Answer:
The total allowance is $18.5, and the amount spent daily is $3.2
Step-by-step explanation:
let T and x represent the total allowance and the amount spent daily respectively.
It was started that the amount remaining after 2 days is $12.10 , which implies the person has spend an equal amount for 2 days
T - 2x =12.10 (equation 1)
It was started that the amount remaining after 5 days is $2.50 , which also implies the person has spend an equal amount for 5 days
T - 5x =2.5 (equation 2)
subtract equation 2 from 1
T - 2x -( T - 5x ) = 12.10 -2.5
T - 2x -T + 5x = 9.6
3x =9.6
Divide both side by 3
x = 9.6/3 =3.2
from equation 1
T - 2x =12.10
T = 12.10 + 2x = 12.10 + 2*3.2
= 12.10 + 6.4 = 18.5
Answer:
Local minimum at x = 0.
Step-by-step explanation:
Local minimums occur when g'(x) = 0 and g"(x) > 0.
Local maximums occur when g'(x) = 0 and g"(x) < 0.
Set g'(x) equal to 0 and solve:
0 = 2x (x − 1)² (x + 1)²
x = 0, 1, or -1
Evaluate g"(x) at each point:
g"(0) = 2
g"(1) = 0
g"(-1) = 0
There is a local minimum at x = 0.
If you would like to write and solve a system of equations that represent the situation above, you can do this using the following steps:
s ... number of songs
m ... number of movies
$55.00 = $1.25 * s + $2.75 * m
55 = 1.25 * s + 2.75 * m
26 songs and movies = s + m
26 = s + m
s = 26 - m
55 = 1.25 * s + 2.75 * m
55 = 1.25 * (26 - m) + 2.75 * m
55 = 1.25 * 26 - 1.25 * m + 2.75 * m
55 - 32.5 = 1.5 * m
22.5 = 1.5 * m
m = 22.5 / 1.5 = 15 movies
s = 26 - m = 26 - 15 = 11 songs
The correct result would be 15 movies and 11 songs.
Answer:
x=-7/9, y=4/3. (-7/9, 4/3).
Step-by-step explanation:
6x+2y=-2
3x-2y=-5
-----------------
9x=-7
x=-7/9
6(-7/9)+2y=-2
-42/9+2y=-2
2y=-2-(-42/9)
2y=-2+42/9
2y=-18/9+42/9
2y=24/9
y=(24/9)/2
y=(24/9)(1/2)
y=24/18
y=4/3
1h 35min + 1h 35min = 3h 10min
