Answer:
x = -4
Step-by-step explanation:
To make this easier to explain and easier to solve, we're going to first multiply the second equation of 9x-7y=-15 by -1 to make the y coefficient positive.
This results in -9x+7y=15.
When we line up the two equations on top of each other now, we'll see that both the first and second equations have opposite y coefficients, which is vital for elimination.
The next step is to add the second equation to the first one. Teachers may tell you to subtract, but I find it easier to add if you make the two y coefficients of negative value to each other.
4x-7y=5
+ -9x+7y=15
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-5x+0y=20, or just -5x=20, because you have successfully eliminated the y variable.
From there, you're going to solve like a normal equation (divide both sides by -5) toget you x=-4.
Answer:
I think it is the 5th one if im wrong i am sorry
Step-by-step explanation:
Answer:
Density = 9 dolphins / mi^2 This is the result.
Step-by-step explanation:
Number of dolphins = 175
Radius = 2.5 mi
1. - Calculate the area
Area = pi* r^2
Area = 3.14*2.5^2
Area = 3.14*6.25
Area = 19.625 mi^2
2. - Calculate the density
density = dolphins/mi^2
- Substitution
density = 175 / 19.625
Result
density = 8.9 dolphins/mi^2
Rounding to the nearest whole number
Density = 9 dolphins / mi^2
Answer:
- north and south sides are 38 8/9 ft long
- east and west sides are 17.5 ft long
Step-by-step explanation:
<u>Short answer</u>: area is maximized when half the cost is spent in each of the orthogonal directions. This means the east and west sides will total $350 at $20 per foot, so will be 17.5 feet. The north and south sides will total $350 at $9 per foot, so will be 38 8/9 feet.
The dimensions that maximize the area are 17.5 ft in the north-south direction by 38 8/9 ft in the east-west direction.
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<u>Long answer</u>: If x represents the length of the north and south sides, and y represents the length of the east and west sides, then the total cost is ...
10y +10y +2x +7x = 700
9x +20y = 700
y = (700 -9x)/20
We want to maximize the area:
A = xy = x(700 -9x)/20
We can do this by differentiating and setting the derivative to zero:
dA/dx = 700/20 -9x/10 = 0
350 -9x = 0 . . . . multiply by 10
x = 350/9 = 38 8/9
y = (700 -9(350/9))/20 = 350/20 = 17.5
The north and south sides are 38 8/9 ft long; the east and west sides are 17.5 ft long to maximize the area for the given cost.
