Answer:
C
Step-by-step explanation:
Solving the inequality
2(x - 2) - 4x > 4 ← distribute and simplify left side
2x - 4 - 4x > 4
- 2x - 4 > 4 ( add 4 to both sides )
- 2x > 8
Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity
x < - 4
The only value from the list less than - 4 is - 5
Thus a solution to the inequality is x = - 5
Answer:
The probability that if a person is chosen at random has run to red light in the last year is 60%.
Step-by-step explanation:
Since a group of people were asked if they had run a red light in the last year, and 456 responded "yes", and 304 responded "no", to find the probability that if a person is chosen at random, they have run a red light in the last year, the following calculation must be performed:
456 + 304 = 760
760 = 100
456 = X
456 x 100/760 = X
45600/760 = X
60 = X
Therefore, the probability that if a person is chosen at random has run to red light in the last year is 60%.
Our goal is to isolate n. In order to do this, we must first get rid of the 15 on the left side of the equation.
To achieve this result, we must do the inverse of the operation on both sides of the equation. In other words, subtract 15 from both sides.
8n + 15 - 15 = 25 - 15
8n = 10
Now we must get rid of the 8, by again doing the inverse of the operation. Since 8 is multiplying n, we must divide it into both sides.
8n / 8 = 10 / 8
n = 1.25
Hopefully, this helps!
We are going to solve this problem two ways:
Solution 1. Graphical
If you plot the equation of temperature
for x between 0 and 160 minutes you'll get the plot in the attachement.
The blue curve represents the variation of the temperature in time. Notice that it crosses the red line (132 degrees <span>Fahrenheit</span>) twice, at around 20 F and 70 F.
So the answer is yes, if will reach 132 F.
Solution 2. Analytical
In order to see if the variation of temperature y(x) intersects 132 F line means to solve the equation:
Step 1. Write the equation in the quadratic form:
Step 2. Calculate the discriminant:
Only by looking at the discriminant we can see that it is positive, which means that it crosses the 132 F line in two points, which also means that there are two roots of the equation, both real numbers.
Step 3 (optional). Calculate the roots of the equation.
As you can see, tha analytic solution matches the graphic solution. At time x=20.5 minutes the temperatures reaches 132 F and is still rising. At time x=69.5 minutes the temperature is again 132 F but this time is decreasing.