Solve the system using a matrix,
3x – 2y = 2
6x - 5y = -1

Answer:

∠ b = 108° , ∠ d = 72°

Step-by-step explanation:

(a)

the sum of the 3 angles in a triangle = 180° , that is

∠ a + ∠ b + ∠ c = 180°

25° + ∠ b + 47° = 180°

∠ b + 72° = 180° ( subtract 72° from both sides )

∠ b = 108°

(b)

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles , then

∠ d = ∠ a + ∠ c = 25° + 47° = 72°

The solution is

a) Option A.

The equation to determine the messages sent by Bria is t/4 = 20

b) Option C.

The student is 1.25 feet above sea level , and the absolute value is 1.25 ft

c) Option C.

The values are opposites of each other , and they are both 5/2 units from zero

What is an 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.

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 data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the number of texts sent by Bria be = t

The number of texts sent by April = 20

April sent one fourth of the texts sent by Bria

So ,

The number of texts sent by Bria t = 4 x number of texts sent by April

Substituting the values in the equation , we get

The number of texts sent by Bria t = 4 x 20

Divide by 4 on both sides of the equation , we get

t/4 = 20   be equation (1)

And , t = 80 texts

Therefore , the number of texts sent by Bria is given by the equation

t/4 = 20

b)

Let the sea level be represented as = 0

The number 1.25 is above the sea level of 0

The absolute value of 1.25 is = 1.25

Therefore , the expression will be the student is 1.25 ft above the sea level and the absolute value is 1.25 ft

c)

Let the first number be = -5/2

Let the second number be = 5/2

Now , the difference of the numbers from the point zero = 5/2 units

Because the distances are always positive

The numbers -5/2 and 5/2 are opposite numbers

Hence , the expression will be the numbers are opposites of each other and they are 5/2 units from 0

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Applying distributive property of multiplication the solution of the multiplication problem is 5 11/56

The distributive property states that multiplying the total of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and adding the products together.

This applied mathematically in the problem

4/7 x 4 5/8

dividing by 4 for the multiplicand and multiplier

4/7 ÷ 4 = 1/7

4 5/8 ÷ 4 = 37/32

4/7 x 4 5/8

= 4 * (1/7 + 37/32) - distributive property applied

= 4 * (291/224)

= 291 / 56

= 5 11/56 as mixed number

using distributive property the solution of the multiplication is 5 11/56

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Answer: No

Step-by-step explanation:  If A − λI has rank 1, then the geometric multiplicity of λ is 4 − 1 = 3, equal to the algebraic multiplicity of λ.

The Matrix A is not defective.

A theorem in linear algebra known as the rank-nullity theorem states that the domain dimension of a linear map is equal to the sum of the rank (or the dimension of its image) and the nullity of the map (the dimension of its kernel).

Given:

We have  A be a 4 x 4 matrix

let λ be an eigenvalue of multiplicity 3 and rank 1, then by rank nullity theorem we have

Rank(A-λI) + Nullity((A-λI) =4

dimN(N-λI) = Nullity(A-λI)

dimN(N-λI) = 4 - Rank(A-λI)

dimN(N-λI)  = 4-1

dimN(N-λI) = 3

As a result, eigenvalue is made up of 3 linearly independent eigenvectors.

This guarantees that there is another eigenvalue other than since is an eigenvalue of multiplicity 3. This provides us 4 linearly independent eigenvectors in the matrix A, in addition to the 3 linearly independent eigenvectors in the eigenspace of. Now we If and only if A has n linearly independent eigenvectors, then A is diagonalizable. A thus has no defects.

Hence, matrix A is not defective.

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Answer:

190

Step-by-step explanation:

500x0.38=190

I just see it that way

The proportion to calculate triangle side LM in the given triangle is 3/2

The side LM is calculated using the idea of similar triangle, in this case the triangles are equal in proportion to each other

To find the proportion we take the ratio of the sides this is done as follows

LM / HJ = MN / JK = LN / HK

substituting the values

MN / JK = 9 / 6 = 3 / 2

the proportion is = 3/2

to find LM

4.5 * 3/2

= 6.75 cm

Using proportion of 3/2 the length of side LM is solved to be 6.75 cm

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The probability that Bela and Jenn pick the same part is; 0.006944

In maps, it is pertinent to note that parallels are the lines that run from east to west and never intersect with each other while meridians run from north to south and intersect at the north and south poles.

