Me i really need it i can’t do this anymore they put too much work on me and i need to catch up with other work

First of all, relax :)

We'll get through this together, okay?

#38, finding the surface area of a prism, all you need to remember is, all three-dimensional shapes are made up of two-dimensional shapes.

So, one of the sides is 5 in. by 6.5 in. So, 5*6.5=32.5 square inches. But remember, there's another square just like this on the other side. So, multiply 32.5 by 2.

32.5*2=65 square inches.

Another square is 7.5 by 6.5

7.5*6.5=48.75

*2

48.75*2=97.5 square inches

One more set:

There's the top and bottom:

7.5 by 5

7.5*5=37.5

*2

37.5*2=75 square inches

So, add all of those up:

65 square inches+97.5 square inches+75 square inches=237.5 square inches.

So, surface area of the prism is

237.5 square inches.

Surface area of the triangular prism is the same. Just find the area of all the shapes.

There are two rectangles that are each 8cm by 5cm.

8*5=40 square cm

*2 (because there are two rectangles).

40*2=80

80 square cm

There is only one rectangle that is 8cm by 6cm (on the bottom), so just multiply the sides.

8*6=48 square cm

Finally, calculate the front and back triangles:

5cm*6cm=30 square cm

divide by 2 (because it's a triangle)

30/2=15 square cm

Then the other triangle, which is just another 15 square cm

15+15=30 square cm

Add up the areas:

48 square cm+80 square cm+30 square cm=158 square cm

Area of the triangular prism is 158 square centimeters.

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.