Answer:
x = -1
Step-by-step explanation:
Solve for x:
12 = 24 - 4 (-6 x - 3)
-4 (-6 x - 3) = 24 x + 12:
12 = 24 x + 12 + 24
Grouping like terms, 24 x + 12 + 24 = 24 x + (12 + 24):
12 = 24 x + (12 + 24)
12 + 24 = 36:
12 = 24 x + 36
12 = 24 x + 36 is equivalent to 24 x + 36 = 12:
24 x + 36 = 12
Subtract 36 from both sides:
24 x + (36 - 36) = 12 - 36
36 - 36 = 0:
24 x = 12 - 36
12 - 36 = -24:
24 x = -24
Divide both sides of 24 x = -24 by 24:
(24 x)/24 = (-24)/24
24/24 = 1:
x = (-24)/24
The gcd of -24 and 24 is 24, so (-24)/24 = (24 (-1))/(24×1) = 24/24×-1 = -1:
Answer: x = -1
#16: Let's clear the fraction on the way to solving this inequality for x. By mult. the given inequality by 2, we'll get -2 (is greater than) x+4. We want x to be positive. So, leave it where it is. Subtract 4 from both sides of this inequality. We end up with -6 (is greater than) x, which is the same thing as x (is less than) -6. What would the graph of that simple inequality look like?
Graph it. (Hint: The graph is a straight dashed line, and you must shade one side of it, but not the other side.
Answer:
Covered: $3712
Still need to pay: $928
Step-by-step explanation:
4/5 --> 0.8 --> 80%
4640 x 0.8 --> 3712
Covered: $3712 (which is 80%)
Still need to pay: $928 (which is 20%)
Answer: r = 4cm/θ
Step-by-step explanation:
For a circle of radius R, the perimeter is:
P = 2*pi*R
Now, if we have an arc with an angle θ, the cord of this arc is:
C = (θ/2*pi)*2*pi*R
Where you can see that if θ = 2*pi (this is the full circle) we have the perimeter of the circle.
In this case, we can see that the cord for an angle θ is 4cm, then:
C = 4cm = (θ/2*pi)*2*pi*r = θ*r
Now we can solve this for r:
r = 4cm/θ
