connexus unit 8 lesson 1 PRACTICE!
1) B
2) C
3) A
4) C
5) B
6) A
7) D
8) A
9) D
10) A
11) A
12) C
13) D
14) C
15) B
16) B
Hope this helps you guys out!
The minimum volume of the tank required for combined lengths of the fish is [tex]\boxed{15\,{\text{gallons}}}[/tex].
Further Explanation:
The graph between the capacity of the tank and the combined length of the fishes present in the tank starts from the point [tex]\left( {0,1} \right)[/tex] and further it passes through the point [tex]\left( {3,4} \right)[/tex].
The expression for the slope of the graph is as given below.
[tex]m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}[/tex]
Substitute the co-ordinates of the points in equation of slope.
[tex]\begin{aligned}m&= \frac{{4 - 1}}{{3 - 0}}\\&= \frac{3}{3}\\&= 1\\\end{aligned}[/tex]
The y-intercept of the graph is [tex]1[/tex].
Write the expression for the equation of line of the graph.
[tex]y = mx + c[/tex]
Substitute [tex]1[/tex] for [tex]m[/tex] and [tex]1[/tex] for [tex]c[/tex] in above expression.
[tex]\begin{aligned}y&= \left( {1 \cdot x} \right) + 1 \hfill\\y&= x + 1 \hfill\\\end{aligned}[/tex]
The total length of all the fishes present inside the tank is.
[tex]\begin{aligned}{L_{total}} &= \left( {4 \times 2} \right) + \left( {3 \times 1} \right) + \left( {1 \times 3} \right) \\&= 8 + 3 + 3\\&= 14\,{\text{inches}}\\\end{aligned}[/tex]
Since the length of the fishes is given on the x-axis, substitute [tex]14\,{\text{inches}}[/tex] for [tex]x[/tex] in equation of line of the graph.
[tex]\begin{aligned}y&= 14 + 1\\&= 15\,{\text{gallons}}\\\end{aligned}[/tex]
Thus, the minimum volume of the tank required for combined lengths of the fish is [tex]\boxed{15\,{\text{gallons}}}[/tex].
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Answer Details:
Grade: High School
Chapter: Units and Measurements
Subject: Physics
Keywords: Aquarium, size of tank, capacity of the tank, combined lengths, the fish, platys, guppies, loach, inch, smallest capacity, gallon.
