The vertex of a parabola is at $(12, -4)$, and its axis of symmetry is vertical. One of the $x$-intercepts is at $(15, 0)$. What
is the $x$-coordinate of the other $x$-intercept?
1 answer:
Answer:
9
Step-by-step explanation:
Since the axis of symmetry is vertical and the vertex of the parabola is at (12,-4), the vertical line x=12 is the axis of symmertry. The x-distance between the axis of symmetry and the first x intercept (15,0) is equal to 15-12=3. Hence, this x-intercept is 3 units to the right of the axis, and because it is symmetric, the other x-intercept must be 3 units to the left of the axis, so its x-coordinate must be 12-3=9. Then, the other x-intercept is at the point (9,0)
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Answer:
40 students
Step-by-step explanation:
In this problem, one is given the ratio ( 8 : 3 ), since a ratio is another way of writing a fraction one can rewrite it as; (8) represent the number of students who want to learn about magnets, and (3) represents the number of students who want to learn about magic tricks.
In the problem, it is also given that 25 more students wanted to learn about magnets compared to magic tricks. If one uses the parameter (x) to represent the factor by which the fraction is reduced, then one can get the equation;
8x = 3x + 25
Use inverse operations to solve,
8x = 3x + 25
-3x
5x = 25
/5
x = 5
Substitute back in to find out how many students want to learn about magnets,
8x
= 8(5)
= 40