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3 years ago

2 kg in the ratio 3:5

Mathematics

1 answer:

olya-2409 [2.1K]3 years ago

3 0

Answer:

3u--> 750g

5u-->1250g

Step-by-step explanation:

2kg = 2000g

3+5=8

8u --> 2000g

1u--> 250g

3u--> 750g

5u-->1250g

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G−16=8 what does g stand for

Misha Larkins [42]

Answer:

G equals 24

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

A) The equilibrium prices P1 and P2 for two goods satisfy the equations:

Allisa [31]

The value of P1 and P2 using the inverse matrix is 5 and 6 respectively.

<h3 />

The equilibrium prices of the three independent commodities using the inverse matrix are P1 = 4, P2 = 7, P3 = 8 respectively.

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

A matrix can be defined as a collection of integers(numbers that are either positive or negative) that are organized in rows and columns to construct a rectangular array. The numbers in this matrix system are referred to as elements.

To determine the values of P1 and P2 for the system of equations given by using an inverse matrix, we have:

9P1 + P2 = 51

3P1 +4P2 = 39

Representing the above data in matrix form, we have:

$\left[\begin{array}{cc}9&1\\3&4\\ \end{array}\right] \left[\begin{array}{c} \mathbf{P_1} \\ \mathbf{P_2}\\ \end{array}\right] = \left[\begin{array}{c} \mathbf{51} \\ \mathbf{39} \\ \end{array}\right]$ which is in the form AX = B

In order for us to determine the values of P1 and P2, Let take the inverse of A⁻¹ on both sides of the AX= B, we have:

$\mathbf{{A^{-1} AX} = A^{-1} B}$

X = A⁻¹ B

Let's start by finding A⁻¹;

$\mathbf{A = \left[\begin{array}{cc}9&1\\3&4\end{array}\right] }$

$\mathbf{A^{-1} = \dfrac{1}{36-3}\left[\begin{array}{cc}4&-1\\3&9\end{array}\right] }$

$\mathbf{A^{-1} = \dfrac{1}{33}\left[\begin{array}{cc}4&-1\\3&9\end{array}\right] }$

Now, Let's Find A⁻¹B;

$\mathbf{A^{-1}B = \dfrac{1}{33}\left[\begin{array}{cc}4&-1\\3&9\end{array}\right] \left[\begin{array}{c}51\\39\\ \end{array}\right] }$

$\mathbf{\implies \dfrac{1}{33}\left[\begin{array}{cc}204&-39\\-153&+351\end{array}\right] }$

$\mathbf{\implies \left[\begin{array}{c}\dfrac{165}{33}\\ \\ \dfrac{198}{33}\end{array}\right] }$

$\mathbf{\implies \left[\begin{array}{c}5\\ \\ 6\end{array}\right] }$

$\left[\begin{array}{c}\mathbf{P_1}\\ \mathbf{P_2}\end{array}\right]= \left[\begin{array}{c}5\\ 6 \end{array}\right] }$

Therefore, we can conclude that the value of P1 and P2 using the inverse matrix is 5 and 6 respectively.

To determine the equilibrium prices of the three independent commodities using the inverse matrix, we have:

P₁ + 2P₂ + 3P₃ = 42

2P₁ + P₂ + 4P₃ = 47

P₁ + 3P₂ + 4P₃ = 57

The matrix in AX = B form is computed as:

$\implies\left[ \begin{array}{ccc}1&2&3\\2&1&4\\1&3&4\end{array}\right] \left[\begin{array}{c}P_1\\P_2\\P_3 \end{array}\right] = \left[\begin{array}{c}42\\47\\ 57\end{array}\right]$

$\mathbf{A^{-1} = \dfrac{1}{|A|} \ (adj \ A)}$

$\mathbf{A^{-1} = \dfrac{1}{1(4-12) -2(8-4) +3(6-1)} \left[\begin{array}{ccc}-8&4&5\\1&1&-1\\5&2&-3\end{array}\right] }^1$