Now, since bella's globe has 12 parallels and 12 great meridians, then it means that the total number of parts in this globe will be 12 * 12 = 144 parts.

Thus, probability that they both pick the same part is;

P(same part picked) = (12/144) * (12/144)

= 0.006944

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On solving the provided question, we can say that -  correlation coefficient , r= .95

The Pearson's correlation coefficient, also known as the Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply correlation coefficient, is a statistical indicator of the linear relationship between two sets of data.

[tex]S_{xx}[/tex] = ∑[tex]x^2[/tex] + [tex]nx^2[/tex] = 60

[tex]S_{yy} = 60[/tex]

r  = .95

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Answer:

a) The function has a minimum value.

b) The minimum value of the function is -27.

c) The minimum value occurs at x=3.

Step-by-step explanation:

The inequality equation of the given description of the inequality graph is;  3x - 2y < 7

Given :

X range is negative 10 to 10, and Y range is negative 10 to 10.

Dotted line on graph has positive slope and runs through points: (-3,-8), (1,-2), and (9,10).

Now, since we know the coordinates through which the graph runs, we can pick two coordinates and use it to find the slope through the formula;

m = (y₂ - y₁)/(x₂ - x₁)

If we pick (-3,-8), (1,-2), we have;

m = (-2 - (-8))/(1 - (-3)

m = 6/4

m = 3/2

We will use formula for equation of a line in point slope form to get;

y - y₁ = m(x - x₁)

y - 10 = (3/2)(x - 9)

2y - 20 = 3x - 27

3x - 2y = 7

Because, above the line is shaded, therefore, the correct inequality matching the graph is 3x - 2y < 7

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After solving the problems the answers obtained are MN ≅ QP  and   MQ ≅ NP, MP ≅ MP, Δ MQP ≅ Δ PNM, ∠ N ≅ ∠ Q.

The phrase "parallelogram" is a translation of the Greek phrase "parallelogrammon," which means "bound by the contract by parallel lines." As a consequence, a quadrilateral that is bordered by parallel lines is called a parallelogram. It has parallel and equal opposite sides on all sides.

1. According to the parallelogram's feature that its opposed sides are congruent, the opposite sides of the given parallelogram MNPQ,

So, MN ≅ QP  and  MQ ≅ NP.

2. According to the reflexive feature of congruence, a line or other geometric figure is both a reflection of and consistent with itself. Therefore, in the example of the parallelogram MNPQ,

So,

MP ≅ MP

3. The SSS congruence postulate, which stands for Side-Side-Side congruence postulate, argues that when three adjacent sides of two triangles are congruent, the two triangles are congruent. As the sides MNQ, MQ, NP, and MP are in the given parallelogram MNPQ

Hence,

Δ MQP ≅ Δ PNM

4. Part 4 demonstrated that MQP and PNM are congruent, hence in accordance with a CPCTC property, 

∠ N ≅ ∠ Q

5. The acronym CPCTC stands for congruent portions of congruent triangles.

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Answer:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and [tex]m=\frac{-5-3}{12+4}[/tex]

Step-by-step explanation:

The correct formula for finding the slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

This formula represents the change in y over a corresponding change in x.  This is a mathematical representation of "rise" (y-axis movement) over "run" (x-axis movement).

For the second question, let

[tex](x_1,y_1)=(-4,3)\\(x_2,y_2)=(12,-5)[/tex]

So,

[tex]m=\frac{(-5)-(3)}{(12)-(-4)}\\m=\frac{-5-3}{12+4}[/tex]

Answer:

length and breadth

Step-by-step explanation:

Since the pipeline has to be laid along the boundary of the garden, we need to know the perimeter of the garden. Here, the two variables necessary are length (l) and breadth (b). Hence we need to know the length and breadth in order to find the total length of the garden

Answer:

Step-by-step explanation:

To find the total length of the pipe needed to lay a pipeline along the boundary of a garden, you would need to know the following information:

The shape of the garden: The total length of the pipe needed will depend on the shape of the garden. For example, a rectangular garden will require less pipe than a circular garden of the same size.

The dimensions of the garden: Knowing the dimensions of the garden (such as its length, width, and perimeter) will allow you to calculate the total length of the pipe needed.

The diameter of the pipe: The length of the pipe needed will depend on the diameter of the pipe being used. A larger diameter pipe will require more length than a smaller diameter pipe.

