Solve the system of equations. y=4x+5 and y=3x-2, what's the solution​

The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

To learn more about linear equations from the given link.

https://brainly.com/question/2030026

#SPJ11

As there are three players, the game will be played in cycles of 3 rounds. After each cycle is completed, the round after will be the round where every single player has 1 token less than they did at the beginning of the previous cycle.

After the first round of the game, player one will have 12 tokens, player two will have 15 and player three will have 14 left. Looking at this sequence, it is evident that player one will finish first.

Go a few rounds to establish the pattern:

Beginning chips: A B C

15 14 13

1st round:

12 15 14

2nd round: 13 12 15

3rd round: 14 13 12

So after 3 rounds and successive 3 rounds each player has one less than he started with at the beginning of the 3 round series.

So after 36 rounds each will be down 12 from the beginning:

                                            A B C

                                             3 2 1

On the 37 round A will give up his 3 to end at 0

37

For more clear understanding:

As player has one token less at the beginning of a new cycle than he/she had at the beginning of the previous cycle we go (12∗3)+1=37(12∗3)+1=37 to see how many turns it will take them to reach zero.

Learn more about Sequence:
https://brainly.com/question/4626313

#SPJ4

Answer:

x = $25,400 [the original price of the Junko car]

Step-by-step explanation:

The price Ben paid, $23,622, is after the 7% discount.  Let x be the original price of the Jinko car.   Ben's prices reflect a 7% discount:

 x*(1-0.07) = $23,622  [The expression (1-0.07) means the original price, 1, is reduced by 7%, -0.07, to give the final price]

(0.93)x = $23,622

x = $25,400

Answer:

36+25= 61

61/600 x 100 = 10.1 %

Step-by-step explanation:   Hope This helped!!!!

Answer:

(0,7/2)    (1,17/4)    (2,5)

Step-by-step explanation:

The first two are suppose to be fractions but, I can't make a fraction so yeah...

Good Luck!!!! :) :) :) :)

Answer:

the equation that is equal to X+3X=36

Step-by-step explanation:

since they have 36 all together, we know thier total is 36. since it says that julie has three times mary, i used x to represent mary. so julie is 3x. now we know the equation x(Marie)+3x(JUlie)=36(total)

Answer:

D. 10.5 ft

Step-by-step explanation:

3 times 3.5 = 10.5.

Answer:

45.29 units.

The possible weights that correctly round to 41.34 kilograms will be:

C. 41.32 kilograms

D. 41.35 kilograms

E 41.263 kilograms

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Based on the options given, the closest numbers are 41.32 kilogram, 41.35 kilograms and 41.263 kilograms

Learn more about expressions on

brainly.com/question/723406

#SPJ1

Answer:

-4

Step-by-step explanation:

The derivative of f(x) = cos(x² - x) is \(3(2x - 1)cos(x^{2} - x)sin(x^{2} - x).\)

To find the derivative of the function f(x) = cos(x² - x), we can use the chain rule.

The chain rule states that if we have a composite function, such as cos(g(x)), the derivative of this composite function is given by the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is cos(u), where u = x² - x, and the inner function is u = x² - x.

The derivative of the outer function cos(u) is -sin(u).

To find the derivative of the inner function u = x² - x, we apply the power rule and the constant rule. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1), and the constant rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function.

Applying the power rule and the constant rule, we find that the derivative of u = x² - x is du/dx = 2x - 1.

Now, using the chain rule, the derivative of f(x) = cos(x² - x) is given by:

df/dx = \(-sin(x^{2} - x) * (2x - 1)\)

Simplifying, we have:

df/dx = -\(2xsin(xx^{2} - x) + sin(x^{2} - x)\)

Therefore, the correct answer is option a. 3(2x-1)cos(x²-x)sin(x²-x).

For more questions on derivative

https://brainly.com/question/31399608
#SPJ8

There are 32 fluid ounces (oz) in a quart (qt).

A fluid ounce is a unit of volume used in measuring liquids and is equal to approximately 1/128th of a gallon. A quart, on the other hand, is a unit of volume that is equal to 4 cups or 2 pints. It is commonly used to measure liquids like milk, water, and other beverages.

Understanding how many ounces are in a quart is essential for many recipes, particularly when working with liquids. For instance, if a recipe calls for 2 quarts of water, you will need 64 fluid ounces. Similarly, if a recipe calls for 16 fluid ounces of milk, you will need half a quart.

Having a basic knowledge of measurement conversions can help in a variety of situations, whether in cooking or other daily activities.

To learn more about ounces here:

https://brainly.com/question/10887933

#SPJ4

As we can see from the table, f(x) = g(x) when x = 1 and x = 4. Thus, the solutions are x = 1 and x = 4. It's important to note that while using a table of values can be helpful in understanding the behavior of functions and finding their intersection points, it may not always provide a completely accurate solution.

To verify our results, we could also solve the equation algebraically by setting f(x) equal to g(x) and solving for x.

solve f(x) = g(x) using a table of values. Since f(x) = x^2 - 6x + 8 and g(x) = x - 4, we want to find the x-value where f(x) and g(x) are equal.

