Please help me I rlly need it

The answer to all the following options is given below along with the suitable reasoning.

a. Incorrect. If a system of linear equations has more unknowns than equations and the reduced row echelon form of the augmented matrix has two nonzero rows, the system is inconsistent and has no solutions.

b. Incorrect. A system of linear equations with more unknowns than equations is underdetermined and can have either no solutions or an infinite number of solutions.

c. Correct. A matrix can be row-reduced to an echelon form, which is a simpler form that makes it easier to find the solution to the system of linear equations represented by the matrix.

d. Correct. Every matrix can be row-reduced to a unique reduced row echelon form by performing a sequence of elementary row operations, which are reversible and preserve the solutions of the system of linear equations.

e. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

f. Correct. If a system of linear equations has three unknowns and the reduced row echelon form of the augmented matrix has three nonzero rows, then the system is consistent and has a unique solution.

g. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

h. Incorrect. Some of the statements are correct.

Therefore, The answer to all the following options is given above along with the suitable reasoning.

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The answer to all the following options is given below along with the suitable reasoning.

a. Incorrect. If a system of linear equations has more unknowns than equations and the reduced row echelon form of the augmented matrix has two nonzero rows, the system is inconsistent and has no solutions.

b. Incorrect. A system of linear equations with more unknowns than equations is underdetermined and can have either no solutions or an infinite number of solutions.

c. Correct. A matrix can be row-reduced to an echelon form, which is a simpler form that makes it easier to find the solution to the system of linear equations represented by the matrix.

d. Correct. Every matrix can be row-reduced to a unique reduced row echelon form by performing a sequence of elementary row operations, which are reversible and preserve the solutions of the system of linear equations.

e. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

f. Correct. If a system of linear equations has three unknowns and the reduced row echelon form of the augmented matrix has three nonzero rows, then the system is consistent and has a unique solution.

g. Correct. Adding a multiple of one row to another row is one type of elementary row operation used in row-reducing a matrix to its reduced row echelon form.

h. Incorrect. Some of the statements are correct.

Therefore, The answer to all the following options is given above along with the suitable reasoning.

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The lengths of the diagonals of rectangle is 66 units

The properties of a rectangle is given as;

From the information given, we have that;

$WY=14x+10

$XZ=11x+22

Since the diagonals are of the same length, we have;

WY = XZ

14x + 10 = 11x + 22

collect like terms

14x - 11x = 22 - 10

subtract the like terms

3x = 12

Make 'x' the subject of the formula

x = 4

WY = 54 + 10 = 66

XZ = 66

Hence, the values are 66

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Pete is standing 4 feet away from a mirror on the ground, if mirror is 20 feet away from the base of the tree the height of tree is 30 feet.

let,

Pete is standing 4 feet away from a mirror on the ground.

Pete is 6 feet tall and can just see the top of the tree in the mirror from where he is standing.

We can say two triangles are formed are similar,

So if the mirror is 20 feet away from the base of the tree

After talkig the similarity theorem we get,

[tex]\frac{6}{4} = \frac{x}{20}[/tex]

So x = 6*5

x = 30 feet.

The height of the mirror is 30 feet.

Height is a measurement of vertical distance, or how high something or someone is (how tall they are) (how "high" a point is).

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Answer:

deductive reasoning

Step-by-step explanation:

Line of fit go through (1, 10) and (10, 1) to best fit the data.

Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.

Line of best fit of the scatterplot should go through as many points as possible of the graph.

If we draw a line passing through the pair of points given in the options, the line passing through (1, 10) and (10, 1) passes through (9, 2), (7, 4) and (3, 8).

No other line drawn through points in the options passes through 5 points.

Hence the line of best fit is the line passing through (1, 10) and (10, 1).

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The answers for all triangle problems are:

10. ΔABC is a equilateral triangle, then:

∠A = ∠B = ∠C = 8x - 44

3 (8x - 44) = 180

24x - 132 = 180

24x = 48

x = 2

11. ΔRST is an isosceles triangle, then:

∠R = ∠T

15x - 31 = 9x + 11

6x = 42

x = 7

∠S + ∠R + ∠T = 180°

∠S + 2∠T = 180°

∠S + 2( 9x + 11) = 180°

∠S + 2(9(7) + 11) = 180°

∠S + 2 (63 + 11) = 180°

∠S + 2 (74) = 180°

∠S = 180 - 144

∠S = 36°

12. Based on the given data:

∠P = 5x - 14

∠Q = x - 5

∠R = 2x - 9

Since ΔPQR is a triangle, then:

