Answer:x>7 or x ≤ -3
Solving the 1st inequality
-6x +14 < -28 --------------- (Collect like terms)
-6x < -28 - 14
-6x < - 42 -------------------- (Divide both sides by -6)
Note: If you decide an inequality expression by a negative value, the inequality sign changes)
-6x/-6 > -42/-6
x > 7
Solving the 2nd inequality
9x + 15 ≤ −12 ----------- (Collect like terms)
9x ≤ −12 - 15
9x ≤ −27 ------------------(Divide both sides by 9)
9
9x/9 ≤ −27/9
x ≤ -3
Bring both results together, we get
x>7 or x ≤ -3
The final result is complex (i.e. can't be combined together).
Step-by-step explanation:
Keep in mind that, when the logarithm base is not explicitly written, base 10 is assumed, therefore,
Answer:
C
Step-by-step explanation:
The sum to n terms of a geometric sequence is
= 
Here a₁ = 4 and r = - 3, thus
= 
= 
= - (729 - 1) = - 728 → C
Answer:
23
Step-by-step explanation:
The sides of a square are all the same length, so if 3 of them total 48, one of them must be 48/3 = 16.
If the length of the rectangle is 7 longer than the side of the square, it is
... 16 + 7 = 23
The probability of an event is given by the number of favorable outcomes divided by the total number of outcomes. Here the event is the alarm clock running out of power. There are 24 hours during which the power can go out. You are asleep during 8 of these. A "favorable" outcome in this case is the power going out while you are sleeping -- that is, during one of those 8 hours. This makes the probability that the power goes out while you are sleeping 8/24.
