Solve the system by substitution.
2 answers:
Answer:
A. no solution
Step-by-step explanation:
We can use the second expression to substitute for y in the first expression. Then we have ...
1/2x +11 = -7x^2 -9x +6
Subtracting the right side, we get
7x^2 +(9 1/2)x +5 = 0
Eliminating fractions by multiplying by 2, this is ...
14x^2 +19x +10 = 0
The discriminant of this equation will tell the number and kind of roots. For a=14, b=19, c=10, the discriminant is ...
b^ -4ac = 19^2 -4·14·10 = 361 - 560 = -199
Since this value is negative, we know the two roots to the quadratic will be complex. There are no real solutions.
The graph in the attachment shows the two curves do not intersect, hence there are no values of x that will make the y-values match.
Answer:
- no solution
Step-by-step explanation:
We can use the second expression to substitute for y in the first expression. Then we have ...
... 1/2x +11 = -7x^2 -9x +6
Subtracting the right side, we get
... 7x^2 +(9 1/2)x +5 = 0
Eliminating fractions by multiplying by 2, this is ...
... 14x^2 +19x +10 = 0
The discriminant of this equation will tell the number and kind of roots. For a=14, b=19, c=10, the discriminant is ...
... b^ -4ac = 19^2 -4·14·10 = 361 - 560 = -199
Since this value is negative, we know the two roots to the quadratic will be complex. There are no real solutions.
_____
The graph shows the two curves do not intersect, hence there are no values of x that will make the y-values match.
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Answer:
The population density is 0.364 fish per gallon.
Step-by-step explanation:
The population density can be defined as the number of individuals (in this case, small tropical fish) per unit of area or volume. In this case, the volume of the aquarium (55 gallon).
The density can be calculated then as:
The population density is 0.364 fish per gallon.