Diagram shows the composite solid formed by a cuboid and a right prism. Trapezium LMNP is the uniform cross section of the prism. It is given the volume of the composite solid is 444cm³. Calculate the length, in cm of MN

MN = 7 cm

Step-by-step explanation:

Well the volume we can separate into pieces

first the ABCDEFGH (? you know this cuboid)

which has a volume of

if you ask where does the 4 come from

it comes from LP = KB = YC and JY + YC =JC

so

this is because JY = MX

the other volume is of BCNPKLXY (hope you understand which one)

and the volume is

and the last one is KYXLMJ (the top "triangle")

the volume is

so now add them up

and has to equal 444

and finally we know that MN = MX + XN = 3+4 = 7

so here is our answer MN = 7 cm

a couple of notes

3. the units don't matter due to the fact that everything is in cm

4. see the picture below to get a better idea of which prism I am talking of

5. tell me if you have questions :D

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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