Answer:
19.2cm=h
Step-by-step explanation:
Let ABCD be a rhombus with AC and BD as its diagonals.
We know that the diagonals of a rhombus bisect each other at right angles.
Let O be the intersecting point of both the diagonals.
Let AC=24cm and BD=32cm
OA=AC/2
OA= 24/2=12cm
OB=BD/2
OB=32/2=16cm
In rt.ΔAOB by Pythagoras theorem we have
AB²=OA²+OB²
=(12)²+(16)²
=144+256
=400
AB=20cm
Hence, each side of the rhombus is of length 20cm
Area of rhombus=1/2*AC*BD
=1/2*24*32
=12*32
Area of rhombus=base*altitude
12*32=20*h
19.2cm=h
HOPE IT HELPS!!!!!!!!
Answer:
9
Step-by-step explanation:
Rotational symmetry is when a shape has the same orientation after being rotated.
For example, an equilateral triangle rotated 120° will line back up with itself. A square rotated 90° will also return to its original orientation. Same with a pentagon rotated 72°.
Basically, an n-gon rotated by a multiple of 360°/n will return to its original position.
θ = k 360°/n
For the first rotation:
160° = k 360°/n
160 / 360 = k / n
4/9 = k/n
For the second rotation:
120° = k 360°/n
120 / 360 = k / n
1/3 = k/n
For the third rotation:
80° = k 360°/n
80 / 360 = k / n
2/9 = k/n
For the fourth rotation:
280° = k 360°/n
280 / 360 = k / n
7/9 = k/n
The total rotation angle is -160°.
160 = k 360/n
160 / 360 = k / n
4/9 = k/n
Comparing the denominators, n must be the smallest multiple of 3 and 9. Therefore, n = 9.
Answer:
a = 15
Step-by-step explanation:
The graph of function g(x) is described by g(x)=ax−7, or y = ax−7.
y = g(x)=ax−7 passes through (1/3, -2). We can subst. -2 for y and 1/3 for x to determine the value of the coefficient a:
-2 = g(1/3) = a(1/3) - 7
Solve for a. First, add 7 to both sides: 5 = a(1/3).
Next, multiply both sides by 3: 15 = a, or a = 15.
Answer:
1 mi/hr
Step-by-step explanation:
Given that:
Speed in still water, s = 5 mi/hr
Let speed of current = x
Time = distance /speed
Upstream (subtract speed of current) = 5 - x
Upstream time = 8 / 5 - x - - - (1)
Downstream (add speed of current) = 5 + x
Downstream time = 12 / 5 + x - - - (2)
Equate (1) and (2)
8 / (5 - x) = 12/ (5 + x)
8(5 + x) = 12(5-x)
40 + 8x = 60 - 12x
40 - 60 = - 12x - 8x
-20 = - 20x
x = 1
Spwed of current = 1 mi/hr
