(18x^3 + 12x^2 -3x)/6x^2
What is the coefficient of x in this division
Nah, 18 x^3 / 6 x^2 = 3 x
so 3
You are correct. I apologize for the mistake in my previous response.
Dividing 18x^3 by 6x^2 gives us 3x, which means the coefficient of x in the expression (18x^3 + 12x^2 - 3x) / 6x^2 is 3.
(3b^2+13b+4)/(b+4)
What is the undefined value
The undefined value in this expression is b = -4.
This is because when we substitute b = -4 into the denominator (b + 4), we get 0 in the denominator. Division by 0 is undefined.
John walked 10 miles on Saturday. He walked twice as fast on the second 5 miles of his walk than he walked on the first 5 miles of his walk. Which expression represents the time he spent walking? Let x = John's speed on the first half of his walk.
If John walked 10 miles total, and the second 5 miles were walked at twice the speed of the first 5 miles, we can set up the following equation:
5/x + 5/(2x) = t
Here, t represents the time it took for John to walk the entire distance. The first term (5/x) is the time it took for John to walk the first 5 miles, where x is his speed during this portion of the walk. The second term (5/(2x)) is the time it took for John to walk the second 5 miles, where his speed was twice that of the first 5 miles.
We can simplify this equation by finding a common denominator for the two fractions:
5/x + 5/(2x) = (10/2x) + (5/x)
Combining like terms, we get:
5/x + 5/(2x) = (15/x) + (10/2x) = (25/x)
So the simplified equation for the time it took for John to walk the entire distance is:
(5/x) + (5/(2x)) = (25/x)
Therefore, the expression that represents the time he spent walking is (5/x) + (5/(2x)).
The coefficient of x in this division is -1/2.
To find this coefficient, we need to simplify the expression first:
(18x^3 + 12x^2 - 3x) / 6x^2 = 3x(6x^2 + 4x - 1) / 6x^2
We can now cancel out the 6 in the numerator and denominator:
3x(6x^2 + 4x - 1) / 6x^2 = x(6x^2 + 4x - 1) / 2x
This expression can be further simplified by dividing each term by 2x:
x(6x^2 + 4x - 1) / 2x = 3x^2 + 2 - 1/2x
The coefficient of x is the number in front of x in this simplified expression, which is -1/2.