Given
Shape of garden: Rectangle
Perimeter: 34 meters
Area: 72 square meters
Length of one side = x
Required
Find the dimension of the rectangle
Let the length of the other side of the rectangle be represented with y.
We start by writing out the perimeter of a rectangle
Perimeter, P = 2(L + B)
Where P is the perimeter; L and B are the length and width of the sides of the rectangle.
In this case L and B are represented by x and y
So,
P = 2(x + y)
By substituting 34 for P
34 = 2(x + y)
Multiply both sides by ½
½ * 34 = ½ * 2(x + y)
17 = x + y
Make y the subject of formula
y = 17 - x
Recall that the sides of the rectangle are represented by x and y.
Hence, the area of the rectangle is as follows.
Area = x * y
Substitute 72 for Area and 17 - x for y
72 = x(17 - x) --- Open bracket
72 = 17x - x² ---- Reorder
x² - 17x + 72 = 0
Now, we have a quadratic equation
Solving by factorisation
x² - 8x - 9x + 72 = 0
x(x - 8) - 9(x - 8) = 0
(x - 8)(x - 9) = 0
x - 8 = 0 or x - 9 = 0
x = 8 or x = 9
Recall that
y = 17 - x.
When x = 8
y = 17 - 8
y = 9
When x = 9
y = 17 - 9
y = 8
Writing out the result, we have
x = 8 , y = 9
Or
x = 9, y = 8
Hence, the dimension of the rectangle is 8 metres by 9 metres
Answer:
Types of Relationships between the Input and Output
The scatter plot can be a useful tool in understanding the type of relationship that exist between the inputs (X’s) and the outputs (Y’s)
Step-by-step explanation:
1. No Relationship: The scatter plot can give an obvious suggestion if the inputs and outputs on the graph are not related. The points will be scattered throughout the graph with no particular pattern. For no relationship to exist, points have to be completely diffused. If some points are in concentration, then maybe a relationship does exist and our analysis has not been able to uncover it.
2. Linear and Non-Linear: A linear correlation exists when all the points are plotted close together. They form a distinct line. On the other hand points could be close together but they could form a relationship which has curves in it. The nature of the relationship has wide ranging implications.
3. Positive and Negative: A positive relationship between the inputs and the outputs is one wherein more of one input leads to more of an output. This is also known as a direct relationship.
On the other hand a negative relationship is one where more of one input leads to less of another output. This is also known as an inverse relationship.
4. Strong and Weak: The strength of the correlation is tested by how closely the data fits the shape. For instance if all the points are scattered very close together to form a very visible line then the relationship is strongly linear. On the other hand, if the relationship does not so obviously fit the shape then the relationship is weak.
I don't know if this was exactly what you were looking for; hope it is! :)
16:24 students made at least 80% on the test. The question is what is the ratio of students who scored below an 80% to the total number of students. 8:24 would be the right answer, but since it is asking for the answer in the simplest form, it would be 1:3.
Step-by-step explanation:
the solution is in the picture
Answer:
560/800 = 0.7 pounds per dollar
