solve the matrix equations
with full explanations and workings please

Answer: 6 and 8

Step-by-step explanation: A right triangle is a triangle with one angle that measures 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. In this case, the hypotenuse is 10cm long.

If one angle of the triangle is 40 degrees, then the other angle must be 90-40 = 50 degrees. The remaining two angles of a triangle must add up to 180 degrees, so the third angle is 180-40-50 = 90 degrees. This means that the triangle is a right triangle, and we can use the Pythagorean theorem to find the lengths of the legs.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. In this case, we have a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse.

Substituting the values from the problem, we have a2 + b2 = 102, which simplifies to a2 + b2 = 100. Since we don't know the values of a and b, we can't solve for them directly. However, we can use the fact that the angle opposite the longer leg is 50 degrees, and the angle opposite the shorter leg is 40 degrees. This means that the longer leg is the opposite side of the 50-degree angle, and the shorter leg is the opposite side of the 40-degree angle.

Since the longer leg is opposite the 50-degree angle, and the shorter leg is opposite the 40-degree angle, we can use the tangent function to find the ratio of the lengths of the legs. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side, so we have tangent(50 degrees) = opposite side / adjacent side = a / b, and tangent(40 degrees) = opposite side / adjacent side = b / a.

Solving for a and b, we have a = b * tangent(50 degrees) and b = a * tangent(40 degrees). Since the legs are the opposite sides of the 40- and 50-degree angles, we can substitute the values from the problem to get a = b * tangent(50 degrees) = 100 * tangent(50 degrees) and b = a * tangent(40 degrees) = 100 * tangent(40 degrees).

To find the values of tangent(50 degrees) and tangent(40 degrees), we can use a calculator or look up the values in a table of trigonometric functions. We find that tangent(50 degrees) = 1.191753592594, and tangent(40 degrees) = 0.839099631177. Substituting these values into the equations for a and b, we have a = 100 * 1.191753592594 = 119.1753592594 and b = 100 * 0.839099631177 = 83.9099631177.

Rounding to the nearest whole number, we have a = 119 and b = 84. The lengths of the legs of the triangle are therefore 6 and 8.

For the given graph, As the x-values increase, the y-values also increase. This represent a positive graph. It is nonlinear function graph.

In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty). In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

Here,

For the given graph, As the x-values increase, the y-values also increase.

This represent a positive graph.

It is nonlinear function graph.

As the x-values rise for the presented graph, the y-values rise as well. This graph shows a favorable trend. It is a graph of a nonlinear function.

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In vertex form the equation of the parabola is [tex]y = -2(x+2)^{2} -5[/tex].

What is Vertex form if Parabola ?

When a graph crosses its symmetry axes, the vertex formula in mathematics may be used to get the vertex coordinate of a parabola. The vertex point is often represented by (h, k). We are aware that a parabola's conventional equation is y=ax2+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x2 is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x2 is negative. The standard form and vertex form of a parabola, as well as the vertex formula, will be covered in this article.

We are aware that the parabola's conventional form is y=ax2+bx+c.

So, y = a(x-h)2 + k is the vertex form of a parabola.

To determine a parabola's vertex, use the vertex formula. There are two methods for locating a parabola's vertex.

Vertex, (h, k) = (-b/2a, -D/4a)

Equation of the parabola,

y = [tex]-2x^{2} - 8x -13[/tex]

here ,

a = -2 , b = -8 and c = -13.

Therefore,

h = -b/2a = +8/-4 = -2 and,

k = -D/ 4a = [tex]-(b^{2} - 4ac)/4a[/tex] = -(64 - 104)/-8 = -40/8 = -5

So, the coordinate of vertex is (-2, -5)

So the vertex form of equation of parabola is

[tex]y = a(x-h)^{2} + k[/tex]

⇒ [tex]y = a(x+2)^{2} -5[/tex]

⇒ [tex]y = ax^{2} + 4ax +4a -5[/tex]

Equating this equation with equation pf parabola we get a = -2

So, in vertex form the equation of the parabola is [tex]y = -2(x+2)^{2} -5[/tex].

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The value of x=10 is y=4 if y=8 if x=20.

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics. It is also used to name specific types of algebraic structures, such as an algebra over a field, which is frequently referred to as an algebra. The word algebra is used to name both a mathematical field and some of its subfields.