∠P + ∠Q + ∠R = 180°

(5x - 14) + (x - 5) + (2x - 9) = 180°

8x - 28 = 180°

8x = 208

x = 26

∠P = 5x - 14 --> 5(26) - 14 = 116°

∠Q = x - 5 --> (26) - 5 = 21°

∠R = 2x - 9 --> 2(26) - 9 = 43°

13. ΔJKL is a triangle, where:

∠J = ∠L - 7

∠K = 2∠L - 21

∠J + ∠K + ∠L = 180

(∠L - 7) + (2∠L - 21) + ∠L = 180°

4∠L - 28 = 180°

4∠L = 208

∠L = 51°

∠J = ∠L - 7 --> (51) - 7 = 44°

∠K = 2∠L - 21 --> 2(51) - 21 = 81°

14. In a triangle ΔBCD:

BD = BD

∠B = 13x - 35

∠C = 5x - 19

∠D = 2x + 14

Since BC = BD; then:

∠C = ∠D

5x - 19 = 2x + 14

3x = 33

x = 11

∠C = ∠D = 2x + 14 --> 2(11) + 14 = 36°

∠B + ∠C + ∠D = 180°

∠B + 36° + 36° = 180°

∠B = 108°

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Answer: $75

Step-by-step explanation:

Price for one person: $4.50+$8

Price for six people: 6($4.50+$8)=$75

The basis for the nullspace is the set {(-3,1,0,1), (0,1,0,0)}.

The basis for the nullspace of the matrix can be found by reducing the augmented matrix to row echelon form and finding the free variables. The free variables correspond to the columns that have a leading entry of 0 and non-zero entries below it, which are the basis vectors for the nullspace.

Using row operations, the augmented matrix can be reduced to:

1  2 -4  5 | 0

0  1 -3  2 | 0

0  0  0  0 | 0

From this, we can see that the free variables are x2 and x4, so the basis for the nullspace is:

-3 x2 + x4

x2

So the basis for the nullspace is the set {(-3,1,0,1), (0,1,0,0)}.

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The coordinate of point C' after transformation is; C'(4, 4)

Dilation is defined as a transformation, that is used to resize the object. Dilation is used to make the objects either larger or smaller. That is a reduction or an enlargement.

Usually when we dilate an object by a scale factor, what we simply do is to multiply the original coordinates by the scale factor to get the new dilated coordinates.

Since the quadrilateral is dilated by a scale factor of 2, we will multiply the original coordinate of point C by 2.

Coordinate of C = (2, 2)

Thus;

Dilated coordinate; C' = (2*2, 2*2) = 4,4

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The probability of getting at least one tails on the last two flips is 8/25.

The probability of getting a tails on a single toss of the coin is 3/5. Therefore the probability of getting tails on the last two flips is (3/5)^2. This is because the coin tosses are independent of one another.

Therefore the probability of getting at least one tails on the last two flips is 1 - (3/5)^2 = 8/25.

This is because the probability of getting two tails is (3/5)^2, and the probability of getting at least one tails is the complement of that. Therefore the probability of getting at least one tails on the last two flips is 8/25.

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For c = 1, we have f(t,y) =-y = 1. Rearranging this equation yields y = 1, which simplifies to y = et. The isoclines for c = -1, 0, 1 are y = e-t, y = 0, and y = et, respectively.

c = -1: y = e-t

c = 0: y = 0

c = 1: y = et

For c = -1, we have f(t,y) = -y = -1. Rearranging this equation yields y = -1, which simplifies to y = e-t.

For c = 0, we have f(t,y) = -y = 0. Rearranging this equation yields y = 0.

For c = 1, we have f(t,y) =-y = 1. Rearranging this equation yields y = 1, which simplifies to y = et.

The isoclines for c = -1, 0, 1 are y = e-t, y = 0, and y = et, respectively.

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Train A takes 20 hours to get to Chicago from Washington whereas Train B takes 16 hours, making a 20: 16 ratio between the two trains.

Given: Time taken by Train A = 16 hours

Time taken by train B = 20 hours

We need to find, the ratios of speeds of trains A and B

The distance exists same (Chicago to Washington) and to finding the speed of train A.

