Let x be the time she ran and y be the time she walked
then distance ran = 25x and distance walked = 5y
so 15x + 5y = 42
and x + y = 4
* second equn. by -5:-
-5x - 5y = -20
add this to the first equn:0
10x = 22
x = 2.2
distance she ran = 2.2 * 15 = 33 km
H(t)=-16t^2+15t+12
(e)
maximum height is reached when h'(t)=-32t+15=0, or tm=15/32 seconds.
maximum height reached = h(tm)=h(15/32)=-16(15/32)^2+15(15/32)+12
=993/64 ft
=15.516 ft.
(f) when Greg reaches water, h(t)=0=-16t^2+15t+12
Solve for t using quadratic formula,
t=[-15+/- sqrt(15^2+4*12*16)]/(2*-16)
=-0.516s or 1.4535s.
Reject negative root so
Greg reaches water at t=1.4535 seconds.
Answer:
Option D is correct .i.e., Vertical translation down 9 units
Step-by-step explanation:
Given Function is y = cosec x - 9
Here basic function or parent function is y = cosec x
1. When constant ' a ' is added to to parent function or basic function then the function is translated vertically upward by a units.
2. When constant ' a ' is subtracted from parent function or basic function then the function is translated vertically downward by a units.
Therefore, Option D is correct .i.e., Vertical translation down 9 units
Answer:
D) infinitely many solutions
Step-by-step explanation:
5 ( x-3 ) - 3x = 8x - 15 - 6x
5x - 3x - 15 = 8x - 6x - 15
2x - 15 = 2x - 15
2x = 2x
Since, equations of both lines are same. Therefore, there are infinitely many solutions.
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m represents the slope of the line
c represents the y intercept
The equation of the given line is
2x + 4y = 20
4y = - 2x + 20
Dividing through by 4, it becomes
y = - x/2 + 5
Comparing with the slope intercept form, slope = - 1/2
If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (- 6, 3) is - 1/2
To determine the y intercept, we would substitute m = - 1/2, x = - 6 and y = 3 into y = mx + c. It becomes
3 = - 1/2 × - 6 + c
3 = 3 + c
c = 3 - 3 = 0
The equation becomes
y = - x/2
