They want the point D such that D is equally distant away from the three gates. Call the gates A, B, and C
They want
AD = BD = CD
If we draw a circle through those three points, then point D would be the center
This circle is known as the circumcircle as it goes through the three points
The center D is the circumcenter
So all you have to do is find the perpendicular bisector of two segments of the triangle, say of AB and BC. Then find where those perpendicular bisectors meet. That intersection would be point D.
Since we don't have actual numbers or coordinates to work with, we can't go further and actually find out where point D is located in terms of (x,y) coordinates. However, you can still get a good idea using a compass and straightedge.
Total students = 24
students earning an A= 14
Probability = 14/24 = 7/12
Answer:
34% = 272 students
100% = 272/34%
= 800 students
Step-by-step explanation:
to check whether the answer is correct
= 34% × 800
= 272 students
Answer + Explanation + Theory
When a number is divided by a number it results in a quotient and a remainder
E.g. 9 / 4 = 2 remainder 1
9 is the dividend
4 is the divisor
2 is the quotient
1 is the remainder
Same way when a polynomial is divided by a linear expression
E.g.
Ax^2 + bx + c / (x-b) = (x+a) + r
Which can be rearranged to
ax^2 + bx + c = (x+a)(x-b) + r
When x = - a or b, only the remainder is left since either (x+a)(x-b) is 0.
If x = - a or b is substituted into the polynomial and the value is 0 then there is no remainder,
This would suggest (x+a) or (x-b) are factors of the polynomial.
Now apply this logic to these questions
1. Let’s assume (x-4) is a factor, this would mean that when x=4 is substituted into the polynomial the answer would be 0.
This is the case, therefore the remainder is 0.
2. Having seen the logic above (applied using the remainder and factor theorem) the linear expression is a factor of the polynomial.
