Which of the following expressions can be used to find how many cubes with edge lengths of 1/3 unit fit in a prisim of 5 units b
1 answer:
Answer:
5400 cubes can be fit into the prism.
Step-by-step explanation:
We are given the dimensions of prism as:
5 units by 5 units by 8 units i.e. 5 units×5 units×8 units.
Hence, the volume of the prism is given by:
Volume of prism=5×5×8=200 cubic units
Also the edge length of cube is given by= 1/3 unit.
Hence volume of 1 cube=
Hence volume of 1 cube= (1/27) cubic units.
Let 'n' cubes can be fitted into the prism.
Hence we have the relation as:
Volume of prism=n×Volume of 1 cube.
200=n×(1/27)
n=200×27
n=5400
Hence 5400 cubes can be fitted into the prism.
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<h2>Answer</h2>
2. The Graph Contains The Point (5, 12)
<h2>Explanation</h2>Remember that in a linear function of the form ,
is the slope/rate of change of the line and
is the y-intercept.
From our equation we can infer that , so the y-intercept of our graph is 12 units above the origin on the point (0, 12). Therefore, choice 2 correctly describe the graph of y = 5x + 12
We can also infer that , so the slope of our line is 5, which is constant, so our line has a constant rate of change. Also, since every integer can be written as a fraction with denominator 1, we can write our slope as
. Therefore, choices 1 and 2 correctly describe the graph of y = 5x + 12.
Now, remember that any point on the plane has coordinates , so, to check if a point is on a line, we just need to replace the
and
values in the line equation and check if the equation holds. Our point is (5, 12), so x = 5 and y = 12. Lets replace the values in our line:
Since the equation equation doesn't hold (12 is not equal 37), we can conclude that the graph doesn't contain the point (5, 12). Therefore, choice 2 does NOT correctly describe the graph y = 5x +12.