15 PINTS!!!!!!!!! PLZ HELP!!!!!!!! The linear function f(x) = 0.5x + 80 represents the average test score in your math class, wh

The average speed for his entire journey from York to Blackpool is about 61.41 km/h.

Here’s a breakdown of how we arrive at this:

The distance he travelled from York to Leeds is 45 km,

and the speed during that section was 54 km/h.

Therefore, the time taken to travel from York to Leeds is 45/54 hours (since Time = Distance/Speed).

Next, the distance from Leeds to Blackpool is 42 km,

and the time for that leg of the journey is 35 minutes, which is 35/60 hours.

This leads to the total duration for his trip as

hours.

The cumulative distance covered equals 45 + 42 = 87 km.

Thus, his average speed is calculated as:

Answer:

  $200

Step-by-step explanation:

The yearly tax obligation is...

  2.4% × $100,000 = $2,400

Monthly, this amounts to...

  $2400/(12 mo) = $200/mo

This means taxes will increase Bonnie's monthly mortgage payment by $200.

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.

\displaystyle f\left(x\right)=x\text{ if }x\ge 0f(x)=x if x≥0

\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.