THERE ARE 120 CHOCOLATES AND SOME BOXES. EACH BOX HOLDS 9 CHOCOLATES. WHAT IS THE LEAST AMOUNT OF BOXES THAT WILL BE NEEDED ?
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Answer:
Step-by-step explanation:
The standard form for a polynomial equation in its factored form is:
Where p and q are the zeros and a is the leading coefficient.
We know that the degree of the polynomial is 5.
We are also given roots at x=3 and x=-2. Hence, our factors are (x-3) and (x+2).
These have a multiplicity of two, so we will square them.
We also know that there is a root at x=4. Hence, the factor is (x-4). This has a multiplicity of 1.
Therefore, our polynomial is now:
We know that the y-intercept is 12. Therefore, if we substitute in 0 for x, we should get 12 for y. Here, we are solving for our a. Therefore:
Evaluate:
Evaluate:
Divide both sides by -144:
Hence, our entire polynomial is:
Given:
Point B has coordinates (4,1).
The x-coordinate of point A is -4.
The distance between point A and point B is 10 units.
To find:
The possible coordinates of point A.
Solution:
Let the y-coordinate of point A be y. Then the two points are A(-4,y) and B(4,1).
Distance formula:
The distance between point A and point B is 10 units.
Taking square on both sides, we get
Taking square root on both sides, we get
and
and
Therefore, the possible coordinates of point A are either (-4,-5) or (-4,7).