Solve the system by graphing

x+2y=3
-x+3y+7

The value of x1 = -4 and the value of x2 = 26/3 for the given inverse of the coefficient matrix.

The placement of numbers in rows and columns to create an array is known as a matrix.

A row is a horizontal arrangement, whereas a column is a vertical arrangement. Every integer in the matrix is referred to as an element, and its location is symbolized by A_mn.

Using the matrix, we can write the equation as:

AX = B

X = A^-1 B

[tex]\left[\begin{array}{c}X_1&X_2\end{array}\right] = \left[\begin{array}{cc}-1&-1\\2&\frac{5}{3} \end{array}\right] \left[\begin{array}{cc}6\\ -2\end{array}\right][/tex]

Using the matrix multiplication, we have:

[tex]\left[\begin{array}{c}X_1&X_2\end{array}\right] = \left[\begin{array}{cc}-4\\ \frac{26}{3} \end{array}\right][/tex]

Hence, the value of x1 = -4 and the value of x2 = 26/3 for the given inverse of the coefficient matrix.

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Multiply the mass in kilogrammes by 2.2046226218 to convert 50 kg to pounds.

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To find your “Aro for once per one week”, you need to first create an account on the Aro app.

Once you have created an account, you can add your weekly commitments, such as meetings, classes, or other activities, to your calendar. You can then set up a recurring event that will occur once per week.

You can also customize the recurring event by setting the date and time, adding a description and location, and inviting other people to join. Once you have created the recurring event, you can view it on your calendar and easily adjust it if something changes.

Aro makes it easy to plan and manage your weekly commitments by allowing you to create recurring events. With Aro, you can easily keep track of your weekly commitments and ensure that you don’t miss any important appointments.

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(f ◦ g)(x) = -2x^2 + 11.

What is Composition of two functions ?

The new function obtained by performing f first and then g is the combination of two functions g and f.

The composition of two functions f and g, denoted by (f ◦ g)(x), is defined as the function that maps x to f(g(x)).

Given the functions f(x) = 2x + 3 and g(x) = -x^2 + 5, the composition of these two functions is:

(f ◦ g)(x) = f(g(x)) = f(-x^2 + 5) = 2(-x^2 + 5) + 3 = -2x^2 + 11

So, (f ◦ g)(x) = -2x^2 + 11.

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Answer:

matt needs to use more than 2% mixture for his aquarium

Step-by-step explanation:

Answer:the answer of this slope is  7 an 24

Step-by-step explanation:

Answer:

q is independent var, r is dependent

Step-by-step explanation:

The probability that their meeting will be held at the station would be = 1/4

Probability is defined as the representation of an expression which shows the possible outcome of an event.

The random time for the arrival of both friends at the station = ,7:20 - 7:00

= 20 minutes.

The extra minutes used to wait for each other which is outside the random time needed to arrive at the station = 5 min.

Therefore the probability for both of them meeting at the station = 5/20 = 1/4.

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The complete table is shown below.

The equation is: y= 53.x + 250.

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. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Mai must spend $250 on wire and $5.30 per bracelet for beads.

a) 5.3 x 20 + 250 = 356 dollar

5.3 x 40 + 250 = 462 dollar

5.3 x 60 + 250 = 568 dollar

so, the complete table is

 Number of bracelets      cost in dollar

                 20                          356

                 40                          462

                 60                          568

b) let the number of bracelets be x and the cost is y dollar

so, the equation is

y= 53.x + 250

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The kind of data we have is Categorical data. Data that can be broken down into groups or categories is known as categorical data.

There are three categories in this case: eggs, cereal, and no breakfast These groups include the 10 students who ate cereal, 5 students who ate eggs, and 3 students who did not eat breakfast at all.

A categorical variable is a variable in statistics that can have one of a limited, typically fixed number of possible values and assign each observational unit to a specific group or nominal category based on some qualitative property.

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Answer:

The total number of markers along the 5-mile walkway is 6.

This includes markers at each mile (5 markers) and one marker at the east end of the walkway.

The inequality is equivalent to the given inequality? -4(x+7)< 3(x-2) is x>-22/7

Inequality is a mathematical statement which shsow that two quantities are not the same or that they are not equal.

The given inequality is -4(x+7) < 3(x-2)

Opening the brackets to have

-4x-28<3x-6

Collecting like terms to have

-4x-3x<-6+28

This shows that -7x<22

Making x the subject of the relation we have

x>-22/7

The inequality that satisfies the given inequality is x>-22/7

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The limit does exist for lim x→49 (x^2 - 7x - 49) and it approaches value of 2009.

The limit can be found using algebraic manipulation. First we will try plug in the value and see if we can determine the limit. We have:

lim x→49 (x^2 - 7x - 49) = 49^2 - 7×49 - 49 = 2009

So limit exist at x^2 - 7x - 49 and it can be found out by simple substitution.

So, as x approaches 49, the expression x^2 - 7x - 49 approaches 2009.

Therefore, lim x→49 x^2 - 7x - 49 = 343.

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The average of the 3-day simple moving averages for these five days to the nearest $0.01 is $105.99, $107.19 and $110.40.

What is a Simple Moving Average?

By dividing the number of periods inside the range by the average of the range of prices, simple moving averages are used.

We are given closing prices of a stock over a 5-day period.

So, 3-day simple moving averages are

For Monday - $104.67

For Tuesday - $103.95

For Wednesday - ($104.67 + $103.95 + $109.35)/3 = $105.99

For Thursday - ($103.95 + $109.35 +$108.27)/3 = $107.19

For Friday - ($113.58 + $109.35 +$108.27)/3 = $110.4

Hence, the average of the 3-day simple moving averages for these five days to the nearest $0.01 is $105.99, $107.19 and $110.40.

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The equation in standard form of the line that passes through the point (6, 1) and is parallel to the line represented by 8x + 3y= 15 is equal to y = -8x + 43.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ -8 = -8

At data point (6, 1), a linear equation of this line can be calculated in point-slope form as follows:

y - 1 = -8(x - 6)

y - 1 = -8x + 42

y = -8x + 42 + 1

y = -8x + 43

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The probability of exactly 2 couples dancing together is 100/45 = 20/9.

To find the probability of the total number of ways to form pairs of 5 couples is C(10, 2) = 45, because there are 10 people and we need to choose 2 at a time.

The number of ways to form exactly 2 couples dancing together is C(5, 2) * C(5, 2) = 10 * 10 = 100. This is because we first choose 2 couples out of the 5 couples and then pair the males and females within each chosen couple.

So the probability of exactly 2 couples dancing together is 100/45 = 20/9.

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The probability of exactly 2 couples dancing together is 100/45 = 20/9.

To find the probability of the total number of ways to form pairs of 5 couples is C(10, 2) = 45, because there are 10 people and we need to choose 2 at a time.

The number of ways to form exactly 2 couples dancing together is C(5, 2) * C(5, 2) = 10 * 10 = 100. This is because we first choose 2 couples out of the 5 couples and then pair the males and females within each chosen couple.

So the probability of exactly 2 couples dancing together is 100/45 = 20/9.

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Answer:

The expression is:

4K

But as an equation, it would be:

T = 4K

Step-by-step explanation:

K = Kelli's age

T = Trey's age

Trey is 4 times older than Kelli

T = (4)(K)

y = -t is  parametric equation of the line passing through a and parallel to b

Parametric Equation = Type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable.

⇒ parametric equation of line passing through a point (a₁, b₁, c₁)

  and parallel to a vector <a, b, c> is given by :

  x =a₁ + at ,   y = b₁ + bt   ,   z = c₁ + ct

now according to question:

given -

point, P(1, 0, -3)

line,   x = −1 + 2t , y = 2−t, and z = 3+3t.

so from the line the vector is=  <2, -1, 3>

now using above formula,

equation of line is =   x = 1 + 2t , y = −t, and z = -3+3t.

we have to solve for 'y' only,

⇒ y = -t    

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Triangle ABC is similar to triangle DEF because their corresponding angles, ∠A and ∠D, and ∠B and ∠E, are equal.

The AAA similarity is a theorem of a triangle which means "angle-angle-angle", that is, two triangles are similar to each other if they both have three corresponding angles that are congruent to each other.

The line BC divides the line AD and AE, we can state that the two triangles are similar by the Angle-Angle-Angle (AAA) Similarity Theorem.

The AAA Similarity Theorem states that if the three angles of one triangle are equal to the three angles of another triangle, then the two triangles are similar.

Here is an example similarity statement based on the Angle-Angle-Angle (AAA) Similarity Theorem: "Triangle ABC is similar to triangle DEF because they both have equal corresponding angles, ∠A and ∠D, ∠B and ∠E, and ∠C and ∠F, and because the line BC divides the line AD and AE."

Hence, Triangle ABC is similar to triangle DEF because their corresponding angles, ∠A and ∠D, and ∠B and ∠E, are equal.

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Answer:

-5(7y+1)

Step-by-step explanation:

-35y-5

Trouver le plus grand facteur commun et le diviser

Le plus grand facteur commun est -5

-35y/-5=7y

-5/-5=1

Simplifiez l'équation

-5(7y+1)

Je ne parle pas français mais j'espère que cela vous aidera.

Answer: 0.56

Step-by-step explanation: convert from fraction to decimal

The solution to the initial-value problem is  y^4 = -2 + (c^4 + 2) e^28(1-cosx)

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable. For example, dy/dx = 5x.

Given Differential Equation is  y^3 dy/dx = (7y^4 + 14) sin(x)

we have to put y^4 = z and

then, reduce the differential equation to find out I.F value.

and next we have to find out general solution of z(I.F) = [tex]\int\limits\, (I.F)Q dx + c[/tex]

and then put y(0) to get c value

so, we get y^4 = -2 + (c^4 + 2) e^28(1-cosx)

Please refer below attached image for complete solving process.

Thus, the solution to the initial-value problem is  y^4 = -2 + (c^4 + 2) e^28(1-cosx)

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The simplifies expression is -5x/6 - 8

The expression "quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity" represents:

-(2/3)x - 6 - ( -14 + (1/6)x)

The process of simplifying an expression involves reducing the expression to its simplest form, making it easier to understand and manipulate. To simplify an expression, we combine like terms by adding or subtracting the coefficients.

We need to simplify this expression into its simplest form.

Thus,

-(2/3)x - 6 - ( -14 + (1/6)x) equals,

= -2x/3 - 6 +14 - x/6

= -(4+1)x/6 - 8

= -5x/6 - 8

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Step-by-step explanation:

The slope of a line can be calculated as the difference of the y-coordinates divided by the difference of the x-coordinates of two points on that line. In this case, we have two points: (10,23) and (20,36).

So, the slope of the line would be:

(36 - 23) / (20 - 10) = 13 / 10 = 1.3.

Therefore, the slope of the line that has the coordinates of (10,23) and (20,36) is 1.3

The answer is B. Both Charlie and Annabeth will have travelled for the same amount of time.

They will have travelled the same amount of time. This is because the time spent traveling is determined by the total distance travelled, not the direction of travel. In this case, the distance between New York and the travellers' current location is decreasing at first and then increasing, suggesting that they have reached their destination and are now returning. Since the total distance travelled is the same regardless of the direction, the time spent traveling will also be the same for both travellers. Therefore, both Charlie and Annabeth will have travelled for the same amount of time.

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The maturity date of the loan is July 31st.

To find the maturity date, you first need to find the number of days between May 11th and the maturity date. The loan was taken out for 82 days, so you add 82 days to May 11th to find the maturity date.

For example, if May 11th is day 1, then day 82 would be July 31st. Therefore, the maturity date of the loan is July 31st.

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The required General Solution Of the Given Differential Equation is Y = e^(-4x) * (X^2/4 + 7x/4 + X^2/2 + 7x + C') + X^2/4 + 7x.

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f (x) In this case, the variables "x" and "y" are independent and dependent, respectively. For illustration, dy/dx = 5x.

The general solution to the differential equation Y' = 4Y + X^2 + 7 can be found by using an integrating factor. The integrating factor is e^(4x), and the solution is:

Y = e^(-4x) * ∫(e^(4x) * (X^2 + 7)) dx - X^2/4 - 7x + C,

where C is an arbitrary constant of integration. The solution can be simplified by solving the definite integral

= ∫(e^(4x) * (X^2 + 7)) dx,

which results in:

Y = e^(-4x) * (X^2/4 + 7x/4 + X^2/2 + 7x + C') + X^2/4 + 7x,

where C' is another arbitrary constant of integration.

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Answer: The numeric coefficient is 3.

Step-by-step explanation: