right)=|x|f(x)=∣x∣. This function applies to all real numbers and yields results that are non-negative, defining absolute value as the magnitude or modulus of a real number regardless of its sign. It indicates the distance from zero on the number line, requiring all outputs to be zero or greater.
<pwhen inputting="" a="" non-negative="" value="" the="" output="" remains="" unchanged:="">
\displaystyle f\left(x\right)=x\text{ if }x\ge 0f(x)=x if x≥0
<pwhen inputting="" a="" negative="" value="" the="" output="" is="" inverse:="">
\displaystyle f\left(x\right)=-x\text{ if }x<0f(x)=−x if x<0
Due to the need for two distinct operations, the absolute value function qualifies as a piecewise function: a function defined by several formulas for different sections of its domain.
Piecewise functions help describe scenarios where rules or relationships alter as the input crosses specific "boundaries." Business contexts often demonstrate this, such as when the cost per unit of an item decreases past a certain order quantity. The concept of tax brackets also illustrates piecewise functions. For instance, in a basic tax system where earnings up to $10,000 face a 10% tax, additional income incurs a 20% tax rate. Thus, the total tax on an income S would be 0.1S when \displaystyle {S}\leS≤ $10,000 and 1000 + 0.2 (S – $10,000) when S > $10,000.
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