Let the equation be

Speed [tex]$=\frac{\text { Distance }}{\text { time }}$[/tex]

Let the distance between Chicago and Washington be x

Speed [tex]${(\text {train } \mathrm{A})}=\frac{\mathrm{x}}{16} \mathrm{~km} / \mathrm{h}$[/tex]

Hence, speed of train [tex]$A=\frac{x}{16} \mathrm{~km} / \mathrm{h}$[/tex]

To find the speed of train B

Speed [tex]${({train~B})}=\frac{\mathrm{x}}{20} \mathrm{~km} / \mathrm{h}$[/tex]

[tex]$\mathbf{S}_{(\{train~A})}: \mathrm{S}_{(\{train} B)} \\[/tex]

[tex]$& \longrightarrow \frac{\mathrm{x}}{16}: \frac{\mathrm{x}}{20} \\[/tex]

= 20 : 16

Therefore, the ratio of train A and train B be 20 : 16.

The complete question is:

Train a take 16 hour to reach Chicago from Washington while train b take 20 hour, the ratio of the speed of both the train.

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After integration, the expression will be[tex]S=8(sin^{3}(t+\frac{\pi}{3} )(-cos(t+\frac{\pi}{3}+t^{2}+\frac{\pi}{12t})-8tsin^{2}(t+\frac{\pi}{3})[/tex]

Integration is the process of calculating an integral. Integrals are used by mathematicians to compute a range of useful quantities, such as areas, volumes, displacement, etc. Usually, when we talk about integrals, we mean definite integrals. Indefinite integrals are used for antiderivatives. Integration is one of the two primary calculus topics in mathematics, along with differentiation (which measure the rate of change of any function with respect to its variables).

An integral that has both the upper and lower boundaries is said to be definite. Only a real line may be used for X to lay. A Riemann Integral is another name for the Definite Integral.

∫f(x)dx from a to b.

The definition of integrals without upper and lower bounds. It appears as follows:

A definite Integral is represented as:

∫f(x)dx = F(x) + C

Where C is any constant and the function f(x) is called the integrand.

Now,

Right expression is

[tex]\frac{dS}{dt} = 8sin^{2}(t+\frac{\pi}{12} )[/tex]

After integration

[tex]S = 8sin^{2} (t+\frac{\pi}{12} ).dt[/tex]

[tex]S=8(sin^{3}(t+\frac{\pi}{3} )(-cos(t+\frac{\pi}{3}+t^{2}+\frac{\pi}{12t})-8tsin^{2}(t+\frac{\pi}{3})[/tex]

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On the map, the two towns are 17 centimeters apart.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

The scale on a map is stated as 1 : 200000.

A main road connects two towns which are 34 kilometers apart.

34 kilometers in centimeters,

= 3400000

So, the road on the map = 3400000/200000

The road on the map = 17 centimeters.

Therefore, the value is 17 centimeters.

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The requried price of an eraser and ruler is given as 0.15 Tetris and 0.25 Tetris respectively.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

1 GEL and 25 tetris = 1.25
1 GEL and 5 tetris = 1.05

We can set up two equations to find the unknown values of x and y:

1.25 = 5x + 2y  - - - - - -(1)

1.05 = 2x + 3y  - - - - - (2)

To solve the system of equations, we can substitute the value of y in the first equation using the second equation:

y = (1.25 - 5x) / 2

Substituting this value of y in the second equation:

1.05 = 2x + 3((1.25 - 5x) / 2)

x = 0.15

Now,
Put x = 0.15 equation 1,
e get
y = 0.25

Thus, the requried price of an eraser and ruler is given as 0.15 Tetris and 0.25 Tetris respectively.

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The minimum length of the third side must be greater than 16 feet.

The minimum length of the third side can be determined using the Triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. The Triangle Inequality Theorem can be expressed by the following inequality: a + b > c, where a, b, and c are the lengths of the three sides of the triangle. In this case, we have two sides of 4 feet and 12 feet, so the inequality can be written as 4 + 12 > c, which simplifies to 16 > c. Solving for c yields c > 16, which means that the minimum length of the third side must be greater than 16 feet.

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No, the length of any pair of sides added together is not necessarily longer than the length of the third side.

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It is true three side lengths of 23, 32, and 45 units will form exactly one unique triangle.

The complete question is

Three side lengths of 23, 32, and 45 units will form exactly one unique triangle. true /false.

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The points are reflections of each other across the y-axis is,

⇒ ( x, - y)

Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.

We have to given that;

One point is in quadrant lll.

And, The points are reflections of each other across the y-axis.

Now, Let a point is in quadrant III = (-x, - y)

Where, x > 0, y > 0

We know that;

The rule of the reflection across the y - axis is,

⇒ (x, y) → (- x, y)

Thus, We get;

The points are reflections of each other across the y-axis is,

⇒ (- x, - y) → (- (-x), - y)

               → (x, - y)

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Answer:

$2280

Step-by-step explanation:

38000*6% =2280

The approximate value of the correlation coefficient for the given graph is D. -1.

