Answer:1/3
Step-by-step explanation:
Answer:
Step-by-step explanation:
True
Answer:
Carter family = 25 hours
Davis family = 31 hours
Step-by-step explanation:
Let's say the number of hours the Carter family used their sprinkler is x and the number of hours the Davis family used their sprinkler for is y.
So combined:
x + y = 45 hours
and we are also told that:
40x + 15y = 1300 L
So we can do simultaneous equations to solve the problem.
With some rearranging, we can figure out that:
y= 45 - x
and by substituting that into the second equation:
40x + 15 (45 -x) = 40x + 675 - 15x = 1300L
25x = 1300 - 675
25x = 625
x = 25 = hours that the Carter family used their sprinkler
and we can substitute that back into the original equation to find how many hours the Davis family used their sprinkler so:
25 + y = 56
y = 31
The Davis family used their sprinkler for 31 hours whilst the Carter family used their sprinkler for 25 hours.
Answer:
80 m^2
Step-by-step explanation:
The given information lets you write two equations involving length (x) and width (y).
- 2(x +y) = 36 . . . . the perimeter is 36 m
- (x+1)(y+2) -xy = 30 . . . . increasing the length and width increases area
The second of these equations simplifies to another linear equation, giving a system of linear equations easily solved.
xy +y +2x + 2 -xy = 30
2x +y = 28 . . . . . . . subtract 2
Dividing the first equation by 2 gives
x +y = 18
and subtracting this from the above equation gives ...
(2x +y) -(x +y) = 28 -18
x = 10
Then
y = 18 -10 = 8
The area of the original rectangle is xy = 10·8 = 80 m^2.
Step-by-step explanation:
Let us consider the task to find the angle between vectors ES and EJ (the first letters are taken to name the vectors).
\overrightarrow{ES} = (4;4) - (4; -3) = \overrightarrow{(0; 7)}
ES
=(4;4)−(4;−3)=
(0;7)
\overrightarrow{EJ} = (-5; -4) - (4; -3) = \overrightarrow{(-9; -1)}
EJ
=(−5;−4)−(4;−3)=
(−9;−1)
cos \alpha=\frac{\overrightarrow{ES}*\overrightarrow{EJ}}{|\overrightarrow{EJ}|*|\overrightarrow{ES}|}cosα=
∣
EJ
∣∗∣
ES
∣
ES
∗
EJ
cos(a) = (0*(-9)+7*(-1)) / (7*9.055) = -0.11043;
a = 96,34°
Solution: 96 degrees.
