Rates like $ per channel is a slope, "m". The added fee is a constant so it's the intercept "b".
y = mx + b
So for the first problem (9)
(a)
y = total cost in dollars
x = number of premium channels
y = 16x + 44
(b) when x = 3 channels
y = 16(3) + 44
y = 92 $
the second problem (10)
(a) every 4 years the tree grows by 12-9=3 ft
So the unit rate or slope will be 3 ft per 4 yrs, (3/4). You can see this also by solving for slope "m" using the given points (4,9) and (8,12).
x = number of years
y = height of tree in ft
y = (3/4)x + b
use one of the points to find the y-intercept "b".
9 = (3/4)(4) + b
9 = 3 + b
9 - 3 = b
6 = b
y = (3/4)x + 6
(b) when x = 16
y = (3/4)(16) + 6
y = 12 + 6
y = 18 ft
Answer:
Step-by-step explanation:
We khow that the equation of a circle is written this way :
(x-a)²+(y-b)²=r² where (x,y) are the coordinates of the cercle's points and (a,b) the coordinates of the cercle's center and r the radius .
Our task is to khow the values of a and b :
- We khow that the center is lying on the line 3x+2y=16⇒ 2y=-3x+16⇒ y=
x+8 - We khow that the points P and Q are two points in the cercle
- Let Ω be the center of this cercle
- we can notice that : PΩ AND QΩ are both equal to the radius ⇒ PΩ=QΩ= r
- So let's write the expression of this distance using vectors KHOWING THAT Ω(a,b)
- Vector PΩ(a-4,b-6) and Vector QΩ(a-8,b-2)
- PΩ=
and QΩ=
- Let's substitute a by x and b by y
- PΩ=QΩ we substitute each distance by its expression
- After simplyfying the expressions we get finally : -12+8x-8y=0
- now we have -12x +8x-8y=0 and the line equation 3x+2y-16=0
- these are simultanious equations so after solving them we get x=3.8 wich is approximatively 4 and y=2
- we substitute a by 4 and y by 2 in PΩ to get the radius
- we get r =
= 4 - so r²= 16
- then the equation is : (x-4)²+(y-2)²=16
Answer: −12f+6g
Step-by-step explanation: