Solve the following system of equations using an augmented matrix and Gauss-Jordan Elimination. Be sure to show your work and explain what you are doing. Then, interpret your answer in terms of the original system.

Solve The Following System Of Equations Using An Augmented Matrix And Gauss-Jordan Elimination. Be Sure

Answers

Answer 1

Okay, here we have this:

Considering the provided equation, we are going to solve the system using an augmented matrix and Gauss-Jordan Elimination. So we obtain the following:

[tex]\begin{gathered} \begin{bmatrix}3x+2y-4z=4 \\ x-3y-10z=8 \\ -5x-4y+12z=-2\end{bmatrix} \\ \begin{bmatrix}\frac{4-2y+4z}{3}-3y-10z=8 \\ -5\cdot\frac{4-2y+4z}{3}-4y+12z=-2\end{bmatrix} \\ \begin{bmatrix}\frac{-11y-26z+4}{3}=8 \\ \frac{-2y+16z-20}{3}=-2\end{bmatrix} \\ \begin{bmatrix}\frac{-2\left(-\frac{26z+20}{11}\right)+16z-20}{3}=-2\end{bmatrix} \\ \begin{bmatrix}\frac{4\left(19z-15\right)}{11}=-2\end{bmatrix} \\ y=-\frac{26\cdot\frac{1}{2}+20}{11} \\ y=-3 \\ x=\frac{4-2\left(-3\right)+4\cdot\frac{1}{2}}{3} \\ x=4 \\ \end{gathered}[/tex]

Finally we obtain that the solution to the system is:

[tex]x=4,\: z=\frac{1}{2},\: y=-3[/tex]


Related Questions

One weekend 5,780 people saw a new movie at (7 different theaters. Each theater sold tickets at ($7.50 a piece. If each theater received the same number of moviegoers, how much did each theater make?

Answers

Each theater sold tickets at ($7.50 a piece, if each theater received the same number of moviegoers, each theater make $6192.85 using arithmetic operations.

What are arithmetic operations?

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or more quantities. They cover topics like the study of numbers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry. Without applying the laws of arithmetic operations, we are unable to solve the issue. The four fundamental rules of mathematics are addition, subtraction, multiplication, and division.

Let the amount of each theater get be x,

No. of theaters are = 7

Cost of each ticket = $7.50

No. of people = 5780

Then we can say,

7x = 5780 ×7.50

x = [tex]\frac{5780\times7.50}{7}[/tex]

= $6192.85

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What would be the first step when solving using the substitution method?
2x + 3y = -12

x = 3y + 3

Answers

The first step of substitution method for given system is put x = 3y +3 in place of x into the equation 2x+3y=-12 .

What is the method of substitution for system of equation in two variables ?

The system of the equations in two variables x and y consists of two equation of the form a₁ x + b₁ y = c₁

and a₂ x + b₂ y = c₂

where a₁, a₂, b₁, b₂ , c₁, c₂ are constants

For substitution method, first expression of one variable is found from one equation and then put this expression in another equation to create a linear equation in second variable. Solve the linear equation in one variable for second variable and then put the value of second variable in first equation to solve for first variable

Given system of equations is :

2x + 3y = -12       .....(1)

x = 3y + 3          .....(2)

So the first step will be take expression for one variable from one equation and put it into another equation.

Take x = 3y +3 which is an expression for x from equation (2),

Then put it into equation (1)

⇒ 2 (3y +3 ) + 3 y = -12 , This is the first step of substitution method for this variable

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How many positive real zeroes does f(x) = x⁵ - 4x³ + 7x² + 3x - 5 have?

Answers

Given -

f(x) = x⁵ - 4x³ + 7x² + 3x - 5

To Find -

How many positive real zeroes does f(x) have =?

Step-by-Step Explanation -

We have

f(x) = x⁵ - 4x³ + 7x² + 3x - 5

where the signs of coefficients are:

+ - + + -

We can see there are three changes in the sign in f(x).

So, from

Descarte's rule,

there are either 3 0r 1 positive real roots

Now,

f(-x) = -x⁵ + 4x³ + 7x² - 3x - 5

Signs: - + + - -

So, here f(-x) has two sign changes.

From this we can conclude there is at least 1 real root and either 4, 2 or 0 imaginary roots.

Final Answer -

Positive real zeroes f(x) have =

Minimum = 1

Maximum = 3

what is the arc measure of ct in radians? what is the arc length in feet?

