Jack is running for city mayor. He stops the first 10 people on the street and asks them what their biggest concern for the city
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Answer:
-3, 1, 4 are the x-intercepts
Step-by-step explanation:
The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).
In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.
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For the given polynomial, we notice that the sum of the coefficients is zero:
1 -2 -11 +12 = 0
This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.
Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...
f(x) = (x -1)(x² -x -12)
We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...
f(x) = (x -1)(x -4)(x +3)
Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.
The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.
The acceleration of the bookshelf is equal to 1.30
<u>Given the following data:</u>
- Mass of bookshelf = 51.5 kilogram
- Net force = 67 Newton
To determine the acceleration of the bookshelf, we would apply Newton's Second Law of Motion:
Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on the object while being inversely proportional to its mass.
Mathematically, Newton's Second Law of Motion is given by this formula;
Substituting the given parameters into the formula, we have;
Acceleration = 1.30
Read more on net force here: brainly.com/question/1121817