Answer:
![g(x)=f(x)+2](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%29%2B2)
is shifted 2 units upwards to become ![g(x)](https://tex.z-dn.net/?f=g%28x%29)
Step-by-step explanation:
Given functions:
![f(x)=4x](https://tex.z-dn.net/?f=f%28x%29%3D4x)
![g(x)=4x+2](https://tex.z-dn.net/?f=g%28x%29%3D4x%2B2)
On comparing the functions we find out that:
![g(x)=f(x)+2](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%29%2B2)
The translation rule for this is given as:
If
the function shifts
units to the up.
If
the function shifts
units to the down.
Thus we can see the unit shift from
to
is 2 units upwards as 2 is being added to function ![f(x)](https://tex.z-dn.net/?f=f%28x%29)
Answer:
q = 4
Step-by-step explanation:
given p and q vary inversely then the equation relating them is
p =
← k is the constant of variation
to find k use the condition p = 29 when q = 16 , then
29 =
( multiply both sides by 16 )
464 = k
p =
← equation of variation
when p = 116 , then
116 =
( multiply both sides by q )
116q = 464 ( divide both sides by 116 )
q = 4
Answer: Spain, France, Britain
Step-by-step explanation:
Answer:
x = 12
Step-by-step explanation:
In a pair of intersecting lines the vertically opposite angles are equal.
(6x + 7)° = (8x - 17)°
6x + 7 = 8x - 17
Subtract 8x + 7 from both sides:
6x + 7 - (8x + 7) = 8x - 17 - (8x + 7)
(6x - 8x) + (7 - 7) = (8x - 8x) + (-17 - 7)
6x - 8x = -2x:
-2x + (7 - 7) = (8x - 8x) + (-17 - 7)
7 - 7 = 0:
-2x = (8x - 8x) + (-17 - 7)
8x - 8x = 0:
-2x = -17 - 7
-17 - 7 = -24:
-2x = -24
Divide both sides by -2:
![\sf \dfrac{-2x}{-2} = \dfrac{-24}{-2}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cdfrac%7B-2x%7D%7B-2%7D%20%3D%20%5Cdfrac%7B-24%7D%7B-2%7D%20)
![\sf \dfrac{-2}{-2} = 1](https://tex.z-dn.net/?f=%20%5Csf%20%5Cdfrac%7B-2%7D%7B-2%7D%20%3D%201%20)
![\sf x = \dfrac{-24}{-2}](https://tex.z-dn.net/?f=%20%5Csf%20x%20%3D%20%5Cdfrac%7B-24%7D%7B-2%7D%20)
![\sf \dfrac{-24}{-2} = 12](https://tex.z-dn.net/?f=%20%5Csf%20%5Cdfrac%7B-24%7D%7B-2%7D%20%3D%2012%20)
x = 12