4(x – 3) + 4 < 10 + 6x
Distribute the 4 on the left side.
4x -12 +4 < 10 + 6x
Combine like terms on the left side.
4x-8<10 +6x
Subtract the 6x from both sides.
-2x -8<10
Add the 8.
-2x <18
Divide by -2 & flip the inequality symbol (it's a math rule which states that if you multiply or divide by a negative, you must flip the inequality symbol).
x> -9
That's your final answer.
It's the same thing, the different is depends in which side was x
ANSWER: 1 is a subset of 3,5,7
Answer:
(1) F(n) = 8050 -400n
(2) 16 days
Step-by-step explanation:
Tylor first day he has left 7,250feet left to climb, this means that he has already climbed his 400ft on his first day
This will produce an arithmetic series for the distances left to climb as each day passes
initial climb = 7,250+400 = 7,650
Arithmetic Series
7650 , 7250 , 6850 , 6450 ......
a = 7650 , d = -400
(1) Explicit formula
F(n) = a + (n-1)d
= 7650 + (n-1)(-400)
= 7650 +400 -400n
F(n) = 8050 -400n
(2) 8050 -400n = 1750
6300 = 400n
n = 6300 /400 = 15.75 = 16 days( approximately)
So after 16days (approximately) Taylor will have 1750ft left to climb.
Answer:
the x-intercepts are (5, 0) and (-3, 0).
Step-by-step explanation:
The standard equation of a vertical parabola with vertex at (h, k) is
y = a(x - h)^2 + k.
Here we are told that the vertex is at (1, -16), which means that h = 1 and y = -16. Thus, we have:
y = a(x - 1)^2 + (-16).
We are told also that the graph passes through (0, -15). Substituting -15 for y and 0 for x, we get:
-15 = a(0 - 1)^2 - 16, or
-15 = a - 16
Then a must be 1, and the equation of the parabola is
y = (x - 1)^2 - 16.
Now to find the x-intercepts: Set y = 0 and solve for x:
0 = (x - 1)^2 - 16, or
(x - 1)^2 = 16, or
x - 1 = ±√16 = ±4
Then x = 1 ± 4, or x = 5 or x = -3, so the x-intercepts are (5, 0) and (-3, 0).
