Answer: x ≥ 3.2 OR x ≤ -0.75
Here's how to solve the compound inequality step-by-step: start by separating it into two inequalities. For the first one, 5x - 4 ≥ 12, add 4 to both sides to remove the constant, leaving 5x ≥ 16. Then divide both sides by 5 to isolate x, resulting in x ≥ 3.2.
Now for the second part, 12x + 5 ≤ -4, subtract 5 from both sides to obtain 12x ≤ -9. Dividing both sides by 12 gives x ≤ -9/12, which simplifies to x ≤ -0.75. So, combining both, the solution is x ≥ 3.2 OR x ≤ -0.75.
Response:
$3,000
Detailed breakdown:
This scenario is centered around compound interest, with the formula for compound interest defined as
Provided Data
A = final amount =?
P = initial principal balance = $2,500
r = interest rate
= 2.1%= 0.021
t = number of time units passed= 14 years
By inserting our data into the compound interest equation, we can determine the final amount
Therefore, rounding to the nearest hundred gives us an account balance of $3,000
Answer:
Step-by-step explanation:
Given:
- Fuel volume = 5/6
- Each trip uses fuel = 1/12
- Number of trips to work = x
Since 1/12 of the tank is used for each trip and the starting volume is 5/6, the equation can be represented as:
By solving the equation, we find:
This means Felitz can make 10 trips to/from work with a tank filled to 5/6.
Great Red Spot
Why does this joke keep lingering in my mind??
Step-by-step explanation:
The benefits of representing the polynomial expression
-7
+ 32x + 240 in its factored form for analyzing this
scenario
Factoring the quadratic expression results in
-7 + 32x + 240
-7 + 60x - 28x + 240
x×(-7x + 60) - 4×(-7x + 60)
(x-4)×(-7x + 60)
The equation's roots are noted as 4,-60/7
Benefits of representing the polynomial expression in factored form:
- the roots are readily identifiable
- graphing the quadratic becomes straightforward
