Find an equation for the line that passes through the points 4,3 and , −5,6 .
1 answer:
Answer:
y -3 = -1/3(x -4)
Step-by-step explanation:
The 2-point form of the equation of a line is useful for this. For points (x1, y1) and (x2, y2), it tells you the equation can be written as ...
... y -y1 = (y2 -y1)/(x2 -x1)·(x -x1)
For your given points, this is ...
... y -3 = (6 -3)/(-5-4)(x -4)
... y -3 = -1/3(x -4) . . . . . simplifiied a bit
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<em>Comment on the solution</em>
The problem asks for "an equation", so no particular form is required. The 2-point form is the most convenient here. In standard form, the equation would be: x +3y = 13.
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Answer:
The volume of the triangular prism in the diagram is:
- <em>105.5</em>
The surface area of the triangular prism in the diagram is:
- <em>10.75</em>
Step-by-step explanation:
First, we're gonna calculate the surface area to obtain the volume, then, to calculate the area of a triangle (because the surface o a triangular prism is just a triangle), you can use the formula:
- Area of a triangle = (base * height) / 2
We have this data from the diagram, where the base of the triangles is 5 inches and, the height is 4.3 inches, replacing this in the formula:
- Area of a triangle = ( 5 in * 4.3 in) / 2
- Area of a triangle = ( 21.5
) / 2
- Area of a triangle = <em>10.75</em>
Now, we can calculate the volume of the triangular prism with the next formula:
- Volume of a triangular prism = surface area * depth
In the diagram, we can see the depth is 14 inches, then:
- Volume of a triangular prism = 10.75
- Volume of a triangular prism = <em>105.5</em>
How you can see with the calculations perfomed, <em>the surface area is 10.75 </em><em> and the volume of that triangular prism is 105.5 </em>
.