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Answer:
The answer is 11, hope i helped!
Answer:
a = 2/27
b = 13/27
Step-by-step explanation:
The given polynomial is presented as follows;
f(x) = a·x³ + b·x² + x + 2/3
Given that x + 3 is a factor, we have;
f(-3) = 0 = a·(-3)³ + b·(-3)² - 3 +2/3 = 0
-27·a + 9·b - 3 + 2/3 = 0
-27·a + 9·b = 7/3........(1)
Also we have
(a·x³ + b·x² + x + 2/3) ÷ (x + 2) the remainder = 5
Therefore;
a·(-2)³ + b·(-2)² + (-2) + 2/3 = 5
-8·a + 4·b - 2 + 2/3 = 5
-8·a + 4·b = 2 - 2/3 = 4/3........(2)
Multiplying equation (1) by 4/9 and subtracting it from equation (2), we have;
-8·a + 4·b - 4/9×(-27·a + 9·b) = 4/3 - 4/9 × 7/3
-8·a + 12·a = 8/27
4·a = 8/27
a = 2/27 ≈ 0.0741
imputing the a value in equation (1) gives;
-27×2/27 + 9·b = 7/3
-2 + 9·b = 7/3
9·b = 7/3 + 2 = 13/3
b = 13/27 ≈ 0.481.
Use the Pythagorean Theorem:
a^2 + b^2= c^2
a= one side= 68 mi
b= second side= 80 mi
c= hypotenuse= Greenville to Columbia mi
a^2 + b^2= c^2
68^2 + 80^2= c^2
square each number
4,624 + 6,400= c^2
11,024= c^2
take square root of both sides
104.995 mi= c
ANSWER: The distance from Greenville to Columbia is 104.995 miles (rounded to 105 miles).
Hope this helps! :)
9 miles, you dont even need much math, just common sense. divide 12 by 4 and you get three. multiply 3 by 3 to get 9.