Here's a table of values for both functions:

x | f(x) | g(x)
---------------
1 | -3   | -3
2 |  0   | -2
3 |  1   | -1
4 |  0   |  0
5 | -1   |  1
6 |  0   |  2
7 |  1   |  3

As we can see from the table, f(x) = g(x) when x = 1 and x = 4. Thus, the solutions are x = 1 and x = 4.

Learn more about the function here:

https://brainly.com/question/12431044

#SPJ11

The factors of the equation are 4 and -1.

Given

Equation; \(\rm x^2+3x-4\)

The polynomial which has the highest degree is 2 is called the quadratic equation.

The standard form of the quadratic equation is;

\(\rm ax^2+bx+c=0\)

The factors of the given equation are;

\(\rm x^2+3x-4=0\\\\x^2-4x+x-4=0\\\\x(x-4)+1(x-4)=0\\\\ (x-4)(x+1)=0\\\\x-4=0, \ \ x=4\\\\x+1=0, \ \ x=-1\)

Hence, the factors of the equation are 4 and -1.

To know more about Factors click the link given below.

https://brainly.com/question/16975319

Answer:

c

Step-by-step explanation:

We anticipate that roughly 480 of the school's 1,500 pupils will choose the gym as the venue for the annual end-of-year dance.

According to the preferences table, 160 of the 500 pupils who participated in the poll picked the school gym as the venue for the yearly dance. We may use the percentage of students who favored the school gym in the sample to calculate the number of students out of 1,500 who would be expected to vote for the gym:

160/500 = 0.32

This indicates that 32% of the sample's students favored using the school gym. Using this ratio, we can determine how many of the 1,500 pupils favor the school gym:

1.5 times 0.32 equals 480 students.

As a result, we anticipate that roughly 480 of the school's 1,500 pupils will choose the gym as the venue for the annual end-of-year dance.

Learn more about percentage here:

brainly.com/question/24159063

#SPJ1

To construct a 90% confidence interval for the difference between the mean solar radiation for the two types of solar trackers, we can use the two-sample t-test with equal variances. Here are the steps to calculate the confidence interval:

(i) Constructing a 90% confidence interval for the difference between means:

1. Calculate the pooled standard deviation (sp) using the formula: sp = sqrt(((n1 - 1)s1^2 + (n2 - 1)s2^2) / (n1 + n2 - 2)), where s1 and s2 are the standard deviations of the two samples, and n1 and n2 are the sample sizes.

2. Calculate the standard error (SE) using the formula: SE = sqrt((sp^2 / n1) + (sp^2 / n2)).

3. Calculate the t-value for a 90% confidence level with (n1 + n2 - 2) degrees of freedom.

4. Calculate the margin of error by multiplying the t-value by the standard error.

5. Construct the confidence interval by subtracting and adding the margin of error to the difference between sample means.

(ii) Constructing a 95% confidence interval for the true variance:

1. Calculate the chi-square values for the lower and upper percentiles of a chi-square distribution with (n - 1) degrees of freedom, where n is the sample size.

2. Divide the sample variance by the chi-square values to obtain the lower and upper bounds of the confidence interval.

These calculations will provide the desired confidence intervals for both questions.

Learn more about sample variance  here: brainly.com/question/15289325

#SPJ11

Answer:

commutative property of algebra

Answer:

5

Step-by-step explanation:

Answer:

- 5 or + 5

Step-by-step explanation:

\(\sqrt{25}\) = ± 5 , since

5 × 5 = 25 and - 5 × - 5 = 25

Answer:

A. 4 2/3

Step-by-step explanation:

4(x-8) > 3 - (2x + 7)

4x-32 > 3 -2x -7

4x - 32 > -4 -2x

6x -32 > -4

6x > 28

divide both sides by 6

6 divide by 6 is 1

28 divide by 6 is simplified to 14/3 which can be changed into a mixed number 4 2/3

TRUNCATED to one decimal place, it's 50.2

ROUNDED to one decimal place, it's 50.3

The round-off of 50.272 to 1 decimal place using rules of rounding

numbers are 50.3.

Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.

Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.

So, 50.272 becomes 50.3 when rounded to one decimal place.

Learn more about rounding numbers here:

https://brainly.com/question/13391706

#SPJ4

The sum of angles 3 and 4 is equal to 180 degrees, therefore: A: true; this would be enough information to say that the lines are definitely parallel.

When two lines are intersected by a transversal, and the same-side interior angles are supplementary, that is are equal to 180 degrees, then we can state that the two lines are parallel to each other based on the converse of the same-side-interior angles theorem.

Given the following information:

Angle 4 and angle 3 are same-side-interior angles, thus:

89 + 91 = 180°

This means that, the sum of angle 4 and 3 are supplementary. Lines g and h are therefore parallel to each other.

In summary, our answer would be: A: true; this would be enough information to say that the lines are definitely parallel.

Learn more about parallel lines on:

https://brainly.com/question/16742265

#SPJ1

Answer:

true

Step-by-step explanation:

Based on the given values, the function p(x) is not a probability mass function since it does not satisfy the requirement that the sum of probabilities equals 1.

