The labor fee is $13.55 and each quart of oil is $2.25
Step-by-step explanation:
Let,
x be the amount of each quart of oil
y be the amount of labor fee
According to given statement;
5x+y=24.80 Eqn 1
7x+y=29.30 Eqn 2
Subtracting Eqn 1 from Eqn 2
Dividing both sides by 2
Putting x=2.25 in Eqn 1
The labor fee is $13.55 and each quart of oil is $2.25
Keywords: linear equation, subtraction
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The vertex form of the function is y = (x + 8)² - 71
The vertex is (-8 , -71)
Step-by-step explanation:
The vertex form of the quadratic equation y = ax² + bx + c is
y = a(x - h)² + k, where
∵ y = x² + 16x - 7
∵ y = ax² + bx + c
∴ a = 1 , b = 16 , c = -7
∵
∴
∴ h = -8
To find k substitute y by k and x by -8 in the equation above
∵ k is the value of y when x = h
∵ h = -8
∴ k = (-8)² + 16(-8) - 7 = -71
∵ The vertex form of the quadratic equation is y = a(x - h)² + k
∵ a = 1 , h = -8 , k = -71
∴ y = (1)(x - (-8))² + (-71)
∴ y = (x + 8)² - 71
∵ (h , k) are the coordinates of the vertex point
∵ h = -8 and k = -71
∴ The vertex is (-8 , -71)
The vertex form of the function is y = (x + 8)² - 71
The vertex is (-8 , -71)
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