T=2r + 3 5r - 4t = 6
2 answers:
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General Idea:
(i) Assign variable for the unknown that we need to find
(ii) Sketch a diagram to help us visualize the problem
(iii) Write the mathematical equation representing the description given.
(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE
Applying the concept:
Given: x represents the length of the pen and y represents the area of the doghouse
<u>Statement 1: </u>"The pen is 3 feet wider than it is long"
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<u>Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"</u>
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<u>Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."</u>
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<u>Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."</u>
Conclusion:
The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.
<h3>Answer: choice 4. f(x) and g(x) have a common x-intercept</h3>
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Explanation:
For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.
The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.
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Side notes:
- Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.
- Choice 2 is not true. Point B is not on the parabola.
- Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.