7x – 2y = -5 Which ordered pair is a solution of the equation

Mathematics

2 answers:

Morgarella [4.7K]3 years ago

5 0

The answer is neither. (X,Y) Plug them into the equation and neither is a solution to the equation.

satela [25.4K]3 years ago

3 0

Answer:

D, neither.

Step-by-step explanation:

If you substitute 1 in for x and 5 in for y, you will get 7-10=-5 and this is incorrect. If you substitute -1 in for x and 1 in for y, you will get -7-2=-5 and this is also incorrect. So the correct answer is D, neither. I hope this helps!

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A peach orchard owner wants to maximize the amount of peaches produced by her orchard.

qaws [65]

Answer:

a) Y(x) = {900, x≤30; 900-40(x-30), x>30}

b) T(x) = {900x, x≤30; 2100x-40x², x>30}

c) dT/dx = {900, x≤30; 2100-80x, x>30}

Step-by-step explanation:

a) The problem statement gives the function for x ≤ 30, and gives an example of evaluating the function for x = 35. So, replacing 35 in the example with x gives the function definition for x > 30.

$\displaystyle Y(x)=\left\{\begin{array}{lcl}900&\text{for}&x\le 30\\900-40(x-30)&\text{for}&x>30\end{array}\right.$

b) The yield per acre is the product of the number of trees and the yield per tree:

T(x) = x·Y(x)

$\displaystyle T(x)=\left \{\begin{array}{lcl}900x&\text{for}&x\le 30\\2100x-40x^2& \text{for}&x>30\end{array}\right.$

c) The derivative is ...

$\displaystyle\frac{dT}{dx}=\left \{\begin{array}{lcl}900&\text{for}&x\le 30\\2100-80x& \text{for}&x>30\end{array}\right.$

_____

The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.