The correlation coefficient is a statistical measure that indicates the strength and direction of the linear relationship between two variables. A correlation coefficient of -1 indicates a perfect negative linear relationship, meaning that as the value of one variable increases, the value of the other variable decreases at a constant rate. In this case, as the number of years increases, the price of the car decreases, so the correlation coefficient is negative.

Based on the definition of congruent triangles, m<X = 45 degrees.

Congruent triangles are two triangles that have exactly the same size and shape, which connotes that every corresponding parts of the triangles are equal.

Given EFG = XYZ, therefore, the measure of angle E will be congruent to the measure of angle X.

m<E = m<X

m<E = 180 - 90 - 60

m<E = 30°

Therefore, m<X = 30°.

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The corresponding angles must be equal for the transversal to join two parallel lines.

In the intersection of two parallel lines and a transversal, corresponding angles are created. The opening and closing of a lunchbox, completing a Rubik's cube, and endless parallel railroad tracks are a few examples of matching angles in daily life.

The angles in the same corners of two lines, which are typically parallel, are referred to as corresponding angles when they cross each other across a plane (a transversal). In two separate shapes, corresponding sides and angles refer to a pair of matching sides or angles that are in the same location.

Every matching angle is not created equally. The transversal must connect two parallel lines in order for the corresponding angles to be equal. The equivalent angles that are created when a transversal encounters a line that is not parallel are not congruent and have no connection to one another.

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Answer:259

Step-by-step explanation:

3+256=269

Answer: 259

Step-by-step explanation: 3 + 256 = 259

The limit does not exist if the graph features a vertical asymptote with one side going toward infinity and the other toward negative infinity.

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The number of planes manufactured by the aeroplane company will be 432.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that an aeroplane factory made 36 aeroplanes per month. The number of aeroplanes made in a year will be calculated as:-

Number = 36 x Months in a year

Number = 36 x 12

Number = 432

Therefore, the number of planes will be 432.

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If 2/9 of the students in a school are in sixth grade.

then 20 students  sixth graders are there if the school has 90 students.

6 students sixth graders are there if the school has 90 students

If the school has a students then 2x/9 the number of sixth graders in terms of x.

Part of a full number and a means of dividing a numbers into equal pieces are represented by fractions. The denominator is the total number of components in the whole, while the numerator is the fraction of equal portions being counted.

a. From the details of the question, we have 2/9 of the students in the school in sixth grade. Hence;

Number of students in sixth grade = 2/9 × 90 = 20 sixth grade students

b. If the school has 27 students, number of sixth graders =  2/9 ×  27 = 6 sixth grade students

c. If we have x students in the school, the number of sixth graders =  2/9 × x = 2/9x students

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255.255.255.0 is written as /24 in slash notation (/n).

Slash notation is a compact way to show or write an IPv4 subnet mask. When you use slash notation, you write the IP address, a forward slash (/), and the subnet mask number.

1- To find the subnet mask number:

2- Convert the decimal representation of the subnet mask to a binary representation.

Count each “1” in the subnet mask. The total is the subnet mask number.

In IPv6, slash notation is used to represent the network identifier prefix for an IPv6 network. The prefix is expressed as a slash (/) followed by the prefix size, which is a decimal number between 1 and 128.

Thus, 255.255.255.0 is written as /24 in slash notation (/n).

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£479.42 is  the income tax Angela gets deducted each month.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Angela earns £35 240 a year. She has to pay income tax. She is allowed to earn £6475 before paying tax. She pays 20% tax on the rest.

So,

taxable income = 35,240-6,475

taxable income = 28,765

Since She pays 20% tax

Thus,

The Total tax = 28,765 * 20%

the total tax = 5,753

Since Her employer deducts the income tax each month.

so,

Income tax deducted each month =  5,753/12

Income tax deducted each month =  479.417

Therefore, the income tax Angela gets deducted each month is £479.42.

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The statement using the specified property i.e  Associative Property of Multiplication will be 14y.

One's identity property is its capacity for multiplication.

7(2y)

The phrase is given as follows:

7(2y)

=14y

The one has the multiplication property, which says:

Any number or expression that is multiplied by one doesn't alter in any way.

The result is: 1xa=a

The identification property is another name for this particular attribute.

The general rule is shown as follows:

Examples include

1 * 2 = 2

1 * x = x

1 * ab = ab

and so forth

So, the property of multiplying by one is an identity property.

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