Answer: 286 minutes
Step-by-step explanation:
x : # of months that has gone by
0.24x : cost of the 24 cent plan after "x" minutes
39.95 + 0.10x : cost of the 10 cent plan after "x" minutes
1. 39.95 + 0.10x > 0.24x
2. 39.95 > 0.24x - 0.10x
3. 39.95 > 0.14x
4. 285.36 > x
x must be AT LEAST 286 minutes for plan #2 (39.95 + 0.10x) to be a better deal
Since A is the midpoint of BC, we can assume BA and AC are equal to each other.
We also know that BC = BA + AC = 23 + 23 = 46
JK = MN because of Given
∠JLK = ∠MLN because of the vertical angle theorem
JL = LN because of definition of midpoint
ΔJLK = MLN because of SAS
∠K = ∠N because corresponding angles of congruent triangles are congruent.
Hope this helps!<span />
Answer:
yes
Step-by-step explanation:
The line intersects each parabola in one point, so is tangent to both.
__
For the first parabola, the point of intersection is ...
y^2 = 4(-y-1)
y^2 +4y +4 = 0
(y+2)^2 = 0
y = -2 . . . . . . . . one solution only
x = -(-2)-1 = 1
The point of intersection is (1, -2).
__
For the second parabola, the equation is the same, but with x and y interchanged:
x^2 = 4(-x-1)
(x +2)^2 = 0
x = -2, y = 1 . . . . . one point of intersection only
___
If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.
_____
Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.
Enrolement increased by 30% that means last year=100%
incease of 30%=30+100=130% now
now=182
percent means parts out of 100 so
130%=130/100=13/10
182=13/10 of x (x represents the number last year)
of means multipy so
182=13/10 times x
multiply both sides by 10/13 to clear fraction
182 times 10/13=x=140
140 students last year