Answers

We will determine the arch lenght (In radians) as follows:

*First: We transform the measure of the angle from degrees to radians, that is:

[tex]\theta=80\cdot\frac{\pi}{180}\Rightarrow\theta=\frac{4\pi}{9}[/tex]

*Second: We find the arc length:

[tex]s=r\theta\Rightarrow s=(13.2)(\frac{4\pi}{9})[/tex][tex]\Rightarrow s=\frac{88}{15}\pi[/tex]

So, the arc length for CT is 88pi/15 radians.

*Third: We find its measure in feet:

[tex]s\approx18.43[/tex]

So, the arch length for CT in feet is approximately 18.43 feet.

Find the opposite of –15.

Answers

Answer:15

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

If there is a negative sign just add a positive sign or remove the sign. And if it's a positive number add a negative sign.

Easy There we go!

How do I solve this problem?By using the pythagorean identities.

Answers

Given the equation:

[tex]\sin ^2x(\csc ^2x-1)[/tex]

Using the Pythagorean identities

so,

[tex]\csc ^2x-1=\cot ^2x[/tex]

so, the equation will be:

[tex]\begin{gathered} \sin ^2x\cdot\cot ^2x \\ \\ =\sin ^2x\cdot\frac{\cos ^2x}{\sin ^2x} \\ \\ =\cos ^2x \end{gathered}[/tex]

The mean Exam score on the SOC 15 Exam 2 is 84.28 with a standard deviation of 6.71Your friend scored an 86 on the exam. What percentage of students scored lower than your friendon the exam?

Answers

First, find the z-score of 86

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{86-84.28}{6.71} \\ z=\frac{1.72}{6.71} \\ z=0.2563 \end{gathered}[/tex]

Rounding to the nearest hundredth, that is 0.26

Next, find z = 0.26 to the left of z in the z-table and we have the following

Multiply by 100%, and we have

[tex]\begin{gathered} P(z<0.26)=0.60257 \\ \\ 0.60257\cdot100\%=60.257\% \end{gathered}[/tex]

Therefore, the percentage of students who scored lower than 86 is 60.257%.

Hi, can you help me answer this question please, thank you!

Answers

Given that

[tex]\begin{gathered} \mu_d=\mu_2-\mu_1=21.1 \\ s_d=14.9 \\ n=8 \end{gathered}[/tex]

a) The formula for the test statistics for this sample is,

[tex]t=\frac{\mu_d}{s_d\sqrt[]{n}}[/tex]

Therefore,

[tex]\begin{gathered} t=\frac{21.1}{14.9\times\sqrt[]{8}}=0.50067 \\ t=0.50067\approx0.501(3\text{ decimal places)} \\ \therefore t=0.501 \end{gathered}[/tex]

Hence, the test statistic for this sample is

[tex]t=0.501[/tex]

b)

4. Find and interpret theaverage rate of change forthe interval. Show your work.1

Answers

Answer:

Average rate of change = -2 celcius / hour

Interpretation: For every unit change in the time (x), there is a change of -2 celcius in the temperature

Explanations:

The average rate of change is to be found for the interval:

[tex]1\text{ }\leq x\leq3[/tex]

From the interval, we can deduce that:

[tex]x_1=1,x_2=3[/tex]

Know the corresponding value of y for each value of x shown above:

[tex]\begin{gathered} \text{When x}_1=1,y_1=\text{ 6} \\ \text{When x}_2=3,y_2=\text{ 0} \end{gathered}[/tex]

The average rate of cgange is given by the formula:

[tex]\begin{gathered} \frac{\delta y}{\delta x}=\text{ }\frac{y_2-y_1}{x_2-x_1} \\ \frac{\delta y}{\delta x}=\text{ }\frac{0-6}{3-1} \\ \frac{\delta y}{\delta x}=\frac{-6}{3} \\ \frac{\delta y}{\delta x}=-2 \end{gathered}[/tex]

The rate of change for the interval is -2 celcius/hour

This can be interpreted as for every unit change in the time (x), there is a change of -2 celcius in the temperature

6.25 ft7.25 cm11 cm8.921.6 m

Answers

The area of the shaded region can determined by substracting the area of rectangle from the area of triangle,

[tex]\begin{gathered} A=A_r-A_t \\ =14\operatorname{cm}\times25\operatorname{cm}-(\frac{1}{2}\times11\operatorname{cm}\times25) \\ =212.5cm^2 \end{gathered}[/tex]

Thus, the area of the shaded region is 212.5 square centimeters.

You have a tree in your yard that is 60 inches around. What is the diameter of the tree?