The spacing between the pipes: If the pipes are being laid side by side, the total length of the pipe needed will depend on the spacing between the pipes. If the pipes are being laid end to end, the spacing between the pipes will not affect the total length of the pipe needed.

Any curves or corners in the garden: If the garden has curves or corners, the total length of the pipe needed will be greater than if the garden were a straight line. You will need to account for the additional length needed to bend the pipes around the curves or corners.

Answer:

d=9

Step-by-step explanation:

42 km is 2 of the 3 legs

51 is the total triathlon

51 - 42 = 9

Answer:

a. x = 1/4

b. x = [tex]+\sqrt{6}[/tex], [tex]-\sqrt{6}[/tex], 1/4

Step-by-step explanation:

a. I factorised the polynomial.

[tex]g(x) = 4x^3 - x^2 -24x +6 = 0[/tex]

[tex]-x^2 (-4x + 1) +6 (-4x +1)[/tex]

[tex](-4x+1)(-x^2+6)[/tex]

  Solved for the roots.

[tex]-4x + 1 = 0[/tex]

[tex]-4x = -1[/tex]

[tex]x = \frac{1}{4}[/tex]

[tex]-x^2+6 = 0[/tex]

[tex]-x^2 = -6[/tex]

[tex]x^2 = 6[/tex]

[tex]x = +\sqrt{6}[/tex]

[tex]x=-\sqrt{6}[/tex]

A rational number is a real number that's digits terminate and/or repeat. Therefore, 1/4 is the only rational zero.

b. All of the zeros we found in part A. are [tex]+\sqrt{6}, -\sqrt{6}, and \frac{1}{4}[/tex]

Answer:This statement is not necessarily true

Step-by-step explanation:In general, the rate at which thermal energy is transferred depends on several factors, including the temperature difference between the material and its surroundings, the type of material, and its thermal conductivity. Some materials, such as air and glass, are poor conductors of heat and are therefore considered insulators. However, other materials, such as metal, are good conductors of heat and are not considered insulators.

Answer:

Standard form: [tex]y^3 -3y^2 + 21y + 4[/tex]

Degree: [tex]3[/tex]

Leading term: [tex]y^3[/tex]

Step-by-step explanation:

Standard form:

⭐  Standard form is a way you can order the terms of an equation so that the exponents of each term decrease in number when reading the equation from left to right.

Degree:

⭐ The degree of an equation is the highest exponent of the equation. You should always write equations in standard form in order to find the degree.

Leading term:

⭐ The leading term is the term that has the highest exponent. In standard form, it is the first term in the equation.

Answer:

Step-by-step explanation:

to find mean you add all numbers and divide by the amount of numbers, 10+4+8+15+17+6+19+16 is 95, 95 divided by 8 is 11.875

Answer:

  (c)  A line that goes through (0, 0) and (3.6, 7.2)

Step-by-step explanation:

You want to find the correct descriptor of the proportional relationship that includes points (x, y) = (2.1, 4.2), (3.6, 7.2), (12.2, 24.4).

The graph of the points in the table will go through points with coordinates that have the x-value of the table listed first. Points (24.4, 12.2), (7.2, 3.6) are not on the graph. (The table y-value is listed first for those ordered pairs.)

A proportional relationship graphs as a straight line through the origin, so this graph can be described as ...

  A line that goes through (0, 0) and (3.6, 7.2)

Answer:

 (c)  A line that goes through (0, 0) and (3.6, 7.2)

Step-by-step explanation:

The recursion tree is log2m and has log2m nodes .

A recursive algorithm calls itself with smaller input values and returns the result for the current input by carrying out basic operations on the returned value for the smaller input.

A iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for recurrence relations of types that occur in the analysis of many divide and conquer algorithms.

Two integers x and y are given. x and y require n bit and m bit respectively. Two algorithms to compute x y need to be analyzed.

Iterative: The pseudocode for this algorithm is as follows.

product = x;

for i = 2 to y do

product = product * x

The result after the multiplication of two integers, one p bits long and another one q bits long requires p q bits to to store. Therefore, for a given i , we are multiplying one ( i − 1)n bits long integer with an n bit long integer. This multiplication cost is ( i − 1)n2 .

The resulting number after the multiplication is i.n bits long. Thus

adding up all the multiplication cost we get

n2 + 2n2 + 3n2 + . . . + (y − 1)n2. Thus the complexity of the iterative algorithm is O(n2y2) which exponential in

the input length of y which is m = log2 y.

