Answer:
Step-by-step explanation:
Let's call hens h and ducks d. The first algebraic equation says that 6 hens (6h) plus (+) 1 duck (1d) cost (=) 40.
The second algebraic equations says that 4 hens (4h) plus (+) 3 ducks (3d) cost (=) 36.
The system is
6h + 1d = 40
4h + 3d = 36
The best way to go about this is to solve it by substitution since we have a 1d in the first equation. We will solve that equation for d since that makes the most sense algebraically. Doing that,
1d = 40 - 6h.
Now that we know what d equals, we can sub it into the second equation where we see a d. In order,
4h + 3d = 36 becomes
4h + 3(40 - 6h) = 36 and then simplify. By substituting into the second equation we eliminated one of the variables. You can only have 1 unknown in a single equation, and now we do!
4h + 120 - 18h = 36 and
-14h = -84 so
h = 6.
That means that each hen costs $6. Since the cost of a duck is found in the bold print equation above, we will sub in a 6 for h to solve for d:
1d = 40 - 6(6) and
d = 40 - 36 so
d = 4.
That means that each duck costs $4.
Answer:
32 minutes
Step-by-step explanation:
49 - 17 = 32
Timothy spent 32 minutes on his math homework.
The system of linear inequalities x + 10y ≤ 80, x ≥ 30 and y ≤ 4 is represented in a graph below
<h3>Graph of Linear Inequality</h3>
The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.
To solve this problem, we would require the use of graph which can easily be done with a graphing calculator.
x + 10y ≤ 80
x ≥ 30
y ≤ 4
The graph of the inequalities is attached below
Learn more on graph of linear inequality here;
brainly.com/question/19443475
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