All categories

4 years ago

Solve the system ⎧⎩⎨⎪⎪⎪⎪⎪⎪4x1−x13x1−3x1−5x2+x2−4x2+3x2+4x3+2x3+6x3+6x3+4x4=+3x4=+7x4=+9x4=3143

Mathematics

1 answer:

ad-work [718]4 years ago

7 0

It appears you have the system with augmented matrxi ...

$\left[\begin{array}{cccc|c}4&-5&4&4&3\\-1&1&2&3&1\\3&-4&6&7&4\\-3&3&6&9&3\end{array}\right]$

Right away, you notice that the 4th row is 3 times the 2nd row, so the equations are dependent and will not have a unique solution.

My calculator tells me the reduced equations can be written

... x1 -14x3 -19x4 = -8

... x2 -12x3 -16x4 = -7

This says there are two dependent equations in the set, not just one.

You might be interested in

Riley is saving up to buy a new television. She needs a total of $1,049.77. Riley has saved $200.79 already and earns $77.18 per

Xelga [282]

11 weeks are required for Riley to work to save enough money to buy the new television

<h3><u>Solution:</u></h3>

Given that Riley needs a total of $1,049.77

Riley has saved $200.79 already and earns $77.18 per week at her job

To find: Number of weeks Riley need to work to save enough money to buy the new television

Remaining amount needed = $1,049.77 - $200.79

Remaining amount needed = $ 848.98

Let "n" be the number of weeks Riley need to work to save enough money to buy the new television

Also she earns $77.18 per week at her job

1 week ⇒ $ 77.18

"n" weeks ⇒ $ 848.98

Therefore, by cross multiplication,

$n \times 77.18 = 1 \times 848.98\\\\n = \frac{848.98}{77.18}\\\\n = 11$

Therefore 11 weeks are required for her to work to save enough money to buy the new television

<h3><u>Method 2:</u></h3>

<em>Total amount = amount already saved + ($77.18 per week at her job)("n" weeks)</em>

1,049.77 = 200.79 + (77.18)(n)

1049.77 - 200.79 = 77.18n

848.98 = 77.18n

$n = \frac{848.98}{77.18}$

n = 11

Therefore 11 weeks are required for her to work to save enough money to buy the new television

5 0

4 years ago

Write an ordered list of five numbers whose values are between 50.98 and 51.6. Tell whether your list is from least to greatest

Vadim26 [7]

One <em><u>possible answer</u></em> is:

51.0, 51.1, 51.2, 5.13, and 51.4; the list is from least to greatest.

Explanation:

51.0 can be written as 51.00. Comparing this to 50.98, we can see that 51.00 is larger.

51.1 is larger than 51.0; 51.2 is larger than 51.1; 51.3 is larger than 51.2; and 51.4 is larger than 51.3. All of these numbers are also smaller than 51.6.

5 0

3 years ago

Please solve this 4 the grade algebra problem? A group of students calculated their average score at a spelling bee. They realiz

In-s [12.5K]

Let x = original average score
let y = be the number of students

We need to write two equation using the information given in the scenario in order to work them simultaneously and obtain the results.

let $\frac{yx + 9}{y} = 81$ .... (1)
so x is the original average, so we multiply that average by the amount of students [y × x] in order to obtain their cumulative score then you add the nine to that score (because a student got 9 more points) [yx + 9]. Then you divide that sum by the amount of student in order to get the new average which the question says would be 81

$\frac{yx - 3}{y} = 78$ ...... (2)
so x is the original average, so we multiply that average by the amount of students [y × x] in order to obtain their cumulative score then you subtract three from that score since one student got three less points [yx - 3]. Then you divide by the number of students (y) and you should 78 like the question says.

$\frac{yx + 9}{y} = 81$ .... (1)
$\frac{yx - 3}{y} = 78$ ...... (2)

Now simplify each equation by separating the LHS
$\frac{yx}{y} + \frac{9}{y} = 81$ ..... (1a)
$\frac{yx}{y} - \frac{3}{y} = 78$ ...... (2a)

By subtracting eq (2a) from eq (1a) in order to eliminate x
$\frac{yx}{y} - \frac{yx}{y} + \frac{9}{y} - (- \frac{3}{y}) = 81 - 78$

$\frac{12}{y} = 3$

$\frac{12}{3} = y$

⇒ y = 4

Since y = the number of students
then the number of students = 4

6 0

3 years ago

Lin's job pays $8.25 an hour plus $10 of transportation allowance each week. She has to work at least 5 hours a week to keep the

Usimov [2.4K]

Y=8.25x+10

10 is the allowance plus the 8.25 times x which is the hours

5 0

3 years ago

On the production budget, the number of units to be produced is computed as

Firlakuza [10]

The answer is <span>unit sales + desired end inventory – beginning inventory. </span>The production budget figures the quantity units of items that must be fabricated and is gotten from a mix of the business estimate and the arranged measure of completed products stock to have close by.
I hope the answer will help you.

7 0

3 years ago