Answer:
Step-by-step explanation:
1. Equation of a circle:
(x - h)² + (y - k)² = r²
where (h, k) is the center and r is the radius.
If (h, k) is (2, 8) and r = 10:
(x - 2)² + (y - 8)² = 100
2. The vertex and focus have the same x-coordinate, so this is a vertical parabola. Equation of a vertical parabola is:
y = 1/(4p) (x - h)² + k
where (h, k) is the vertex and p is the distance from the vertex to the focus.
If (h, k) is (2, 2) and p = 5-2 = 3:
y = 1/12 (x - 2)² + 2
3. The directrix is a vertical line, so this is a horizontal parabola. Equation of a horizontal parabola is:
x = 1/(4p) (y - k)² + h
The distance between the directrix and the vertex is the same as p.
If (h, k) is (5, 2) and p = 5-3 = 2:
x = 1/8 (y - 2)² + 5
Answer:
7
Step-by-step explanation:
Step 1:
18 - 5w + 7w - 4 = 28
Step 2:
14 + 2w = 28
Step 3:
2w = 14
Answer:
w = 7
Hope This Helps :)
The correct answer is D.
In fact, when written in the form , represents the slope of the line, and two lines are parallel if they have the same slope.
In this case, the slopes are not the same (they are and , respectively), so option C is wrong.
And neither they are the same line, because the equations are different, so option A is wrong as well.
Finally, the lines intersect, because if you ask
you get
and so is the point of intersection, and option B is wrong as well.
The standard formula for a parabola are
(x-h)^2 = +/- 4a (y-k) or (y-k)^2 = +/- 4a(x-h)
where
(h,k) is the coordinates of the vertex
a is the length of the focus from the vertes
+4a if the parabola opens upwards or to the right
-4a if the parabola opens downwards or to the left
The vertex (2,13) is situated in the 1st quadrant of the Cartesian plane. It only has y-intercept. This means that it only passes the y-axis once. Therefore, the parabola must open downwards and it passes the x-axis twice. The intersections at the x-axis are the x-intercepts. If the parabola has 2 x-intercepts, then the equation would be (x-h)^2 = -4a(y-k).
Let's use the y-intercept (0,5) to determine 4a:
(0-2)^2=-4a(5-13)
4a = 0.5
Therefore, the equation of the parabola is (x-2)^2 = -1/2(y-13). To find the x-intercepts, let y=0.
(x-2)^2 = -1/2(0-13) = 6.5
x-2 = +/- √6.5 = +/- 2.55
x = 4.55 and and -0.55
The x-intercepts are (-0.55,0) and (4.55,0).
Answer:
60%
Step-by-step explanation:
15 of the 25 students are boys
number of boys over the total number of students in the class multiplied by 100% gives the percentage of boy students in the class
=15/25 ×100%
=60%