Answer:
9*(6+7)
Step-by-step explanation:
First, we have to find the Greatest Common Factor (GCF), to do this we have to see all the factors of 54 and 63 and find the greatest factor that they have in common.
Factors of 54
1,2,3,6,9,18,27,54
Factors of 63
1,3,7,9,21,63
The GCF is 9 because is the greatest factor that is common to both numbers.
Now we have to divide 54/9 and 63/9
54/9 = 6
63/9 = 7
So now we can write the product of the GCF and another sum:
9*(6+7)
<em>We can prove this by solving both expressions:</em>
<em>54+63 = 9*(6+7)</em>
<em>117 = 9*13</em>
<em>117 = 117 </em>
<em>The results are equal so we prove it is right.</em>
78. 11(9-6) = 33. 3(6+9) = 45. 33+45 = 78
Answer:
<h3>240.72 miles</h3>
Step-by-step explanation:
First, in the picture we have a drawing of this exercise. In this case, I will call A to the western station, and B the eastern station.
According to this, we have a triangle there, and we need to calculate the distance between C and A (Distance AC). This is the diagonal of that triangle. We only have the length of side AB which is 117 miles, and now, to get the side AC we need to use the sin law.
First, let's calculate the angle in B:
<ABC = 15 + 90 = 105°
This is the angle of that side of the triangle.
The angle in A:
<CAB = 90 - 43 = 47°
The angle in C:
<ACB = 180 - 47 - 105 = 28°
We have the three angles now.
Now the sin law is:
Sin< = opossite leg / hypotenuse
hypotenuse = opposite leg / sin<
Equaling both we have:
hypotenuse = AB / sin<ACB = AC/sin<ABC
AC = AB sin<ABC / sin<ACB
Solving for AC we have:
AC = 117sin105 / sin28
AC = 240.72 miles
Well first find the area of the semi-circle.
If the area of a cricle is equal to pi*radius^2 , then you can just find that and divide by 2.
So, A = pi*2^2. = 4pi
We know that the radius is 2 because the length of the side of the rectangle is 4, meaning that the diameter of the semi-circle is 4, and so the radius is 2 as it is half of the diameter.
We can easily calculate the area of the rectangle, which is
Length * width = 6*4 = 24.
Next we divide 4pi by 2 in order to get the area of the semi-circle, giving us an area of 2pi
We can just subtract 2pi from 24 and get the area of the shaded region.
Area of the shaded region (answer): 17.7
