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Andrej [43]
3 years ago
13

Robert has $50 to spend on his utility bills each month. The basic monthly charge is 23.77 electricity costs 0.1117 for each kil

owatt hour used, x. The inequality 0.1116x + 23.77 < 50 represents Roberts monthly utility budget. To the nearest kilowatt hour what is the maximum number of kilowatt hours used without going over his monthly budget?
Mathematics
1 answer:
Lilit [14]3 years ago
7 0

Answer:

<em>The maximum number of kilowatt-hours is 235</em>

Step-by-step explanation:

<u>Inequalities</u>

Robert's monthly utility budget is represented by the inequality:

0.1116x + 23.77 < 50

Where x is the number of kilowatts of electricity used.

We are required to find the maximum number of kilowatts-hours used without going over the monthly budget. Solve the above inequality:

0.1116x + 23.77 < 50

Subtracting 23.77:

0.1116x < 50 - 23.77

0.1116x < 26.23

Dividing by 0.1116:

x < 26.23/0.1116

x < 235

The maximum number of kilowatt-hours is 235

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Answer:

Part A: 2531.25; It means the maximum amount of profit that can be obtained at a specific amount of price reduction (x-value) for the shirts' market price.

Part B:  (0,2500); It represents the profit that can be made by reducing $0 in the shirts' price.

Part C: Yes, it has a zero. Its zero is (25,0) and that represents the amount of profit made by reducing $25 from the price of each shirt being sold, which means if it sells for $0 by reducing $25 from the price of each shirt, then the x-coordinate must also represent the original price of each shirt, $25.

Step-by-step explanation:

Part A: Look at the graph! The highest y-value should be the maximum of each graph, which can be located at the vertex of a quadratic function. In this graph, the vertex is (2.5, 2531.25), where which its y-value contains the highest point of a graph, since the graph is concave down.  

<u>Part B</u>

y=a(x-2.5)^{2} +2531.25\\

0=a(25-2.5)^{2} +2531.25\\

a(22.5)^{2} =-2531.25

506.25a =2531.25

a=-5

y=-5(x-2.5) ^{2}+2531.25

y=-5(0-2.5)^{2} +2531.25

y=-31.25+2531.25

y=2500

y-intercept: (0,2500)

<u>Part C</u>

The graph only has a zero if the function touches the x-axis, also known as the line, y=0. In this case the graph does intersect the x-axis at the point, (25,0). Therefore, it has a zero, and the value of the x coordinate at the zero is 25. This value represents the profit generated from reducing the price of each shirt by $25, which is $0. Therefore, this also represents the original price of each shirt without any price reduction, since there is no profit made by completely reducing the price of each shirt at that specific point in the graph, which is 25 or $25. Therefore, this displays that.

4 0
3 years ago
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Answer:

6

Step-by-step explanation:

8(1/4) is 2 bc 1/4 of 8 is 2

2-1=.5(10)

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then you get 2-1+5 then after that you get 6

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Answer:

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Step-by-step explanation:

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6 0
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3 years ago
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