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4 years ago

There are 140 people in a singing competition. The graph shows the results for the first five rounds

Mathematics

1 answer:

SOVA2 [1]4 years ago

4 0

a) The expression is y = 140 - 15 x

b ) There are 5 participants in the 9th round

Step-by-step explanation:

Step 1 :

From the graph we can see that,

Number of people in the singing competition = 140

Number of people in the first round = 125

Number of people in the second round = 110

Number of people in the third round = 95

Number of people in the fourth round = 80

Number of people in the fifth round = 65

Step 2 :

From the given data, We can get that the difference between the number of people participating in each round is 15 less than the previous round .

The first round has 15 people less than the total number 140

Let x represent the number of the round and y represent the number of people participating in each round .

Then the expression to represent this would be

y = 140 - 15 x

Step 3 :

To find the number of participants in the 9th round given the same pattern continues.

For the 9th round x = 9, as x represents the number of the round

Substituting this in the equation obtained in step 2, we get

y = 140 -15 (9) = 140 - 135 = 5

There are 5 participants in the 9th round

Step 4 :

Answer :

a) The expression is y = 140 - 15 x

b ) There are 5 participants in the 9th round

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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.

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

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

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

$506.25a =2531.25$

$a=-5$

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

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

$y=-31.25+2531.25$

$y=2500$

y-intercept: $(0,2500)$

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.