How do I solve for x
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The length of the square base is thus = A
<h3>What is hemisphere?</h3>
Consequently, a hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape. It is created by precisely cutting a spherical along its diameter, leaving behind two identical hemispheres.
EXPLANATION; Let ABCDE be the pyramid with ABCD as the square base. Let O and M be the center of square ABCD and the midpoint of side AB respectively. Lastly, let the hemisphere be tangent to the triangular face ABE at P.
Notice that triangle EOM has a right angle at O. Since the hemisphere is tangent to the triangular face ABE at P, angle EPO is also 90 degree. Hence, triangle EOM is similar to triangle EPO.
OM/2 = 6/EP
OM = 6/EP x 2
OM =
The length of the square base is thus = A
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Equation 1: 
Equation 2:
We can either use the 'elimination' method or the 'substitution' method to solve this simultaneous equation.
In some cases one method is easier to use than the other. For this one, it would be easier to use the elimination method
We need to eliminate either the 'x' or the 'y' to begin with. Say we want to eliminate the 'x' terms, then the next step is to make the constant the same
Equation 1: the constant of 'x' is 5
Equation 2: the constant of 'x' is 2
To make the two constants the same, think of common multiple. The lowest common multiple for 5 and 2 is 10
Equation 1: Multiply all terms by 2 to achieve 10x
Equation 2: Multiply all terms by 5 to achieve 10x
Equation 1:
Equation 2:
Once the constant of 'x' is the same, then we can start the elimination process. Since our aim is to eliminate, one of the 'x' need to be in negative form. We can either multiply Equation 1 or Equation 2 by (-1)
Equation 1: -10x - 14y = -62
Equation 2: 10x + 20y = 80
Hence the correct answer is: Third option
Equation 2:
We can either use the 'elimination' method or the 'substitution' method to solve this simultaneous equation.
In some cases one method is easier to use than the other. For this one, it would be easier to use the elimination method
We need to eliminate either the 'x' or the 'y' to begin with. Say we want to eliminate the 'x' terms, then the next step is to make the constant the same
Equation 1: the constant of 'x' is 5
Equation 2: the constant of 'x' is 2
To make the two constants the same, think of common multiple. The lowest common multiple for 5 and 2 is 10
Equation 1: Multiply all terms by 2 to achieve 10x
Equation 2: Multiply all terms by 5 to achieve 10x
Equation 1:
Equation 2:
Once the constant of 'x' is the same, then we can start the elimination process. Since our aim is to eliminate, one of the 'x' need to be in negative form. We can either multiply Equation 1 or Equation 2 by (-1)
Equation 1: -10x - 14y = -62
Equation 2: 10x + 20y = 80
Hence the correct answer is: Third option