Answers

Given : a tree in your yard that is 60 inches around

60 inches represents the circumference of the tree

The circumference =

[tex]\pi\cdot d[/tex]

Where d is the diameter of the tree

so,

[tex]\begin{gathered} \pi\cdot d=60 \\ \\ d=\frac{60}{\pi}\approx19.1 \end{gathered}[/tex]

So, the answer is : the diameter of the tree is a bout 19.1 inches

A space shuttle is moving in a straight line and is traveling at a constant speed. It takes 3 hours to get from A to B and 1 hour to get from B to C. Relative to a suitable set of axes, A is the point (4,-1,7) and B is the point (16,-10,10). Find the coordinates of C.

Answers

We will solve as follows:

First: We will use the i, j, k vector notation to describe each point as a vector:

[tex]A=4i-j+7k[/tex][tex]B=16i-10j+10k[/tex]

Now, we have that the time it takes to get from A to B is 3 hours (t1). And the time it takes from B to C is 1 hour (t2).

Second: We determine the speed from A to B:

[tex]v=\frac{B-A}{t_1}\Rightarrow v=\frac{(16-4)i+(-10+1)j+(10-7)k}{3}[/tex][tex]\Rightarrow v=\frac{12i-9j+3k}{3}\Rightarrow v=4i-3j+k[/tex]

Third: We now determine the value of C:

[tex]C=B+vt_2\Rightarrow C=(16+4)i+(-10-3)j+(10+1)k[/tex][tex]\Rightarrow C=20i-13j+11k[/tex]

So, we would have that the coordinates of C are:

[tex]C=(20,-13,11)[/tex]

Keisha is making potato casserole for a party. she needs 3/2 of a potato per guest. how many potatoes will she need for 15 guest

Answers

Keisha needs 3/2 of potato per guest ( i.e one guest is equivalent to 3/2 potato)

Thus, for 15 guests

she needs;

[tex]\begin{gathered} 15\text{ }\times\frac{3}{2} \\ \frac{15\times3}{2}=\frac{45}{2} \\ 22\frac{1}{2} \end{gathered}[/tex]

Keisha needs 45/2 potatoes for 15 guests

Write a function to model the geometric sequence in the table. n: (1 2 3 4 5)a: (75 15 3 3/5 3/25)a) f(n) = 75 (1/5) nb) f(n) = 75 (1/5) n-1c) f(n) = 1/5 (75) nd) f(n) = 1/5 (75) n-1

Answers

First let's find the ratio of the sequence, by dividing one term by the term before:

[tex]\begin{gathered} \text{second term: 15} \\ \text{first term: 75} \\ ratio=\frac{15}{75}=\frac{1}{5} \end{gathered}[/tex]

So the ratio is 1/5 and the first term is 75.

Now, we can use the following formula for the nth term of a geometric sequence:

[tex]a_n=a_1\cdot q^{n-1}[/tex]

Where q is the ratio and a1 is the first term. So we have:

[tex]a_n=75(\frac{1}{5})^{n-1}[/tex]

Substituting an by the function f(n), we have:

[tex]f(n)=75(\frac{1}{5})^{n-1}[/tex]

So the correct option is b)

Solve for brainliest and 20 points please

Answers

Answer:

C.

Step-by-step explanation:

540

Answer:

540

Step-by-step explanation:

you can use this equation to find the sum of angles for a shape
(n-2)180 with n being the number of sides. Since a pentagon has 5,
its 5-2= 3 then times 180 is 540

Use the table to find the products od the two polynomials. Write your answer in descending order l.

Answers

Answer:

To use the given table to find product of the two polynomials.

Given that,

[tex](x^2+x-2)(4x^2-8x)[/tex]

Explanation:

Using the table, we get it as,

we get,

[tex](x^2+x-2)(4x^2-8x)=4x^4-8x^3+4x^3-8x^2-8x^2+16x[/tex][tex]=4x^4-4x^3-16x^2+16[/tex]

we get,

[tex](x^2+x-2)(4x^2-8x)=4x^4-4x^3-16x^2+16[/tex]

Answer is:

[tex](x^2+x-2)(4x^2-8x)=4x^4-4x^3-16x^2+16[/tex]

10^-6/10^-2 this is my question

Answers

Answer:

[tex] \frac{1}{10000} [/tex]

or Decimal

[tex]0.0001[/tex]

Step-by-step explanation:

Greetings !

look at the figure i have attached above

Hope it helps !!

