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Advocard [28]
3 years ago
12

Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 2y – 3z

= 4 3x – y + 5z = 2 4x + y +(a– 14)z = a +2
Mathematics
1 answer:
Luden [163]3 years ago
5 0

Answer:

a) If a=20 the system has no solutions.

b) If a≠20 the system has exactly one solution.

Step-by-step explanation:

The augmented matrix of the system is \left[\begin{array}{cccc}1&2&-3&4\\3&-1&5&2\\4&1&a-14&a+2\end{array}\right].

Using rows operations we obtain the echelon form of the matrix, ie,

\left[\begin{array}{cccc}1&2&-3&4\\0&-7&-4&-10\\0&0&a-20&a+4\end{array}\right]

Since the echelon form of the matrix does not have free variables then the problem has exactly one solution or has no solutions.

a) If a=20 the system has no solutions because in the last equation solving for x3 it has that 0=24. Then the system is inconsistent.

b) If a≠20, the the system has exactly one solution that is obtained solving the system of the echelon form matrix.

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the sum of three number number in an artithmetic product is 21. if second number isreduced by 1 and third term is increased by 1
grin007 [14]

The three numbers will be 12, 7, 2 and 3, 7, 11.

<h3>What is a sequence?</h3>

A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.

Let the three consecutive numbers be a, a + d, and a + 2d

The sum of three numbers which are consecutive terms of an A.P. is 21.

a + a + d + a + 2d = 21

3(a + d) = 21

a = 7 - d

If the second number is reduced by 1 and the third term is increased by 1 we obtain the geometric product.

Then the number will be a, a + d − 1, a + 2d + 1. Then we have

\rm \dfrac{a + d - 1}{a} = \dfrac{a + 2d + 1}{a + d - 1}

On simplifying, we have

36 = a (8 + d)

a² - 15a + 36 = 0

On factorizing, the value of a will be

a² - 15a + 36 = 0

a² - 12a  - 3a + 36 = 0

(a - 12)(a - 3) = 0

a = 3, 12

If a = 12, then the value of d will be

d = 7 - 12

d = -5

If a = 3, then the value of d will be

d = 7 - 3

d = 4

Then the three numbers will be 12, 7, 2 and 3, 7, 11.

More about the sequence link is given below.

brainly.com/question/21961097

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2 years ago
Find the slope of the line that passes through the given points
7nadin3 [17]

The slope should be m= -9/11

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3 years ago
There were 16 bald eagles in an area some years later there were 28 bald eagle‘s in the area what is the percent game
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3 years ago
Answer<br><br> -10 – (-2) =
Allisa [31]

Answer:

8

Step-by-step explanation:

- (-2) is the same as + 2

-10 + 2 = -8

8 0
3 years ago
Read 2 more answers
An electric bulb is sold in a box measuring 5 cm by 4 cm by 4 cm. If the shopkeeper receives them in a carton measuring 50 cm by
katen-ka-za [31]

Answer:

250

Step-by-step explanation:

Bulb box and carton both are of cuboidal shape.

<u>For bulb </u><u>box</u><u> </u><u>the </u><u>d</u><u>imensions</u><u> </u><u>are:</u>

  • l = 5 cm, w = 4 cm, h = 4 cm

  • V_{Bulb\: box} =lwh

  • \implies V_{Bulb\: box} =5(4)(4)

  • \implies V_{Bulb\: box} =80\: cm^3

<u>For </u><u>Carton </u><u>the dimensions are</u><u>:</u>

  • l = 50 cm, w = 20 cm, h = 20 cm

  • V_{Carton} =lwh

  • \implies V_{Carton} =50(20)(20)

  • \implies V_{Bulb\: box} =20,000\: cm^3

To find the number of bulbs packed in the carton, divide the V_{Carton} by V_{Bulb\: box}

  • Number \:of \:bulbs =\frac{V_{Carton}}{V_{Bulb\: box}}

  • \implies Number \:of \:bulbs =\frac{20,000}{80}

  • \implies Number \:of \:bulbs = 250

So, 250 bulbs will be packed in one carton.

3 0
2 years ago
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