$\mathbf{A^{-1}B = -1 \left[\begin{array}{ccc}-8&1&5\\-4&1&2\\5&2&-3\end{array}\right] }\left[\begin{array}{c}42\\47\\57\end{array}\right]$

$\mathbf{A^{-1}B = -\left[\begin{array}{ccc}-336&+47&+285\\-168&+47&+114\\210&-47&-171\end{array}\right] }$

$\mathbf{A^{-1}B = -\left[\begin{array}{c}-4\\-7\\-8\end{array}\right] }$

$\mathbf{A^{-1}B = \left[\begin{array}{c}4\\7\\8\end{array}\right] }$

Therefore, we can conclude that the values of P1 = 4, P2 = 7, P3 = 8 respectively.

Learn more about matrix here:

brainly.com/question/1821869

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2 years ago

PLEASE HELP!!!!!

kipiarov [429]

Answer:X + Y ≥ 4

$2.20X + $2.95Y ≤ $10.00

Strawberries cost $2.20 per pound

Raspberries cost $2.95 per pound

Jada only has $10.00 to spend

She wants to buy at least 4 pounds

Assumption: She buys X pounds of strawberries and Y pounds of raspberries.

<u />

<u>Solution:</u>

Number of pounds can't be less than 4

i.e X + Y ≥ 4

The cost of buying strawberries and raspberries has to be $10.00 or less than $10.00

i.e $2.20X + $2.95Y ≤ $10.00

So the system of equations is;

X + Y ≥ 4

$2.20X + $2.95Y ≤ $10.00

Step-by-step explanation:

Hopefully this helped, if not HMU and I will get you a better answer.

<em>-Have a great day! :)</em>

<em />

8 0

3 years ago

Enter the decimal 1.81 repeating as an improper fraction in simplest form.

Elodia [21]

Answer:

1 9/11

Step-by-step explanation:

1.81 repeating is the equivalent to 1 9/11

6 0

3 years ago

Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use the result to factor the po

Flura [38]

You didn't state the value of x which you want to be shown to be a solution of the given polynomial

3x³ - 19x² + 30x - 8 = 0.

This polynomial of degree three obviously, has three solutions, and 2 is one of the solutions.

I will assume 2 to be the value of x you didn't state, and work with it. But the number is not 2, then it must be one of the remaining two solutions which would follow the same procedure that I will show here.

Answer:

The solutions to the equation

3x³ - 19x² + 30x - 8 = 0

are x = (2, 4, 1/3).

Step-by-step explanation:

Given the polynomial

3x³ - 19x² + 30x - 8 = 0

We need to show that x = 2 is a solution using synthetic division. If x = 2 is a solution, the remainder obtained from the synthetic division

(3x³ - 19x² + 30x - 8) ÷ (x - 2)

is zero.

SYNTHETIC DIVISION

2 | 3 ..... -19 ..... 30 ..... -8

................. 6 .... -26 ...... 8

.... 3........ -13 ........4 .......0->Remainder

Explanation:

The first row:

2 is from the divisor (x - 2). Always take the opposite of what you have. If the divisor is (x + 5), take -5.

(3, -19, 30, -8) are the coefficients of the divisor, the polynomial of degree three.

The coefficient of x³ is dropped to the third column.

2 is multiplied by 3 in the third column to obtain 6 in the second column.

6 is added to -19 to obtain -13.

Again, multiply 2 by -13 in the third column, to obtain -26 in the second column. Add this to 30 to obtain 4

Repeat this process, 2 × 4 = 8

8 + (-8) = 0.

Since 0 is the remainder, x = 2 is a solution to the polynomial.

The remaining factors can be found from the resulting polynomial of degree two whose coefficients were obtained from the synthetic division.

The coefficients of the polynomial are: 3, -13, 4

So, the polynomial is: 3x² - 13x + 4.

The zeros of this polynomial are the remaining factors we are looking for.

We solve

3x² - 13x + 4 = 0

(x - 4)(3x - 1) = 0

x - 4 = 0

=> x = 4

3x - 1 = 0

=> x = 1/3

x = 4, 1/3

The solutions to the equation are x = (2, 4, 1/3).

3 0

3 years ago