The inequality that represents the range of k so that inequality 1 has real solution is -3 < k < 5
<h3>How to determine the range?</h3>
<u>Inequality 1</u>
x^2 + (k + 1)x + k + 4 > 0
The discriminant is calculated using
D = b^2 - 4ac
So, we have:
D = (k + 1)^2 - 4 * 1 * (k + 4)
Evaluate
D = k^2 + 2k + 1 - 4k - 16
This gives
D = k^2- 2k - 15
Factorize the equation
D = (k+ 3)(k -5)
Solve for k
k = -3 and k = 5
Express the k values as inequalities
-3 < k < 5
<u>Inequality 2</u>
The inequality cannot be read, because of the image quality
Read more about discriminant at:
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Answer:<em> 11 is a prime number, but 10 is not</em>
Step-by-step explanation:
Answer:
The expression that represents his total time is given by "t = 7.5/s" where s is his speed against the wind.
Step-by-step explanation:
In order to solve this problem we will assign a variable to Curtis speed on the first leg of the trip, this will be called "s". Since the speed on the first part is "s" and the speed on the second part is 20% higher, then the speed on the second part is "1.2s". Each leg of the course is 9 miles long, therefore the time it took to go each way is given by:
time = distance/speed
First part:
t1 = 9/s
Second part:
t2 = 9/1.2s = 7.5/s
The expression for the whole course is the sum of each, so we have:
t = t1 + t2
t = 9/s + 7.5/s
t = (9 + 7.5)/s = (16.5)/s