7TH GRADE MATH, BRAINLIEST WILL BE AWARDED

Answers

Answers:

Q1.a: 11g

Q1.b: 3m

Q1.3: [tex]-k^{2}[/tex]

Q2.a:  8x + 11y

Q2.b: 2a + b - 2c

Q3.a: 5q + 7

Q3.b: 6r + 3s + 7t

Step-by-step explanation:

Q1) simplify each of these expressions:

a. [tex]4g + 6g + g[/tex]

= g(4 + 6 + 1)

= 11g

____________

b. [tex]4m - m[/tex]

= m(4 - 1)

= 3m

____________

c. [tex]5k^{2} -4k^{2} -2k^{2}[/tex]

= [tex]k^{2} (5 - 4 - 2)\\[/tex]

= [tex]-1k^{2}[/tex]

= [tex]-k^{2}[/tex]

__________________________________

Q2) copy and complete the workings to simplify these expressions:

a. [tex]5x + 3x+6y+5y\\[/tex]

= x(5 + 3) + y(6 + 5)

= 8x + 11y

____________

b.[tex]2a+4b+6c-3b-8c[/tex]

combine terms b:

2a + b + 6c - 8c

combine terms c:

= 2a + b - 2c

__________________________________

Q3) simplify these expressions by collecting like terms:

a.[tex]9q-4q+15-8[/tex]

combine terms q:

5q + 15 - 8

combine numbers:

= 5q + 7

____________

b. [tex]8r+2s+4t-2r+s+3t[/tex]

combine terms r:

6r + 2s + 4t + s + 3t

combine terms s:

6r + 3s + 4t + 3t

combine terms t:

= 6r + 3s + 7t

Help me asp please!!

Answers

It is an ongoing function. A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

What is function?In mathematics, a function is an expression, rule, or law that defines a connection between one variable (the independent variable) and another variable (the dependent variable).A function is defined as a relationship between a set of inputs and one output for each. A function is an input-output relationship in which each input corresponds to exactly one output.Every function has a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x is the input. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this.

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A cone has a volume of 3014.4 cubic inches and a radius of 12 inches.what is the height?

Answers

Answer:

h = 20inches

Explanations:

The formula for calculating the volume of a cone is expressed as:

[tex]V=\frac{1}{3}\pi r^2h[/tex]

where:

r is the radius

h is the height

Given the following

r = 12 inches

V = 3014.4 cubic inches

Substitute to determine the height

[tex]\begin{gathered} 3014.4=\frac{1}{3}\times3.14\times12^2\times h \\ 3014.4\times3=452.16h \\ h=\frac{9043.2}{452.16} \\ h=20inches \end{gathered}[/tex]

Hence the height of the cone will be 20inches

A group of friends were working on a student film. They spent all their budget on equipment and props. They spent $369 on equipment and 55% of the total budget on props. What was the total budget for their student film

Answers

Answer: t = 820

Step-by-step explanation:

1) Set up the equation

369 + 55%t = t

2) Simplify the percentage

369+ 0.55t = t

3) Minus 0.55 t on both sides

369 = 0.45t

4) Set t by itself.

t = 820

Can you please also give all forms of the end behavior such as ups/downs, as_,_ , and limits #25

Answers

[tex]f(x)=\frac{x}{2x+1}[/tex]

The given function is a rational function

We will find the zeros of the denominator

[tex]\begin{gathered} 2x+1=0 \\ 2x=-1 \\ x=\frac{-1}{2} \end{gathered}[/tex]

The end behavior of the function will be as follows:

[tex]\begin{gathered} x\rightarrow(-\frac{1}{2})^-;f(x)\rightarrow\infty \\ x\rightarrow(-\frac{1}{2})^+;f(x)\rightarrow-\infty \\ x\rightarrow\infty;f(x)\rightarrow\frac{1}{2} \\ x\rightarrow-\infty;f(x)\rightarrow\frac{1}{2} \end{gathered}[/tex]

The graph of the function is as follows:

this. this is sucking my soul away.

Answers

Check the picture below.

let's recall that twin sides stemming from a common vertex, make twin angles at the base.

Create a data set that has 4 values with a mode of 3, a median of 6, and a meanof 10

Answers

We are to create a data set of 4

that is a, b, c, d

mode means a number that occur the most

Median means the middle number

Mean means the average number

in the set, we must have a mode of 3

3, 3,

to get a median of 6, we need a number when we add to three and divide by 2 will give us 6

the number is 9

3 + 9 / 2

12/ 2 =

3, 3 , 9, d

the last number is d and it is unknown

since means is 10

mean = summation of all the numbers in the data set / the total number

the total number is 4

mean = 10

10 = 3 + 3 + 9 + d / 4

cross multiplication

10 x 4 = 3 + 3 + 9 + d

40 = 6 + 9 + d

40 = 15 + d

isolate d

d = 40 - 15

d = 25

therefore, the data set with a mode of 3, median of 6 and a mean of 10 are

3 , 3 , 9, 25

Please answer correctly and tell me if its linear quadratic or exponential please.

Answers

Answer:

Exponential

Step-by-step explanation:

If the initial difference has the same value, the model will be linear.

If the value of the second difference is the same, the model will be quadratic.

If the difference has been calculated more than five times before duplicate values are discovered, the model might be exponential or involve another unique equation.

Hope this helps!

This table represents what would be an exponential graph.

When graphing these points on a coordinate plane, we will find that it forms a curvy pattern.

When a graph forms a pattern of the points to form a curve, the graph is exponential.

When a graph forms a pattern of the points in resemblance of a “U” shape, the graph is quadratic.

When a graph forms a pattern of the points in resemblance of a straight line, the graph is linear.

For an example of an exponential graph, see the picture attached.

A recipe that makes 10 pancakes calls for 13/4 cups of milk. If you want to scale down the recipe so that it makes only 2 pancakes, about how much milk should you use? A. 3/4 cup B. 1/2 cupC. 7/20 cup D. 3/10 cup E. 7/12 cup

Answers

Answer:

13/20 cups

Explanations:

The recipe makes 10 Pancakes with 13/4 cups of milk

The recipe will make 1 pancake with x cups of milk

[tex]\begin{gathered} x\text{ = }\frac{13}{4}\div10 \\ x\text{ = }\frac{13}{4}\times\frac{1}{10} \\ x\text{ = }\frac{13}{40} \\ \end{gathered}[/tex]

The recipe will make 1 pancake with 13/40 cups of milk

The recipe will make 2 pancakes with (2 x 13/40) cups of milk

= 26 / 40

= 13 / 20

The recipe will make 2 pancakes with 13/20 cups of milk

the store bought a bike from the factory for 90$ and sold it to Andre for 117 what percentage was the markup?

Answers

The markup percentage was

[tex]\begin{gathered} P=\frac{117-90}{90}\cdot100 \\ P=\frac{27}{90}\cdot100 \\ P=30 \end{gathered}[/tex]

The markup percentage was 30%.

Write the domain and range of g as intervals or unions of intervals

Answers

It's important to know that empty circles refer to open intervals or parenthesis.

In this case, we observe that the first interval of the domain is (-1, 1) and the second interval of the domain is (2, 5), so the whole domain would be the union of these two intervals.

[tex]\text{Domain}=(-1,1)\cup(2,5)[/tex]

To obtain the range, let's observe the y-values. The function goes from y = -5 to y = 3, so the range would be

[tex]Range=(-5,3)[/tex]

Writing out and solving inequalities a number divided by three less two is at most two

Answers

The inequlaity is ;

[tex]\begin{gathered} \frac{x}{3\text{ }}\text{ - 2}\leq2 \\ \end{gathered}[/tex]

And the solution is;

[tex]x\text{ }\leq\text{ 12}[/tex]

Let the number be x

The number divided by 3

That is x/3

less two means minus 2

x/3 - 2

Is at most 2 means it is less than or equal to 2

so the inequality is;

[tex]\begin{gathered} \frac{x}{3}\text{ - 2}\leq\text{ 2} \\ \\ \text{Solving the inequality, we have} \\ \\ \frac{x}{3}\text{ }\leq\text{ 2 + 2} \\ \\ \frac{x}{3}\text{ }\leq\text{ 4} \\ \\ x\text{ }\leq\text{ 3 }\times\text{ 4 } \\ x\text{ }\leq\text{ 12} \end{gathered}[/tex]

A line contains points F, G, H, I, J. The space between F G is 2. The space between H and I is 1. The space between F and I is 7.
If FG = 2 units, FI = 7 units, and HI = 1 unit, what is GH?

3 units
4 units
5 units
6 units

Answers

The measure of GH is 4 units.

The correct option is (B)

What is equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.

Given:

FG = 2 units, FI = 7 units, and HI = 1 unit

Now,

FI = FG+ GH +HI

7= 2 + GH + 1

7= 3 + GH

GH = 7-3

GH = 4 units

Hence, the measure of GH is 4 units.

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