Drag each equation to show if it could be a correct first step to solving the equation
1 answer:
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Answer:
The system that represent the scenario is
The solution in the attached figure
Step-by-step explanation:
Let
x-----> the acres of corn
y----> the acres of cotton
we know that
------> inequality A
-----> inequality B
using a graphing tool
the solution is the shaded area in the attached figure
Answer:
25
Step-by-step explanation:
Let n be the first integer.
Then the second integer will be (n + 1).
And the third will be (n + 2).
The sum is 78. Therefore:
Solve for n. Combine like terms:
So:
Therefore:
Therefore, the first integer is 25.
So our sequene is 25, 26, and 27.
The integer closest to zero will thus be 25.
The length of the shorter leg is 14 inches.
We will set up two equations for this; first, for the perimeter. We will call the legs a and b:
a + b + 50 = 112
Subtract 50 from both sides:
a + b + 50 - 50 = 112 - 50
a + b = 62
We will isolate a, so we can use substitution. Subtract b from both sides:
a + b - b = 62 - b
a = 62 - b
Now we will set up our Pythagorean theorem equation:
a² + b² = 50²
a² + b² = 2500
We will substitute our value for a from the first equation into this one:
(62-b)² + b² = 2500
(62 - b)(62 - b) + b² = 2500
Multiplying the binomials, we have:
62*62 - b*62 - b*62 -b(-b) + b² = 2500
3844 - 62b - 62b + b² + b² = 2500
Combining like terms:
3844 - 124b + 2b² = 2500
To set it equal to 0 and solve, we subtract 2500 from both sides:
3844 - 124b + 2b² - 2500 = 2500 - 2500
1344 - 124b + 2b² = 0
In standard form, we have
2b² - 124b + 1344 = 0
Using the quadratic formula,
The shorter leg is 14 and the longer one is 48.
We will set up two equations for this; first, for the perimeter. We will call the legs a and b:
a + b + 50 = 112
Subtract 50 from both sides:
a + b + 50 - 50 = 112 - 50
a + b = 62
We will isolate a, so we can use substitution. Subtract b from both sides:
a + b - b = 62 - b
a = 62 - b
Now we will set up our Pythagorean theorem equation:
a² + b² = 50²
a² + b² = 2500
We will substitute our value for a from the first equation into this one:
(62-b)² + b² = 2500
(62 - b)(62 - b) + b² = 2500
Multiplying the binomials, we have:
62*62 - b*62 - b*62 -b(-b) + b² = 2500
3844 - 62b - 62b + b² + b² = 2500
Combining like terms:
3844 - 124b + 2b² = 2500
To set it equal to 0 and solve, we subtract 2500 from both sides:
3844 - 124b + 2b² - 2500 = 2500 - 2500
1344 - 124b + 2b² = 0
In standard form, we have
2b² - 124b + 1344 = 0
Using the quadratic formula,
The shorter leg is 14 and the longer one is 48.