A right rectangular prism has a length of 10 in., a width of 12 in., and a height of 16 in. the dimensions of the prism are halv
2 answers:
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Answer:
see the explanation
the graph in the attached figure
Step-by-step explanation:
Let
x ----> the number of bags of popcorn
y ---> the number of drinks
we know that
The price of each bag of popcorn was $5
The price of each drink was half the price of a bag of popcorn
so
The price of each drink was $5/2=$2.5
Remember that
The number of bags of popcorn and drinks Judy bought, multiplied by their prices, should equal $30.
The linear equation that represent this situation is
To graph the linear equation , find the intercepts
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
In the context of the situation, the y-intercept represent the number of drinks Judy can buy when the number of bags of popcorn equals zero
so
For x=0
The y-intercept is the point (0,12)
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
In the context of the situation, the x-intercept represent the number of bag of popcorn Judy can buy when the number of drinks equals zero
so
For y=0
The x-intercept is the point (6,0)
To graph the line plot the intercepts and join the points
using a graphing tool
The graph in the attached figure
The area of the considered regular hexagon which has got 14.7 inches of apothem and a perimeter of 101.8 inches is 748.2 sq. inches.
<h3>What is apothem?</h3>Apothem for a regular polygon is a line segment which originates from the center of the regular polygon and touches the mid of one of the sides of the regular polygon. It is perpendicular to the regular polygon's side it touches.
Regular polygons have all side same and that apothem bisects the side in two parts, (provable by symmetry).
Consider the diagram attached below.
The area of the regular hexagon considered = 6 times (area of triangle ABC) (because of symmetry).
Also, we have:
Area of triangle ABC = 2 times (Area of triangle ABD).
Thus, we get:
Area of the considered hexagon = 6×2×(Area of triangle ABD)
Area of the considered hexagon = 12×(Area of triangle ABD)
Perimeter of a closed figure = sum of its sides' lengths.
There are 6 equal sides in a regular hexagon (due to it being regular).
Thus, if each side is of 'a' inch length, then:
Perimeter = 6×a inches
This is bisected by the apothem.
Thus, we get:
Length of the line segment BD = |BD| = a/2 ≈ 8.483 inches
Since it is given that the length of the apothem = |AD| = 14.7 inches, therefore, we get:
Thus, we get:
Area of the considered hexagon = 12×(Area of triangle ABD)
Area of the considered hexagon
Thus, the area of the considered regular hexagon which has got 14.7 inches of apothem and a perimeter of 101.8 inches is 748.2 sq. inches.
Learn more about apothem here:
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