I think the correct answer is 560ft^2.
Answer: Armando used the wrong dimensions for the triangular prism.
Step-by-step explanation:
Hi, to answer this question we have to analyze Armando’s work.
Total Volume = Volume of rectangular prism + volume of triangular prism
Total Volume = 5 (8) (18) + one-half (6) (18) (8)
Total Volume= 720 + 432
Total volume = 1,152 cubic inches.
He made a mistake in the second step, where used h=8 for the triangular prism instead of h= 5 . (h=height)
The correct way to solve this is.
Total Volume = 5 (8) (18) + one-half (6) (18) (5)
Total Volume= 720 + 270
Total volume = 990 cubic inches.
Recall that the direction of a vector can be seen from its slope, namely b/a.
let's take a peek at a couple of vectors, and multiply them by a scalar of 2.
hmmm say < 3 , 7 > , it has a slope of 7/3, now if we use a scalar of 2
2<3,7> => < 6 , 14 >, now, the slope of that is 14/6 which simplifies to, yeap, you guessed it, to 7/3, no change in the slope.
and say hmmmm < 11 , -2 >, slope of -2/11, let's multiply it by 2
2<11,-2> => <22 , -4 >, slope is -4/22 which simplifies to -2/11.
so, the vector's magnitude gets blown up, but the slope remains the same.
Answer:
25.6 units
Step-by-step explanation: From the figure we can infer that our triangle has vertices A = (-5, 4), B = (1, 4), and C = (3, -4).
First thing we are doing is find the lengths of AB, BC, and AC using the distance formula:
d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}}
where
(x_1,y_1) are the coordinates of the first point
(x_2,y_2) are the coordinates of the second point
- For AB:
d=\sqrt{[1-(-5)]^{2}+(4-4)^2}
d=\sqrt{(1+5)^{2}+(0)^2}
d=\sqrt{(6)^{2}}
d=6
- For BC:
d=\sqrt{(3-1)^{2} +(-4-4)^{2}}
d=\sqrt{(2)^{2} +(-8)^{2}}
d=\sqrt{4+64}
d=\sqrt{68}
d=8.24
- For AC:
d=\sqrt{[3-(-5)]^{2} +(-4-4)^{2}}
d=\sqrt{(3+5)^{2} +(-8)^{2}}
d=\sqrt{(8)^{2} +64}
d=\sqrt{64+64}
d=\sqrt{128}
d=11.31
Next, now that we have our lengths, we can add them to find the perimeter of our triangle:
p=AB+BC+AC
p=6+8.24+11.31
p=25.55
p=25.6
We can conclude that the perimeter of the triangle shown in the figure is 25.6 units.
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