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.
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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
Answer:
18 + 81 = 9(x² + 6x + 9) 11 = (x + 3)²
Explanation:
because This is the value that completes the square. However, since the entire square is multiplied by 9, this value must be multiplied by 9 before we can add it across the equals:
18 + 9 (9) = 9 (x² + 6x + 9)
18 + 81 = 9 (x² + 6x + 9)
99 = 9 (x² + 6x + 9)
Dividing both sides by 9, we have:
11 = x² + 6x + 9
11 = (x + 3) ²
Answer:
C. head of household
Explanation:
Taxation can be defined as the involuntary or compulsory fees levied on individuals or business entities by the government to generate revenues used for funding public institutions and activities.
The different types of tax include the following;
1. Income tax: a tax on the money made by workers in the state. This type of tax is paid by employees with respect to the amount of money they receive as their wages or salary.
2. Property tax: a tax based on the value of a person's home or business. It is mainly taxed on physical assets or properties such as land, building, cars, business, etc.
3. Sales tax: a tax that is a percent of the price of goods sold in retail stores. It is being paid by the consumers (buyers) of finished goods and services and then, transfered to the appropriate authorities by the seller.
In the United States of America, a head of household is a tax filing status for taxpayers that are saddled with the responsibility of paying more than half of the support and housing expenses (costs) of a qualifying person for at least a year. Also, to be eligible to file as a head of household, the taxpayer must be single or unmarried at the end of the year.
Generally, a head of household gets a lower tax rate and higher standard deductions than other taxpayers.
In this scenario, Monique is a single mom who is raising her three young children on her own. When she files her taxes this year, the tax status that will best fit her situation is head of household because she's solely responsible for catering to the needs of her kids.
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