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Vikki [24]
3 years ago
12

Tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola.

Mathematics
1 answer:
Rus_ich [418]3 years ago
5 0

Answer:

b must equal 7 and a second solution to the system must be located at (2, 5).

Step-by-step explanation:

Rearranging the first equation:

y = (x - 3)^2 + 4

From this we see that the vertex is at the point (3,4).

So one solution of equation 2 is (3 ,4).

Substituting in equation 2:

4 = -3 + b

b = 7.

So equation 2 is y = - x + 7.

Now we check if  (2, 5) is on this line:

5 = -2 + 7 = 5 , therefore  (2, 5) is on this line.

Verifying if (2, 5)  is also on y = (x - 3)^2 + 4:

5 = (2 - 3)^2 + 4 =  1 + 4 = 5

- so it is. and a second solution to the system is (2, 5).

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Using the following national income accounting data, compute (a) GDP, (b) NDP, and (c) NI. All figures are in billions. Category
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Answer:

(a) GDP = $333.9 billion

(b) NDP = $322.1 billion

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Step-by-step explanation:

(a) Compute GDP

This can be computed using the following formula:

GDP = Gross Domestic Product = Personal consumption expenditure + net private domestic investment + government purchases + (US exports of goods - US Imports of goods) ......... (1)

Substituting the values into equation (1), we have:

GDP = $219.1 + $52.1 + $59.4 + ($19.8 - $16.5) = $333.9

Since all figures are in billions, we have:

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This can be computed using the following formula:

NDP = Net domestic product = GDP - Consumption of fixed capital ................... (2)

Substituting the values into equation (2), we have:

NDP = $333.90 - $11.8 = $322.1

Since all figures are in billions, we have:

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This can be computed using the following formula:

NI = National Income = NDP - Taxes on production and imports  - Statistical discrepancy ........... (3)

Substituting the relevant values into equation (3), we have:

NI = $322.1 - $14.4 - $0.0 = $307.7

Since all figures are in billions, we have:

NI = $307.7 billion

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