Recursive: The pseudocode for this algorithm is as follows:

function recursive (x ,y)

if y is even then return (x(by2c))2

if y is odd then return x ∗ (x(by2)c)2.

Computing (x(by2c))2

requires a multiplication involving two y2

n bits integers. The cost of this operation is y24.n2 which is O(y2n2). The recurrence relation for this

recursive routine is

T(y) = O(n) when y is 1-bit long.

T(y) = T(y2) + O(y2n2) otherwise.

Applying the Master Theorem we can conclude that T(y) ∈ O(y2n2). The height

of the recursion tree is log2m and has log2m nodes.

Thus both the algorithms have the same worst case complexity.

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Two integers x and y are given. x and y require n bit and m bit respectively. Two algorithms to compute x y need to be analyzed.

product = x;

for i = 2 to y do

product = product * x

The result after the multiplication of two integers, one p bits long and another one q bits long requires p q bits to to store. Therefore, for a given i , we are multiplying one ( i − 1)n bits long integer with an n bit long integer. This multiplication cost is ( i − 1)n2 .

n2 + 2n2 + 3n2 + . . . + (y − 1)n2. Thus the complexity of the iterative algorithm is O(n2y2) which exponential in

the input length of y which is m = log2 y.

function recursive (x ,y)

if y is even then return (x(by2c))2

if y is odd then return x ∗ (x(by2)c)2.

Computing (x(by2c))2

requires a multiplication involving two y2

n bits integers. The cost of this operation is y24.n2 which is O(y2n2). The recurrence relation for this

recursive routine is

T(y) = O(n) when y is 1-bit long.

T(y) = T(y2) + O(y2n2) otherwise.

Thus both the algorithms have the same worst case complexity.

The management assertions for the given parts is explains below.

What is assertion?

Management assertions are statements made about specific elements of a business by members of management. The idea is mainly applied to the auditing of financial statements of a company, where the auditors rely on various business assertions.

Consider, the following.

(a) Recorded sales transactions have been recorded

          Category of management.              Classes of transactions                

           Name of assertion.          .               Occurance

(b)  There are no lines are other restrictions in accounts receivable

          Category of management.             Account balances                

          Name of assertion.                          Rights and obligations.          

(c) All sales transactions have been recorded

           Category of management.             Classes of transactions                

            Name of assertion.                        Completeness

(d) Receivables are appropriately classified as to trade and other receivables in the financial  statements and are clearly described.

       Category of management.              Presentation and disclosure

       Name of assertion.                        Classification and understandabilty

(e) sales transactions have been recorded in proper period

         Category of management.                   Classes of transactions.            

          Name of assertion.                               Cut off.  

(f) Account receivables recorded at correct amounts

         Category of management.                  Account balances      

         Name of assertion.                              Valuation and allocation

(g) sales transactions recorded at appropriate accounts

         Category of management.                 Class of transactions                

          Name of assertion.                            Classification

(h) All required disclosure about sales and receivables are at recorded amounts

     Category of management.                 Presentation and disclosure                  

     Name of assertion.                             Completeness

(k) Sales transactions have been recorded at correct amounts

        Category of management.                   Account balances                  

        Name of assertion.                         Completeness

(L) Recorded accounts receivable exist

        Category of management.                Account balances.                  

        Name of assertion.                            Existence

(m) Disclosure related to sales and receivable relate to entity

         Category of management.               Presentation and disclosure                

         Name of assertion.                           Occurance and obligation

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Answer:

y = -x - 4

Step-by-step explanation:

m = y2-y1 / x2-x1

(-4, 0) and (1, -5)

m = -5+0 / 1+4

m = -5 / 5

m = -1

y = -x + b

0 = -(-4) + b

0 = 4 + b

b = -4

y = -x - 4

Table

Top right: [tex]5+194=199[/tex]

Middle right: [tex]217+13=230[/tex]

Bottom left: [tex]5+217=222[/tex]

Bottom middle: [tex]194+13=207[/tex]

Bottom right: [tex]222+207=429[/tex]

Question 1

[tex]\frac{207}{429} \approx \boxed{0.4825}[/tex]

Question 2

[tex]\frac{13}{429} \approx \boxed{0.0303}[/tex]

Question 3

[tex]\frac{194+217}{429} \approx \boxed{0.9580}[/tex]