Find the volume of the triangular prism.

Volume(V) of the triangular prism 31.5 cubic inches.

Step-by-step explanation:

Since this figure represents the triangular Prism.

Given in the figure:

Length of triangular prism is 4.5 in.

In the right triangular cross-section,

Base (b) = 2 in and the height (h) = 7 in.

Volume of  triangular prism formula: - A triangular prism whose length is l units, and whose right triangular cross section has base b units and height h units, then

Volume(V) of the right triangular prism is given by;

cubic unit

Using the above values; solve for V;    where A is the area of right triangle, or we can write it as

⇒ cubic inches.

On simplifying we get,

Hence, the volume of the triangular Prism is, 31.5 cubic inches.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be