Answer:
x = 20
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Using ΔAHC , then
∠ACH = 180 - (2x + 100) = 180 - 2x - 100 = 80 - 2x
∠ECD = ∠ACB ( vertical angles are congruent ), thus
∠ECD = ∠ACH + ∠HCB, that is
3x = 80 - 2x + x
3x = 80 - x ( add x to both sides )
4x = 80 ( divide both sides by 4 )
x = 20
If 5x - 17 ≥ 0, then |5x - 17| = 5x - 17 and the equation reduces to
-8 - 2 (5x - 17) = -14
-8 - 10x + 34 = -14
-10x = -40
x = 4
If 5x - 17 < 0, then |5x - 17| = -(5x - 17) = -5x + 17 and we have
-8 - 2 (-5x + 17) = -14
-8 + 10x - 34 = -14
10x = 28
x = 2.8
$281 = 5%
The total amount would be $5,620
Answer:
The mean for the second week is $2 less than the first and in percentage it is 22% less.
Step-by-step explanation:
The mean is given by the sum of all individual values divided by the number of values. For the first week the sum is:
sum1 = 6.5 + 8 + 7.25 + 13.5 + 9.75
sum1 = 45
Since she spent 10 less in the second week the sum is:
sum2 = sum1 - 10 = 45 - 10 = 35
The mean for each week is:
mean1 = sum1/5 = 45/5 = 9
mean2 = sum2/5 = 35/5 = 7
difference = mean1 - mean2 = 9-7 = 2
difference(%) = [2/9]*100 = 0.22*100 = 22%
The mean for the second week is $2 less than the first and in percentage it is 22% less.
A system is inconsistent when there are no solutions between the two equations. Graphically, the lines will be parallel (they never meet!) and the slopes will be the same. But the y-intercepts will be different.
Let's look at the four equations, with each solved as needed, into y = mx + b form.
A: 2x + y = 5
y = 5 - 2x
y = -2x + 5
Compared to y = 2x + 5, the slopes are different, so this system won't be inconsistent. Not a good choice.
B: y = 2x + 5
Compared to y = 2x + 5, the slopes are the same and the y intercepts are the same. This system has infinitely many solutions. Not a good choice.
C: 2x - 4y = 10
-4y = 10 - 2x
-4y = -2x + 10
y = 2/4x -10/4
Here the slopes are different, so, like A this is not a good choice.
D: 2y - 4x = -10
2y = =10 + 4x
2y = 4x - 10
y = 2x - 5
Compared to y = 2x + 5 we have the same slopes and different y intercepts. The lines will be parallel and the system is inconsistent.
Thus, D is the best choice.
