A company sells boxes of duck calls (d) for $35 and boxes of turkey calls (t) for $45. They make batches of duck calls that fill
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Answer:
<h2>The lengths of the bases of the trapezoid:</h2><h2>42/h cm and 84/h cm.</h2>Step-by-step explanation:
The formula of an area of a triangle:
<em>b</em><em> </em>- base
<em>h</em> - height
We have <em>b = 21cm, h = 6cm</em>.
Substitute:
The formula of an area of a trapezoid:
<em>b₁, b₂</em> - bases
<em>h</em><em> - </em>height
We have <em>b₁ = 2b₂</em>, therefore <em>b₁ + b₂ = 2b₂ + b₂ = 3b₂</em>.
The area of a triangle and the area of a trapezoid are the same.
Therefore
<em>multiply both sides by 2</em>
<em>divide both sides by 3</em>
<em>divide both sides by h</em>
Answer:
See the attached figure.
Step-by-step explanation:
Modeling each part as a function.
Let x is hours of the working day
The company packs 80 boxes of toys every hour for the first 3 hours of the day. ⇒ y₁ = 80 x , x ∈ [0,3]
At the end of the 3 hours The company packs = 80 * 3 = 240
They stop packaging for the next 2 hours in order to carry out a training session. ⇒ y₂ = 240 , x ∈ [3,5]
Then, for the next 4 hours, they pack 20 boxes of toys every hour
y₃ = 20x + c , x ∈ [5,9]
To find c, y₂ = y₃ at x =5
∴ 240 = 20 * 5 + c
∴ c = 240 - 20 * 5 =240 - 100 = 140
∴ y₃ = 20x + 140 , x ∈ [5,9]
So,
y₁ = 80 x , x ∈ [0,3]
y₂ = 240 , x ∈ [3,5]
y₃ = 20x + 140 , x ∈ [5,9]
The graph models the piecewise function for the given situation is as shown in the attached figure.
