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Rainbow [258]
2 years ago
13

For how many integers $n$ does the inequality $x^2 + nx + 15 < 0$ have no real solutions $x$?.

SAT
1 answer:
Rom4ik [11]2 years ago
3 0

By making the determinant equal to or smaller than zero, we will see that there are 15 values of n such that the inequality has no real solution.

<h3>Solving the inequality:</h3>

Here we have the inequality:

x^2 + n*x + 15 < 0

We want to see for which values of n we don't have real solutions.

Now, we can write the quadratic equation:

y = x^2 + nx + 15.

If the determinant of this quadratic equation is negative or 0, then we have a single root or we don't have roots, and because the leading coefficient is positive, that would mean that the function never becomes negative. Then for these cases, the inequality has no real solutions.

Then we must have:

n^2 - 4*15*1  ≤ 0

Now we can solve this for n.

n^2 ≤ 60

Then if n^2  is smaller than 60, we don't have real solutions, and we know that:

√60 = 7.75

Then we have:

-7.75 ≤ n ≤ 7.75

But n can only be an integer, so we can write:

-7  ≤ n ≤ 7

From -7 to 7 there are 15 integers, then there are 15 values of n such that the inequality has no real solutions.

If you want to learn more about inequalities, you can read:

brainly.com/question/11234618

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Julia, ernesto y pablo están esperándolo. (julia, ernesto y pablo are waiting for it (the bus).)
Eddi Din [679]

Julia, Ernesto y Pablo are waiting for it (the bus).) is a correct statement.

<h3>What is the statement about?</h3>

The statement Julia, Ernesto y Pablo están esperándolo is a response to a previously given question which is Julia, Ernesto and Pablo are waiting for him in English.

Julia, Ernesto y Pablo are waiting for it the bus is also known to be the response to the first question and as such the tenses are correct.

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6 0
2 years ago
A 3-column table with 2 rows. The first column is labeled Gender with entries Men and Women. The second column is labeled Percen
Semenov [28]

Answer:

I DONT KNOW DO YOU WANT TO BE MY FRIEND I DONT KNOW DO YOU WANT TO BE MY FRIEND

Explanation:

3 0
2 years ago
According to research by fergus i. M. Craik and endel tulving on levels of processing, which of the following would most improve
Vesnalui [34]

According to the levels of processing, deciding whether an umbrella would be useful to pack for a trip, would most improve the ability to recall the word "umbrella". This model focuses on the depth of processing in memory.

The 'levels of processing' is a model developed by the cognitive psychologists F. Craik and R. Lockhart in 1972.

This model (levels of processing model) puts focus on the depth of processing developed for memory tasks.

This model can be used to predict how information is processed, where memory can be considered as an outcome of processing information.

Learn more about the levels of processing here:

brainly.com/question/5475845

8 0
2 years ago
Who is Sajan Bajgain?
exis [7]

Explanation:

Sajan Bajgain?

Sajan Bajgain is a Computer Programmer, IT Professional, and Technology researcher from Nepal. He was born on April 18 2000 A.D in Kavrepalanchowk District. His interest on computer science is very high. He always keep researching new technologies and enthusiasts to learn how things actually work.He has written blogs on topics like cybersecurity, machine learning, artificial intelligence, programming, etc. His main work area is Database administration, Network Administration and System Administration.

8 0
3 years ago
How much would you pay in move-in costs for the two-bedroom hometown apartment if you pay first and last month's rent, a $185 se
Darina [25.2K]

The total rent payed for the apartment =

$1,370

<h3>Calculation of move-in cost </h3>

The complete question:

How much would you pay in move-in costs for the two-bedroom hometown apartment if you pay first and last month's rent, a $185 security deposit, and a 30 percent fee to the rental agent? round to the nearest dollar

2 bedroom hometown: $515 plus utilities

$1,515 $1,370 $1,245 $855

The cost of 2 bedroom apartment = $515 ×2 = $1,030

The security deposit= $185

The rental agent fee = 30/100× 515

= 15,450/100 = $154.5

Therefore the total rent payed for the apartment

= $1,030 + $185 + $154.5

= $1,369.5

~ $1,370

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brainly.com/question/2281972

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6 0
1 year ago
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