3 (2x+8) = 60 x=____
2 answers:
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Answer: They can order from 0 to 449 bars, but no more.
Step-by-step explanation:
Given: The school band is ordering health bars to sell for a fundraiser. The company that sells the bars charges $0.40 per bar plus $20.00 for shipping regardless of the size of the order. The band must spend less than $200.00 on bars for the fundraiser.
The inequality below relates x, the number of bars that could be ordered, with the shipping costs and their spending requirements.
To solve for x, subtract 20 on both sides, we get
Divide 0.40 on both sides, we get
......... → the number of bars that could be ordered, with the shipping costs and their spending requirements must less than 450.
Thus, they can order from 0 to 449 bars, but no more.
Answer:
A) See attached for graph.
B) (-3, 0) (0, 0) (18, 0)
C) (-3, 0) ∪ [3, 18)
Step-by-step explanation:
Piecewise functions have <u>multiple pieces</u> of curves/lines where each piece corresponds to its definition over an <u>interval</u>.
Given piecewise function:
Therefore, the function has two definitions:
When <u>graphing</u> piecewise functions:
- Use an open circle where the value of x is <u>not included</u> in the interval.
- Use a closed circle where the value of x is <u>included</u> in the interval.
- Use an arrow to show that the function <u>continues indefinitely</u>.
<u>First piece of function</u>
Substitute the endpoint of the interval into the corresponding function:
Place an open circle at point (3, 0).
Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.
<u>Second piece of function</u>
Substitute the endpoint of the interval into the corresponding function:
Place an closed circle at point (3, 2).
Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.
See attached for graph.
<h3><u>Part B</u></h3>The x-intercepts are where the curve crosses the x-axis, so when y = 0.
Set the <u>first piece</u> of the function to zero and solve for x:
Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.
Set the <u>second piece</u> to zero and solve for x:
Therefore, the x-intercept for the second piece is (18, 0).
So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).
<h3><u>Part C</u></h3>From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.
Interval notation: (-3, 0) ∪ [3, 18)
Learn more about piecewise functions here:
