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Mashutka [201]
3 years ago
11

For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: not all thr

ee possibilities need occur.] (If the answer is an interval of numbers, enter your answer using interval notation. If an answer does not exist, enter DNE.) 3x1 − x2 = 2 9x1 − 3x2 = k
Mathematics
1 answer:
viktelen [127]3 years ago
4 0

Answer:

The system has an infinite solution at k = 6, otherwise for any value of k, it has zero solution.

Step-by-step explanation:

Consider the system of linear equations:

3x_{1} -x_{2}=2\;\;\;\;\;\;(1)\\ 9x_{1} -3x_{2}=k\;\;\;\;\;(2)

The system of linear equations can have zero, one, or an infinite number of solutions:

simplify equation (1):

x_{2}=3x_{1} -2

substitute in equation (2), we get

9x_{1} -3(3x_{1}-2)=k\\9x_{1} -9x_{1}+6=k\\0+6=k

we cannot find the value of x_{1} and x_{2}.

so, there is no solution.

Multiply the equation (1) with 3 and put k is 6,

3(3x_{1} -x_{2})=3\times2\\9x_{1} -3x_{2})=6

it means both equations are overlapped. Then, the solution has infinite solutions.

Hence, the system has an infinite solutions at k is 6 otherwise for any value of k it has no solution.

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What is your sister’s total cost under each of the two plans?2. Suppose your sister doubles her monthly usage to 3,500 minutes a
chubhunter [2.5K]

Answer:

(1) The total cost under Plan A is <u>$92</u> and the total cost under Plan B is <u>$515</u>.

(2) The total cost under Plan A is <u>$92</u> and the total cost under Plan B is <u>$1,030</u>.

Step-by-step explanation:

<u><em>The question is incomplete, so the complete question is below:</em></u>

A\ cell \ phone \ company\  offers\  two \ different \ plans.

Plan\ A\ costs\ \$92\ per\ month\ for\ unlimited\ talk\ and\ text.\ Plan\ B\ costs \ $0.20\ per\ minute\ plus\ \$0.10\ per\ text\ message\ sent.You\  need \  to\   purchase \  a \  plan \  for\   your \  14-year-old \  sister.Your\  sister\  currently \ uses\  1,750 \ minutes\  and \ sends\  1,650 \ texts\  each \ month.(1) What\  is\   your \  sister's\   total\   cost\   under \  each\   of\   the\   two\   plans?

(2) Suppose\  your\  sister\  doubles\  her\  monthly\  usage \ to\  3,500\  minutes \ and\  sends\  3,300 \ texts.What \ is \  your  \ sister's \  total \  cost \  under \  each \  of  \ the \  two \  plans?

Now, to find (1) total cost for each of the two plans. (2) Total cost under each of the two plans, if sister doubles her monthly usage to 3,500 minutes and sends 3,300 texts.

<h3>(1) </h3>

As, the Plan A is for unlimited talk and text

Cost of the Plan A = $92.

<u><em>Now, to find the cost under Plan B:</em></u>

According to question:

Rate of call per minute is $0.20 and per text is $0.10.

Calls she uses currently is 1,750 minutes and text 1,650.

<u><em>So, to get the cost of Plan B:</em></u>

0.20\times 1750+0.10\times 1650

=350+165

=515.

Thus, Plan B costs $515.

<h3>(2)</h3>

<u><em>Now, to get the total cost as, sister doubles her monthly usage to 3,500 minutes and sends 3,300 texts.</em></u>

As, the Plan A is same in both cases and is for unlimited text and calls.

So, cost of Plan A = $92.

As, the monthly usage is double.

Calls in minutes are 3,500.

Texts are 3,300.

<u><em>Now, to get the total cost under Plan B:</em></u>

0.20\times 3500+0.10\times 3300

=700+330

=1030.

Hence, the cost of Plan B = $1,030.

Therefore, (1) The total cost under Plan A is $92 and the total cost under Plan B is $515.

(2) The total cost under Plan A is $92 and the total cost under Plan B is $1,030.

7 0
3 years ago
Which number line represents the solutions to |x - 2|= 6?
Alexeev081 [22]

Answer:8 and -4

Step-by-step explanation:

[x-2]=6 ,x-2 =6 ,x=8 and x-2=-6 ,x=-4

4 0
3 years ago
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daser333 [38]

Answer:

Step-by-step explanation:

. should be a right angle triangle,

. must have 2 sides given

7 0
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I have two story problems.
vekshin1
Let lucy = l & neighbour= n
l = n +4
l + n= 14 years
substitute l with n +4
(n +4) + n = 14
2n +4 =14
n=5 years
l = n + 4 lets substitute n with 5
l = 5 + 4
lucy = 9 years

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2 years ago
62.8 x 10a = 628,000, when a =
klio [65]

Answer:a=10000

Step-by-step explanation:

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