2. A sculptor is planning to make two triangular prisms out of steel. The sculptor will use ΔABC for the bases of one prism and ΔDEF for the bases of the other prism.

(a) Is ΔABC similar to ΔDEF ? Explain, and show your work. If you are showing that these triangles are similar you need to show which angles are congruent and show that the sides are proportional (3 points). Do not just say “yes” you will not receive credit. Please also state the similarity theorem or postulate you use (2 points)
(b) Suppose the sculptor makes both prisms with the same height. Which prism will have a greater volume (1 point)? How many times greater (1 point)? Show your work (3 points).

a) SAS

b) Volume of DEF is 4 times the Volume of ABC

Step-by-step explanation:

a) since they have one same/congruent angle (angle B and angle E) and other two sides are in the same ratio, they are similar by SAS similarity theorem.

40/20 = 30/15 = 2

Therefore Δ ABC is similar to Δ DEF

b) Volume of a prism

= base area × height

Let height be 'h cm'

With Base ABC:

Volume = ½×20×15×h = 150h cm³

With Base DEF:

Volume = ½×40×30×h = 600h cm³

600h/150h = 4

Prism with base DEF has a greater volume; it's 4 times of the volume of the prism with base ABC

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.