2:3:4
2:3:4 can be written as 2x:3x:4x
2x+3x+4x=180
9x=180
x=20
Therefore it is
40:60:80
Answer:
AC ≈ 17.3 , BC ≈ 5.3
Step-by-step explanation:
using the tangent ratio in right triangle ACD
tan51° = = = ( multiply both sides by 14 )
14 × tan51° = AC , then
AC ≈ 17.3 ( to the nearest tenth )
using the cosine ratio in right triangle ABC
cos72° = = = ( multiply both sides by 17.3 )
17.3 × cos72° = BC , then
BC ≈ 5.3 ( to the nearest tenth )
Answer:
$199.8 (This is what I personally got it could be wrong)
Step-by-step explanation
7.25 x 32 = 232
232 x 1/4 = 58
58 - 25.50 = 32.5
232 - 32.5 = 199.8
Answer: $199.8 in profit
All you need to do is plug 2 in for x
Answer:
<em>not</em> a rectangle
Step-by-step explanation:
There are several ways to determine whether the quadrilateral is a rectangle. Computing slope is one of the more time-consuming. We can already learn that the figure is not a rectangle by seeing if the midpoint of AC is the same as that of BD. (It is not.) A+C = (-5+4, 5+2) = (-1, 7). B+D = (1-2, 8-2) = (-1, 6). (A+C)/2 ≠ (B+D)/2, so the midpoints of the diagonals are different points.
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The slope of AB is ∆y/∆x, where the ∆y is the change in y-coordinates, and ∆x is the change in x-coordinates.
... AB slope = (8-5)/(1-(-5)) = 3/6 = 1/2
The slope of AD is computed in similar fashion.
... AD slope = (-2-5)/(-2-(-5)) = -7/3
The product of these slopes is (1/2)(-7/3) = -7/6 ≠ -1. Since the product is not -1, the segments AB and AD are not perpendicular to each other. Adjacent sides of a rectangle are perpendicular, so this figure is not a rectangle.
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Our preliminary work with the diagonals showed us the figure was not a parallelogram (hence not a rectangle). For our slope calculation, we "magically" chose two sides that were not perpendicular. In fact, this choice was by "trial and error". Side BC <em>is perpendicular</em> to AB, so we needed to choose a different side to find one that wasn't. A graph of the points is informative, but we didn't start with that.