To determine if the function p(x) is a probability mass function (PMF), we need to check if it satisfies the properties of a valid PMF.

1. Non-negativity: The values of p(x) must be non-negative. In the given function, p(x) takes the values 0, 0.3, 0.6, and 0.2, all of which are non-negative. So, the first property is satisfied.

2. Sum of probabilities: The sum of all probabilities p(x) must be equal to 1. Let's check if this property holds:

  p(1) + p(2) + p(4) + p(7) = 0 + 0.3 + 0.6 + 0.2 = 1.1

  Since the sum of probabilities is greater than 1 (1.1 in this case), the function p(x) does not satisfy the property of a valid PMF.

Therefore, based on the given values, the function p(x) is not a probability mass function since it does not satisfy the requirement that the sum of probabilities equals 1.

Learn more about function p(x)

brainly.com/question/7904943

#SPJ11

Question:

Vincent bought a 25-pound bag of rice. He cooked 6.25 pounds of the rice. He stored the rest of the rice in \(3\frac{3}{4}\) - pound portions. What is the maximum number of \(3\frac{3}{4}\) - pound portions he stored?

Answer:

The maximum number of portion he stored is 5 portion

Step-by-step explanation:

Given

Size of Rice = 25 lb

Size of Cooked Rice = 6.25 lb

Portions saved = \(3\frac{3}{4}\) lb

Required

Number of portion saved;

First, the size of rice after cooking needs to be calculated;

If 6.25lb of rice was cooked from a total of 25lb;

Then, the size of rice left is

\(Size = 25lb - 6.25lb\)

\(Size = 18.75lb\)

Now that we have the amount left after cooking; we can simply calculate the maximum number of portions;

This is calculated by dividing size of rice left by portions of saved rice;

i.e.

Maximum number of portion = Size of rice left / Portions of saved rice

Maximum number of portion = \(\frac{18.75lb}{3\frac{3}{4}lb}\)

Convert  \(3\frac{3}{4}\) to mixed fraction

Maximum number of portion = \(\frac{18.75lb}{\frac{15}{4}lb}\)

Maximum number of portion = \(\frac{18.75}{\frac{15}{4}}\)

Rewrite expression

Maximum number of portion = \(18.75 / \frac{15}{4}\)

Change divide (/) sign to multiplication (*)

Maximum number of portion = \(18.75 * \frac{4}{15}\)

Maximum number of portion = \(\frac{75}{15}\)

Maximum number of portion = 5

Hence, the maximum number of portion he stored is 5 portions

Answer:

b) around 6 years

c) around 2,500

Step-by-step explanation:

Answer:

The perimeter of the rectangle that contains the 3 squares is 24x + 36 units

Step-by-step explanation:

Here, we have a square with side length 2x + 3

The perimeter of this square would be calculated using the mathematical formula;

P = 4L

P = 4(2x + 3) = 8x + 12 units

Now, this particular rectangle is composed of three of these squares.

The expression which would represent the perimeter of the rectangle is equal to the sum of the perimeters of the 3 squares.

That would be 8x + 12 + 8x + 12 + 8x + 12 or simply 3(8x + 12) = 24x + 36

Answer:

Well x would be 103° because it forms a line (180°) with the 77° but I have no idea what those arrows are asking...

The shortest length of fence that the rancher can use is 6000ft

Given that

x = width of rectangle

y = length of rectangle

A = area of rectangle = x*y = 1500000 \(ft^{2}\)

L = length of fencing needed = 2(x + y) + x = 3x + 2y

L = 3x + 2(\(\frac{1500000}{x}\)) = 3x + 3(\(10^{6}\))\(x^{-1}\)

As x –> 0+, L –> +inf.

As x –> +inf, L –> (3x)+.

There will be a minimum in Quadrant I.

dL/dx = 3 - 3(\(10^{6}\))\(x^{-2}\)

dL/dx = 0:

3 - 3(\(10^{6}\))\(x^{-2}\) = 0

3(\(10^{6}\))\(x^{-2}\)= 3

(\(10^{6}\))\(x^{-2}\) = 1

\(x^{2}\) = \(10^{6}\)

x > 0, so x = 1000 feet for shortest length.

Shortest L = 3000 + 3(\(10^{6}\))(\((10^{3} )^{-1}\))= 6000 feet.

The shortest length of fence that the rancher can use is 6000ft

To learn more about area:

https://brainly.com/question/11952845

#SPJ4

Answer:

612 quarts

Step-by-step explanation:

First, let's set up this situation into a proportion.

Now, let's simplify the proportion.

As you can see, we have to multiple one by thirty-six to get to thirty-six. Whatever we do the denominators, we have to do to the numerators. Thus, 17 multiplied by 36 is 612 quarts.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

612 quarts

Step-by-step explanation:

If 170 quarts of ice cream is made in 10 hours. Then, in 1 hour (170/10) = 17 quarts of ice cream are made.

Therefore, in 36 hours (17×36) = 612 quarts of ice cream are made

Answer:

The angle sign doesn't look like 56.6 degrees

Step-by-step explanation:

Answer:

work is shown and pictured