<span>First, the inequality needs to be solved. The first step is to subtract 8 from both sides of the inequality, leading to 5r < 55. Dividing 5 out from both sides, this will leave r < 11. Next, to form a set notation, the inequality is written in such form: {r | r < 11}.</span>
Answer:
-3
Step-by-step explanation:
coefficent of x enough to understand slope
Answer:
Step-by-step explanation:
A linear equation is written as 
, "m" being the slope and "b" being the y-intercept.
The slope is how many times you rise/run in order to get from one point on the line to the next. You rise (go up/down) 1 unit and run (go left/right) 3 units. Plug in the numbers and you get 1/3.
The y-intercept is where the graph lands on the y-axis, which is 4.
Answer:
Step-by-step explanation:
a. Since the parabola is compressed by a factor of 1/3 we can state:
- a parabola is written this way : y=(x-h)²+k
- h stands for the translation to the left ⇒ 2*3=6
- k for the units down ⇒4*3=12
So the equation is : y=(x-6)²+12
b.Here the parabola is stretched by a factor of 2 so we must multiply by 1/2
- We khow that a parabola is written this way : y=(x-h)²+k
- (h,k) are the coordinates of the vertex
- the maximum value is 7*0.5=3.5
- we khow tha the derivative of a quadratic function is null in the maximum value
- so let's derivate (x-h)²+k= x²+h²-2xh+k
- f'(x)= 2x-2h h is 1 since the axe of simmetry is x=1
- f'(x)=2x-2 ⇒2x-2=0⇒ x= 1
- Now we khow that 1 is the point where the derivative is null
- f(1)=3.5
- 3.5=(x-1)²+k
- 3.5= (1-1)²+k⇒ k=3.5
So the equation is : y=(x-1)²+3.5
7.
the maximum height is where the derivative equals 0
- h= -5.25(t-4)²+86
- h= -5.25(t²-8t+16)+86
- h=-5.25t²+42t-84+86
- h=-5.25t²+42t+2
Let's derivate it :
- f(x)= -10.5t+42
- -10.5t+42=0
- 42=10.5t
- t= 42/10.5=4
When the height was at max t=4s
- h(max)= -5.25(4-4)²+86 = 86 m
h was 86m
L = liz's age now
J = Jack's age now
L-1 and J-1 are their ages one year ago
L-1=3(J-1)
L-1=3J-3
L=3J-3+1
L=3J-2 (to be used later)
L+2 and J+2 are their ages in two years
L+2=2(J+2)
replace L by 3J-2
3J-2+2=2(J+2)
3J=2J+4
3J-2J=4
J=4 is Jack's age now
L-1=3(J-1)
L-1=3(4-1)
L-1=3*3
L-1=9
L=9+1
L=10 is Liz's age now
