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artcher [175]
2 years ago
13

İn the system equations above, n is a constant. İf the system has no solution, what is the value of n

Mathematics
1 answer:
jarptica [38.1K]2 years ago
4 0

Answer:

  • n = - 6

Step-by-step explanation:

<u>Given is the system of linear equations:</u>

  • nx + 3y = 6
  • 12x - 6y = 0

<u>Convert both equations into slope intercept form:</u>

  • nx + 3y = 6 ⇒ 3y = - nx + 6 ⇒ y = - 1/3nx + 2
  • 12x - 6y = 0 ⇒ 6y = 12x ⇒ y = 2x

<u>The system has no solution if lines have equal slopes with different y-intercepts:</u>

  • -1/3n = 2
  • n = - 6
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Given a term and the common difference, find the explicit formula.<br> 8. a(19) = 135<br> d = 15
Rasek [7]

The explicit formula is a(n) = 15(n – 10)

<u>Solution:</u>

Given, a term a(19) = 135 and common difference d = 15

We have to find the explicit formula.

Now, we know that, a(n) = a + (n – 1)d where a(n) is nth term, a is first term, d is common difference,

So, for a(19)  

\begin{array}{l}{\rightarrow a(19)=a+(19-1) 15} \\\\ {\rightarrow 135=a+18 \times 15} \\\\ {\rightarrow a=135-270} \\\\ {\rightarrow a=-135}\end{array}

Now, we know that, an explicit formula is an expression for finding the nth term,  

So, in our problem, expression for finding nth term is a + (n – 1)d  

\begin{array}{l}{\rightarrow-135+(n-1) 15} \\\\ {\rightarrow-135+15 n-15} \\\\ {\rightarrow 15 n-150} \\\\ {\rightarrow 15(n-10)}\end{array}

Hence, the explicit formula is a(n) = 15(n – 10).

7 0
3 years ago
What is 25% of 50000
juin [17]

Answer:

25% of 50000 is 12500

Step-by-step explanation:

To find: 25% of 50000

solution:

25% = \frac{25}{100}

hence, 25% of 50000 = \frac{25}{100}\times50000

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Therefore, the answer is 12500.

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UkoKoshka [18]

Answer:

Step-by-step explanation:

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3 years ago
Ratio of boys to girls in a class of 27 is 1:2 how many boys will there be?
labwork [276]

Answer:

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Step-by-step explanation:

6 0
3 years ago
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Suppose that the probability of landing an interview after applying for a professional position is 0.13. A job seeker applies fo
andrew11 [14]

Answer:

The expected number of interviews is 3.25.

Step-by-step explanation:

For each person applying for a profissional position, there are only two possible outcomes. Either they land an interview, or they do not. The probability of a person landing an interview is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

E(X) = np

In this problem, we have that:

n = 25, p = 0.13

So

E(X) = np = 25*0.13 = 3.25

The expected number of interviews is 3.25.

8 0
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