Answer:
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The first mechanic worked for 10 hours and the second mechanic worked for 15 hours.
Step-by-step explanation:
Given,
Charges of first mechanic = $95 per hour
Charges of second mechanic = $115 per hour
Total hours = 25
Total amount charged = $2675
Let,
The number of hours worked by first mechanic = x
The number of hours worked by second mechanic = y
According to given statement;
x+y=25 Eqn 1
95x+115y=2675 Eqn 2
Multiplying Eqn 1 by 95
Subtracting Eqn 3 from Eqn 2
Dividing both sides by 20
Putting y=15 in Eqn 1
The first mechanic worked for 10 hours and the second mechanic worked for 15 hours.
Keywords: linear equation, elimination method
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Answer:
r=8
Step-by-step explanation:
The formula for slope is
m = (y2-y1)/ (x2-x1)
Substitute in what we know.
8/3 = (-7-1)/(5-r)
Simplify
8/3 = -8/(5-r)
We can use cross products to help us solve.
8 * (5-r) = 3 * (-8)
divide each side by 8
8/8 * (5-r) = 3 * (-8)/8
5-r = -3
Subtract 5 from each side
5-r-5 = -3-5
-r = -8
Multiply by -1
r = 8
Answer:
We conclude that at x = 0 and x = -1, the value of f(x) = 2ˣ - 1 and g(x) = 1/2x is the same.
Therefore, the solution to f(x) = g(x) is:
Step-by-step explanation:
Given the table
x f(x) = 2ˣ - 1 g(x) = 1/2x
-2 -3/4 -1
-1 -1/2 -1/2
0 0 0
1 1 1/2
2 3 1
If we carefully observe, we can determine that
at x = 0, the value of f(x) = 2ˣ - 1 and g(x) = 1/2x is the same.
In other words,
at x = 0
Thus,
at x = 0
f(x) = g(x)
Also at x = -1, the value of f(x) = 2ˣ - 1 and g(x) = 1/2x is the same.
In other words,
at x = -1
Thus,
at x = -1
f(x) = g(x)
Summary:
Thus, we conclude that at x = 0 and x = -1, the value of f(x) = 2ˣ - 1 and g(x) = 1/2x is the same.
Therefore, the solution to f(x) = g(x) is:
