Find the 23rd term 20,-2,-24 and find explicit formula

The solution to the system of equations is x = −7 and y = −1.

To solve the given system of equations using an inverse matrix, we can represent the system in matrix form, Ax=B, then find the inverse of matrix A to solve for 'x'.

Given matrix:

[tex]\left\{\begin{array}{ccc}x-6y=-1\\-2x+9y=5\end{array}\right[/tex]

[tex]\hrulefill[/tex]

First, we rewrite the system of equations in matrix for, Ax=B:

[tex]A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right], \ x = \left[\begin{array}{cc}x\\y\\\end{array}\right], \ B = \left[\begin{array}{cc}-1\\5\\\end{array}\right][/tex]

So, Ax=B can be written as:

[tex]\Longrightarrow \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right] \left[\begin{array}{cc}x\\y\\\end{array}\right] = \left[\begin{array}{cc}-1\\5\\\end{array}\right][/tex]

[tex]\hrulefill[/tex]

[tex]\boxed{\left\begin{array}{ccc}\text{The inverse of a 2x2 matrix,} \ \left(\begin{array}{ccc}a&b\\c&d\end{array}\right), \ \text{is given by:}\\\\\\A^{-1}= \dfrac{1}{ad-bc}\left(\begin{array}{ccc}d&-b\\-c&a\end{array}\right)\end{array}\right}[/tex]

Here,

[tex]\Longrightarrow A = \left[\begin{array}{cc}1&-6\\-2&9\\\end{array}\right][/tex]

The determinant ∣A∣ is:

[tex]\Longrightarrow |A|=(1)(9)-(-6)(-2)=9-12\\\\\\\\\therefore |A|=-3[/tex]

Since the determinant is not zero, A has an inverse, which can be calculated as:

[tex]\Longrightarrow A^{-1}= \dfrac{1}{-3}\left(\begin{array}{ccc}9&6\\2&1\end{array}\right)\\\\\\\\\therefore A^{-1}=\left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)[/tex]

[tex]\hrulefill[/tex]

We can solve for 'x' using x=A⁻¹B:

[tex]\Longrightarrow x = \left(\begin{array}{ccc}-3&-2\\-2/3&-1/3\end{array}\right)\left(\begin{array}{cc}-1\\5\\\end{array}\right)[/tex]

Upon multiplication, we get:

[tex]\Longrightarrow x = \left(\begin{array}{cc}(-3)(-1)+(-2)(5)\\(-2/3)(-1)+(-1/3)(5)\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}3-10\\2/3-5/3\\\end{array}\right)\\\\\\\\\Longrightarrow x = \left(\begin{array}{cc}-7\\-3/3\\\end{array}\right)\\\\\\\\\therefore \boxed{\boxed{x=\left(\begin{array}{cc}-7\\-1\\\end{array}\right)}}[/tex]

Thus, the solution to the system of equations is x = −7 and y = −1.

The required length of AE will be 14 units on the given rhombus.

We know that all sides of a rhombus are equal, then note that AD equals DC, that is;

4x + 2 = 7x - 13

2 + 13 = 7x - 4x

15 = 3x

Divide both sides of the equation by 3

5 = x

If AD = 4x + 2, then when x  = 5

AD = 4(5) + 2

AD = 20 + 2

AD = 22

So, triangle ADE may now be separated, with AD measuring 22 units and ED measuring 17 units (midpoint between points B and D). Line AE may be determined using Pythagoras' theorem, which states:

AC² = AB² + BC²

Where AC is the hypotenuse, and AB and BC are the two other sides

Substituting for values as given in the question, we now have;

AD² = ED² + AE²

22² = 17² + AE²

484 = 289 + AE²

484 - 289 = AE²

195 = AE²

√195 = AE

13.96 = AE

So, length AE ≈ 14 units (to the nearest whole number)

Thus, the required length of AE will be 14 units on the given rhombus.

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Answer:

3,4

Step-by-step explanation:

use section formula,as it divides in 1 :1

7+x/2 =5 so x is 3

Answer:

square root of 43 is irrational and thus square root of 43 + 5 is also irrational.

Step-by-step explanation:

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The standard deviation of a binomial distribution is C. 3.46

Standard deviation is the measure of spread of a set of data.

Since a binomial trial has a probability of success of 0.2, and 75 trials are performed. To find the standard deviation, we use the formula for standard deviation of a binomial distribution.

The standard deviation of a binomial distribution is given by σ = √(npq) where

Given that for our binomial trial

So, substituting the values of the variables into the equation, we have that

σ = √(npq)

σ = √(75 × 0.2 × 0.8)

σ = √(75 × 0.16)

σ = √12

σ = 3.464

σ ≅ 3.46

So, the standard deviation is C. 3.46

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Answer:

The top left table.

Step-by-step explanation:

An initial value is the y-intercept, which is where the function touches the y-axis. If the initial value is 3, the coordinate must be (0,3). This rules out the both tables on the right.

The rate of change is how much the function's y values increase or decrease. If the rate change is 4, the y values increase by 4 each unit, which matches the top left table.

Based on the triangle midsegment theorem, the length of CZ is calculated as: 7.2 m.

The triangle midsegment theorem states that when two sides of a triangle are joined together by a line segment at their midpoint, the line segment is called the midsegment, and it is parallel to the third side whose measure is twice its length.

This implies that, AB is a midsegment in the image shown for triangle XYZ. It is parallel to YZ.

Therefore:

AB = 1/2(the length of YZ)

Substitute the value of AB into the equation:

7.2 = 1/2(YZ)

2(7.2) = YZ

YZ = 14.4 m.

The length of CZ = 1/2(the length of YZ) [this is because YC = CZ]

CZ = 1/2(14.4)

CZ = 7.2 m.

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Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

No it is not

y = 13x ,y = x - 2 and y = 2x + 11 represents a straight line which is proportional to x i.e. a linear function .

The proportional relation equation is y = kx .

The letters y and x are the variables, which can change, and the letter k is the constant of proportionality.

According to the question ,

Given: y = 13x

since y ∝ x,

Therefore the equation is said to be proportional .

Given: y = x²

Since the term y is proportional to the square of square ,so we can't say say that the equation is proportional .

Given: y = x - 2

Since ,y is in the form of the equation y = mx + c and y is proportional to x as well ,therefore we say that x is proportional to x .

Given : y = 2x + 11

Since y is in the form of y = mx + c and y is proportional to x

As the given expression represents a straight line , so its proportional to x .

Hence, all the given expressions are proportional to x except the second option which is proportional to square of x and is not forming a linear equation that is a straight line.

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The outside temperature t when Josefina ate breakfast was 55F.

What are equations?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

According to the given question:

Let the temperature outside at the time of breakfast be t.

Temperature dropped by 20F by the time for dinner.

So the temperature at the time of breakfast was t - 20

Now, when she ate dinner the temperature was 35F

So the equation for outside temperature t when Josefina ate breakfast is

t - 20 = 35

Solving to get t that is temperature in the morning

t = 35 + 20

t = 55F

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Answer:

A= I + P

for real? And why is high-school question

Answer:

16.5

Step-by-step explanation:

8.25+8.25=16.5

Entonces, la distancia entre los puntos A y B es de aproximadamente 15.

Generalmente, Para encontrar la distancia entre los puntos A y B, puedes utilizar la fórmula de la distancia euclidiana:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

En este caso, la distancia sería:

d = √((3 - (-6))² + (-7 - 5)²)

The square root of ((3 - (-6))² + (-7 - 5)²) is equal to:

=√((3 - (-6))² + (-7 - 5)²)

= √((9)² + (-7 - 5)²)

= √(81 + 144)

= √225

d ≈15

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Encontró la pregunta completa

El punto A está en (-6,5) y el punto B está en (3,-7). ¿Cuál es la distancia entre los puntos

After fitting a bookcase with a height of 2.5 feet into a space with a width of 3.25 feet, 0.375 feet will be left on each side.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Here,

Width of bookshelf=2.5 feet

Space to keep the bookshelf=3.25 feet

Total difference for the remaining space near bookshelf,

=3.25-2.5

=0.75 feet

Space remaining on either side of bookshelf,

=0.75/2

=0.375 feet

A space of 0.375 feet will be remaining on each side after keeping a bookshelf of size 2.5 feet in a space of 3.25 feet.

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Answer:

C

Step-by-step explanation:

4x + 3y = 24

3y = -4x + 24

y = -3/4x + 8

May I please have brainliest? It will really help me get to the next level! Thank you!

Answer:

Y= -4/3x + 8

Step-by-step explanation:

4x + 3y = 24

-4x             -4x

3y = -4x + 24

/3      /3     /3

Y = -4/3x + 8

Answer:

Step-by-step explanation:

You want it to be in y=mx+b form.

B= y intercept

mx= slope (3x)

Y=3x+-2

Answer:

? = 180

Step-by-step explanation:

The pound as a unit of mass , 14 x (1ounce)= 14 ounce.

The British imperial and American customary systems of measurement both utilize the pound as a unit of mass. The international avoirdupois pound, which is legally defined as exactly 0.45359237 kilograms and is divided into 16 avoirdupois ounces, is the definition that is currently most frequently used.

The avoirdupois pound is represented by the worldwide standard symbol, lbm (for the majority of pound definitions), (mostly in the U.S.),  and  (particularly for the apothecaries' pound).

The currency came from the Roman libra (hence the abbreviation "lb"). The Dutch term pond, the Swedish word pund, and the German word pfund are all cognates of the English word pound.

Older and no longer in use, these units (replaced by the metric system).

Hence, 14 x (1ounce)= 14 ounce.

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The greatest common factor of 15n^5, 30n^3, and 45n^2 is 15n^2

In this question we need to find the greatest common factor of 15n^5, 30n^3, and 45n^2.

we know that the greatest common factor of given numbers is nothing but the highest number that divides given numbers.

If we look at the variable part of given monomials, then the highest power of n that divide given monomials is n^2.

And the greatest common factor os (15, 30, 45) is 15

So, we get a monomial 15n^2

Therefore, the greatest common factor is 15n^2

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to get the slope of any straight line, we simply need two points off of it, let's use those in the picture above.

[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +4}{1 +5} \implies {\Large \begin{array}{llll} \cfrac{ 1 }{ 6 } \end{array}}[/tex]

Answer:

Approximately 2.6% of the total number of parking spots are designated as accessible.

Step-by-step explanation:

If the ratio of accessible parking spots to general parking spots is 2:75, this means that for every 2 accessible parking spots, there are 75 general parking spots. This can also be written as a fraction: 2/(2+75) = 2/77.

The fraction represents the proportion of the total number of parking spots that are designated as accessible. In this case, 2/(2+75) = 2/77 = approximately 0.026, or 2.6%. This means that approximately 2.6% of the total number of parking spots are designated as accessible.

It's important to note that the number of accessible parking spots should be determined based on the needs of the community and should meet or exceed the minimum requirements set by law. In the United States, the Americans with Disabilities Act (ADA) sets minimum requirements for the number of accessible parking spaces that must be provided in public parking lots. The exact number of spaces required depends on the size and type of the parking lot.

With a total pay last week of $4720 and a 2.5% commission on sales, she made 275 in sales.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Here,

The money earned by sales=2.5%*600

=$15

Let the total sales be x,

600+15x=4720

15x=4720-600

15x=4120

x=274.67

x=275 sales

Her last week sales was 275 as her total salary last week was $4720 and she receives 2.5% commission on sales.

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The value of x = 3 for y = 9 is a solution of the linear equation -4x = y - 21.

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.

Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalises the two sides of the equation.

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.

Basically, there are infinitely many solutions to a linear equation with two variables.

The solution of the equation (x,9).

For the equation -4x = y -21

here, y = 9

-4x = 9 - 21

⇒ -4x = -12

⇒ x = 3.

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Answer:

y = 2/3x - 2

Step-by-step explanation:

To Literally Solve for y, we must first isolate it. This means putting it and its coefficient on the own side of the equation.

If you add, multiply, divide, subtract, put something to the power/root both sides of an equation, the final result will stay the same.

4x - 6y = 12

Subtract 4x on both sides.

4x - 4x -6y = 12 - 4x

Simplify.

-6y = 12 - 4x

Divide both sides by -6.

y = -2 + 2/3x

Adjusted the equation for clarity.

y = 2/3x - 2

Answer:

x = 0 and y = 2

Step-by-step explanation:

5x + 3y = 6

-5x - 3y = -6

Adding the equations gives 0 = 0, so the equations are equivalent.

x = 0 and y = 2

Answer:

The graph of x - y = 4 is D.

Step-by-step explanation:

substituting a random value for either x or y will give you a value for the other unknown

that's to say,if x is 2 ,then y will be -2

More pairs of coordinates then are got using the same method

these are plotted and a graph similar to the one in D is got.

The boy should throw the ball at a speed of 17.15 m/s.

Newton’s first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This tendency to resist changes in a state of motion is inertia. If all the external forces cancel each other out, then there is no net force acting on the object.  If there is no net force acting on the object, then the object will maintain a constant velocity. His second law defines a force to be equal to change in momentum (mass times velocity) per change in time. Momentum is defined to be the mass m of an object times its velocity V.

From Newton's equations of motion,

v = u + at

Here, v = 0 m/s

a = g = -9.8 m/s²

t = 3.5/2 = 1.75 s

Put these values in the above equation:

u = v - at

u = 0 - (-9.8)(1.75)

∴ u = 17.15 m/s

Thus, the boy should throw the ball at a speed of 17.15 m/s.

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Answer: 80

Step-by-step explanation:

The owners will need 80 racks to hold all 7,200 comic books. (7,200 / 90 = 80)