The governor is making a visit to your school and you need to assign seating for 14 students. unfortunately there are only six s
1 answer:
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Answer:
Option D.(60, 135)
Step-by-step explanation:
Let
x -----> the number of acres of peas
y ----> the number of acres of carrots
we know that
The inequality that represent the problem is equal to
so
<em>Verify each case</em>
case A) (-50,160)
substitute the value of x and the value of y in the inequality and then compare the result
----> is true
The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number
case B) (80,160)
substitute the value of x and the value of y in the inequality and then compare the result
----> is not true
therefore
The point is not a solution
case C) (75,-200)
substitute the value of x and the value of y in the inequality and then compare the result
----> is true
The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number
case D) (60,135)
substitute the value of x and the value of y in the inequality and then compare the result
----> is true
therefore
The point is a viable solution
Check the picture below.
keeping in mind that the point of tangency for a radius line and a tangent is alway a right-angle, since the "red" chord is parallel to the "green" tangent line outside, then the chord is cutting the "green" radius there in two equal halves at a right-angle, as you see in the picture.
we know the chord is 10 units long, so 5 + 5, since is perpendicularity with the radius will also cut the chord in two equal halves.
anyhow, all that said, we end up with triangle you see on the right-hand-side, and then we can just use the pythagorean theorem.
keeping in mind that the point of tangency for a radius line and a tangent is alway a right-angle, since the "red" chord is parallel to the "green" tangent line outside, then the chord is cutting the "green" radius there in two equal halves at a right-angle, as you see in the picture.
we know the chord is 10 units long, so 5 + 5, since is perpendicularity with the radius will also cut the chord in two equal halves.
anyhow, all that said, we end up with triangle you see on the right-hand-side, and then we can just use the pythagorean theorem.
The solution to a system of (linear) equations is the point where the graphs intersect. Consider two parallel lines. By definition, two parallel lines never intersect each other, but all pairs of non-parallel lines will eventually intersect. That means they will also have a solution.
Let's consider what makes a line parallel to another line. It basically looks identical, having the same steepness (slope), but the graph is just shifted over. That is, a parallel line would have the same slope and a different y-intercept. For our equation
, or 
in slope-intercept form, a parallel line will be of the form 
.
That describes the form of a parallel line, which we do not want. Any other line, however, will give a solution to our system, so we merely want a line where the slope does not equal 2.
We can have any equation of the form
.
Let's consider what makes a line parallel to another line. It basically looks identical, having the same steepness (slope), but the graph is just shifted over. That is, a parallel line would have the same slope and a different y-intercept. For our equation
That describes the form of a parallel line, which we do not want. Any other line, however, will give a solution to our system, so we merely want a line where the slope does not equal 2.
We can have any equation of the form