Answer:
(a) x=5
(b) x= -1 1/3
(c) x= 1
Step-by-step explanation:
(a) (b) (c)
2(x-3)=4 −3(2x+1)=5 a(bx+c)=d
x−3=4/2 2x+1= − 5/3 d^1−1
x−3=2 2x= -5/3-3/3 d^0
x=2+3 2x= -5-3/3 x=1
x=5 2x= -8/3*2
x= -8/6
x= -4/3
Solve each of the equations independently, then determine if the are continuous or discontinuous.
15≥-3x [start here]
-5≤x [divide both sides by (-3). *Dividing by a negative number means the direction of the sign changes!]
x≥-5 [just turned around for analysis]
Next equation:
2/3x≥-2 [start here]
x≥-2(3/2) [multiply both sides of the equation by the reciprocal, 3/2)
x≥-3
So, (according to the first equation) all values of x must be greater than, or equal to -5.
(According to the second equation) all values of x must be greater than, or equal to -3.
So, when graphed on a number line, both equations graph in the same direction, so they are continuous.
Answer:
5.25 seconds
Step-by-step explanation:
When the ball hits the ground the height is zero
Equate f(t) to zero and solve for t , that is
- 16t² + 84t = 0 ← factor out - 4t from each term
- 4t(4t - 21) = 0
Equate each factor to zero and solve for t
- 4t = 0 ⇒ t = 0
4t - 21 = 0 ⇒ 4t = 21 ⇒ t = 
= 5.25
t = 0 is the time when the ball is kicked
t = 5.25 is the time taken for the ball to hit the ground
