Answer: We discover two outcomes:
1000 - 998 = 2
1001 - 999 = 2
Step-by-step explanation:
The problem can be stated as:
****-*** = 2
Where each asterisk symbolizes a distinct digit; here with a 4-digit number subtracting a 3-digit number to yield a difference of 2.
This can be represented as 99*, where we can increase any digit from 1 to 9 and we will achieve a 4-digit result:
So we rewrite it this way:
1000 - 998 = 2
When we add one to each side, the difference remains preserved, maintaining equal digit counts:[
1000 - 998 + 1 - 1 = 2
(1000 + 1) - (998 + 1) = 2
Thus, 1001 - 999 = 2
A simple case would also yield further solutions where digits can be zeros, for instance:
0004 - 0002 = 2
However, this trivial solution may be disregarded. This leads us to conclude that we have two unique solutions.
We will create the equations for this scenario:
(1) 1100*y + z = 113
(2) 1500*y + z = 153
Find z: Monthly administration fee is represented by z, which is the question of this problem.
The amounts of kilowatt hours consumed are 1100 and 1500 respectively.
The cost for each kilowatt hour is denoted by y, although its value is not required for this math problem, we can compute it regardless.
This results in a system of two equations with two unknowns, which can be solved using the substitution method:
(1) 1100*y + z = 113
(2) 1500*y + z = 153
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(1) z = 113 - 1100*y [substituting z (right side) into equation (2) instead of z]:
(2) 1500*y + (113 - 1100*y) = 153
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(1) z = 113 - 1100*y
(2) 1500*y + 113 - 1100*y = 153
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(1) z = 113 - 1100*y
(2) 400*y + 113 = 153
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(1) z = 113 - 1100*y
(2) 400*y = 153 - 113
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(1) z = 113 - 1100*y
(2) 400*y = 40
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(1) z = 113 - 1100*y
(2) y = 40/400
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(1) z = 113 - 1100*y
(2) y = 1/10
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by placing the calculated value of y back into equation (1), we can find z:
(1) z = 113 - 1100*(1/10)
(1) z = 113 - 110
(1) z = 3 dollars serves as the monthly fee.
I have included a screenshot of the entire question along with its accompanying diagram.
Answer:∠1 = 163°
Explanation:1- finding angle 2:Given that ∠2 together with 17° creates a straight angle, their total is 180°.
Thus:
180 = 17 + ∠2
Solving for ∠2 gives us:
∠2 = 180 - 17
∠2 = 163°
2- finding angle 1:Since lines a and b are parallel, ∠1 and ∠2 are alternate angles and therefore equal.
We determined that ∠2 = 163°, leading to:
∠1 = 163°
I hope this clarifies things!:)
