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2 years ago

Find four consecutive integers whose sum is 17802.

1 answer:

6 0

The four numbers will each be about ¼ of 17802, which is 4450.5. Take two numbers on each side of 4450.5 and we have 4449, 4450, 4451, and 4452, which sum to 17802.

Or write an equation: x + (x + 1) + (x + 2) + (x + 3) = 17802.

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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.

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

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

$a(22.5)^{2} =-2531.25$

$506.25a =2531.25$

$a=-5$

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

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

$y=-31.25+2531.25$

$y=2500$

y-intercept: $(0,2500)$

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2 years ago

In a certain clothing store, 6 shirts and 3 ties cost $79.50, and 3 shirts and 2 ties cost $41. Determine the cost of each tie.

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