A rectangular garden has a length that is modeled by the expression 2 x – 7 and a width of 3 x 2 + 4 x. Part A: What is the area
2 answers:
Answer:
Area(A) and perimeter(P) of rectangle is given by:
where,
l is the length and w is the width of the rectangle.
As per the statement:
A rectangular garden has a length that is modeled by the expression:
and a width(w) =
A.
To find the area of the garden.
then;
Combine like terms;
square units.
Therefore, the area of the garden is, square units.
B.
The owner of the garden wants to put a fence around the perimeter of the garden.
then;
Therefore, the perimeter of the garden is, units
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Answer:
- B) One solution
- The solution is (2, -2)
- The graph is below.
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Explanation:
I used GeoGebra to graph the two lines. Desmos is another free tool you can use. There are other graphing calculators out there to choose from as well.
Once you have the two lines graphed, notice that they cross at (2, -2) which is where the solution is located. This point is on both lines, so it satisfies both equations simultaneously. There's only one such intersection point, so there's only one solution.
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To graph these equations by hand, plug in various x values to find corresponding y values. For instance, if you plugged in x = 0 into the first equation, then,
y = (-3/2)x+1
y = (-3/2)*0+1
y = 1
The point (0,1) is on the first line. The point (2,-2) is also on this line. Draw a straight line through the two points to finish that equation. The other equation is handled in a similar fashion.
