B. The statement is true because if the degree of the numerator of a rational function equals the degree of the denominator, then the rational function has a horizontal asymptote that is equal to the ratio of the leading coefficients.
The setup boxes in the synthetic division are (b)
<h3>How to determine the setup boxes?</h3>
The dividend is given as:
x^3 + 4x^2 + x - 6
The divisor is given as:
x - 2
Set the divisor to 0
x - 2 = 0
Solve for x
x = 2
Remove the variables in the dividend
1 + 4 + 1 - 6
Remove the arithmetic signs
1 4 1 - 6
So, the setup is:
2 | 1 4 1 - 6
Hence, the setup boxes are (b)
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Answer:
x = - 8, x = 6
Step-by-step explanation:
Given the 2 equations
x² + y² = 100 → (1)
y = x + 2 → (2)
Substitute y = x + 2 into (1)
x² + (x + 2)² = 100
x² + x² + 4x + 4 = 100
2x² + 4x + 4 = 100 ( subtract 100 from both sides )
2x² + 4x - 96 = 0 ( divide through by 2 )
x² + 2x - 48 = 0 ← in standard form
(x + 8)(x - 6) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 8 = 0 ⇒ x = - 8
x - 6 = 0 ⇒ x = 6
Answer:
The vehicle covers 126 miles on 7 gallons of fuel.
Step-by-step explanation:
Given:
The distance traveled is directly proportional to the amount of fuel.
For 
gallons of fuel distance traveled 
miles can be given as:
∝
where 
is constant of proportionality.
The vehicle covers 
miles on 
gallons.
So
Dividing both sides by 5.
∴ 
When 
gallons
miles
∴ The vehicle covers 126 miles on 7 gallons of fuel.
We can write a proportion for this problem
10,000drops of a liquid is 10 fluid ounces
100 drops of a liquid is x fluid ounces
x=100*10/10000 =1/10 = 0.1 fluid ounces
