The energy economy of an area is composed of four industries: gas, coal, hydroelectric, and nuclear. The three main consumers of energy are area residential consumers, a manufacturing plant, and a university. Assume that each consumer may use some of the energy produced by each industry, and also that each industry uses some of the energy produced by each of the other industries. The energy needs of each consumer and industry is represented by a demand vector whose entries, in order, give the amount of gas, coal, hydroelectric, and nuclear energy needed by each consumer or industry, in some convenient units. The demand vectors for the consumers are: 
src="https://sciemce.com/media/4/ppg__tttt0616191201__f1q140g2.jpg" alt="" style="vertical-align: -8.0px;" /> 
and the demand vectors for the industries are: 
The price of gas is 
per unit, the price of coal is 
per unit, the price of hydroelectric power is 
per unit, and the price of nuclear energy is 
per unit. These prices can be represented by the (column) price vector: P = 
Find the income earned by the nuclear industry and its cost for the other forms of energy it uses. Then calculate its profit.
What will be an ideal response?
Income = $108,000
Cost = $61,000
Profit = $47,000
Mathematics
src="https://sciemce.com/media/4/ppg__tttt0616191201__f1q140g2.jpg" alt="" style="vertical-align: -8.0px;" /> and the demand vectors for the industries are: The price of gas is per unit, the price of coal is per unit, the price of hydroelectric power is per unit, and the price of nuclear energy is per unit. These prices can be represented by the (column) price vector: P = Find the income earned by the nuclear industry and its cost for the other forms of energy it uses. Then calculate its profit.
What will be an ideal response?
| Income = | $108,000 |
| Cost = | $61,000 |
| Profit = | $47,000 |
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Answer the following statement(s) true (T) or false (F)
1. If two triangles are congruent, then they are similar. 2. If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are similar. 3. If PQ is the altitude to the hypotenuse, AM, in right triangle ?PAM, then PQ is the mean proportional of AQ and MQ. 4. Every triangle has exactly one midsegment. 5. In ?PXR, if ?R is a right angle, then tan X = XR / RP
Simplify.
A. 
B. 2
C. 
D. 
Find the domain of the function.f(x) = 
A. (-?, 8) ? (8, ?)
B. 
? 
? (8, ?)
C. (-?, -8) ? 
? 
D. 
? 
Use a calculator to graph the rational function in the window indicated. Use the graph to (a) give the x- and y-intercepts, (b) explain why there are no vertical asymptotes, (c) give the equation of the oblique asymptote, and (d) give the domain and range.f(x) = 
; [-6, 6] by [-10, 10]
A. (a) x-intercepts: (-4, 0), 
, (4, 0); y-intercept: 
;
(b) The denominator has no real zeros because the discriminant, -15, is negative.;
(c) y = 3x - 1;
(d) The domain and range are both (-?, ?).
B. (a) x-intercepts: (-4, 0), 
, (4, 0); y-intercept: 
;
(b) The denominator has no real zeros because the discriminant, -17, is negative.;
(c) y = 3x - 1;
(d) The domain and range are both [0, ?).
C. (a) x-intercepts: (-2, 0), 
, (2, 0); y-intercept: 
;
(b) The denominator has no real zeros because the discriminant, -17, is negative.;
(c) y = 3x + 7;
(d) The domain and range are both (-?, ?).
D. (a) x-intercepts: (-2, 0), 
, 
; y-intercept: 
;
(b) The denominator has no real zeros because the discriminant, -15, is negative.;
(c) y = 3x + 1;
(d) The domain and range are both [0, ?).