Simplify : 3/4 (1/2x - 12) + 4/5
2 answers:
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length = 3234 m and width = 1614 m
let the width = w then length = 2w + 6
Perimeter = 2 ( length + width )
= 2 (2w + 6 + w ) = 2 ( 3w + 6 ) = 6w + 12
given perimeter = 9696 the equating gives
6w + 12 = 9696
subtract 12 from both sides
6w = 9696 - 12 = 9684
divide both sides by 6
w = = 1614
width = 1614 m and length = (2 × 1614 ) + 6 = 3234 m
Draw an accurate picture of the points in the coordinate axis, as shown in the figure.
D, F have equal x coordinate, so DF is perpendicular to the x-axis.
D, E have equal x coordinate, so DE is perpendicular to the y-axis.
this means DF and DE are perpendicular, so DEF is a right triangle, with m(D)=90°.
Let A be the midpoint of DF. The x coordinate of A is 1 and the y coordinate can be found as follows:
subtract the y coordinate of D from the y coordinate of F, that is 5-1=4.
Divide by 2 and add to the y coordinate of D, that is 4/2+1=2+1=3 is the y coordinate of A.
Let B be the midpoint of DE, follow the previous procedure to find the coordinates of B.
A(1, 3) and B(4, 1).
draw the perpendicular through A and the perpendicular through B, thet meet at point C(4, 3), which is the circumcenter.
Answer: C(4, 3)
D, F have equal x coordinate, so DF is perpendicular to the x-axis.
D, E have equal x coordinate, so DE is perpendicular to the y-axis.
this means DF and DE are perpendicular, so DEF is a right triangle, with m(D)=90°.
Let A be the midpoint of DF. The x coordinate of A is 1 and the y coordinate can be found as follows:
subtract the y coordinate of D from the y coordinate of F, that is 5-1=4.
Divide by 2 and add to the y coordinate of D, that is 4/2+1=2+1=3 is the y coordinate of A.
Let B be the midpoint of DE, follow the previous procedure to find the coordinates of B.
A(1, 3) and B(4, 1).
draw the perpendicular through A and the perpendicular through B, thet meet at point C(4, 3), which is the circumcenter.
Answer: C(4, 3)