When x=20, y=8

The value of y is 0.4 times of x.

y=0.4×20

y=8

So, when x=10

y=0.4×10

y=4

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A linear regression equation that represents the data set is y = -29.97x + 1048.80. Also, the number of new cases for 2026 is equal to 689 cases.

In this scenario, the Year since 2014 (x) would be plotted on the x-axis of the scatterplot while the New cases (y) would be plotted on the x-axis of the scatterplot.

On the Excel sheet, you should right click on any data point on the scatterplot, select format trend line and then tick the box to display an equation for the linear regression (line of best fit) on the graph.

By critically observing the scatterplot (see attachment) which models the relationship given in the table, an equation for the linear regression is given by:

y = -29.97x + 1048.80

For 2026, the value of x is given by:

x = 2026 - 2014 = 12 years.

Now, we can determine the new cases for 2026:

y = -29.97(12) + 1048.80

y = -359.64 + 1048.80

y = 689.16 ≈ 689 cases.

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To determine the point and slope from the given equation, we can rewrite the equation in the standard form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).

In this case, the equation is already in the standard form, so we can immediately see that the slope is -5 and the y-intercept is (0, 4). This means that the point at which the line crosses the y-axis is (0, 4), and the slope of the line is -5.

Therefore, the correct answer is:

Point: (0, 4)

Slope: -5

Part A: A system of equations to model this situation includes:

Equation 1: x + y = 461

Equation 2: 3x + 4y = 1624.

Part B: The solutions of the equations show that 220 students bought tickets at $3 each, while 241 adults bought the tickets at $4 each to give the total sales revenue as $1,624.

A system of equations means simultaneous equations.

Simultaneous equations are two or more equations solved at the same time.

Simultaneous equations can be solved by graphing, substitution, and elimination methods.

In this situation, we decided to solve the equations by substitution after equating x = 461 - y from the first equation.

The total number of tickets sold for the school play = 461

The cost of student tickets per unit = $3

The cost of adult tickets per unit = $4

The total revenue raised = $1,624

Let the number of students = x

Let the number of adults = y

x + y = 461  ... Equation 1

3x + 4y = 1624  ... Equation 2

From Equation 1:

x = 461 - y  ... Equation 3

Substitute x in Equation 2

3(461 - y) + 4y = 1624

1,383 - 3y + 4y = 1624

y = 241

From Equation 1:

x = 461 - y

= 461 - 241

= 220

Check:

3x + 4y = 1624

3(220) + 4(241) = 1624

660 + 964 = 1624

1624 = 1624

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i think it would be 200

Answer:9 less than 9 is 0

Step-by-step explanation:

9-9=0

Answer:

9

Step-by-step explanation:

Less means minus, so basically X ( something ) - 9 is 0

X - 9 = 0

You add 9 on each side

X = 0 + 9

X = 9

Basically, all you're doing is the reverse, you start with 0 and do the opposite of taking away 9 which is adding nine so that you get the number:

0 + 9 = 9

Hence the number is 9

:)

( sorry if I misunderstood )

Answer:

what we have do with these lines?... please complete your questions

Answer:

neither

Step-by-step explanation

3*1/3= 1

3 and 1/3 are multiplicative inverses

it is supposed to be 3*(-1/3) or -3*(1/3) = -1

Task 1:a) The measure of angle  Y'Z'X'= 22  degrees

Task2:b) The measure of angle X'Y'Z'= 75 degrees.

An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are located in the plane where the rays are located. The meeting of two planes can also create an angle. Angle can also be used to describe the size of an angle or of a rotation. This metric represents the proportion of a circular arc's length to radius.

Angle Y'Z'X' = YZX = 22 degrees (in a triangle, angle dilation does not

modify angle size). Only the sides' length varies.

The sum of the triangle's angles for the XYZ angle is 180 - 83

-22 = 75 degrees. Since there are already two angles supplied, the third

angle is 75 degrees, so X'Y'Z' = XYZ = 75 degrees. The dilation angle size remains unchanged (for the same reason as in the previous challenge).

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The complete question is:

"Triangle XYZ is taken by a dilation with center Y and scale factor 5/2 to Triangle X’Y’Z’. The measure of angle YXZ is 83 degrees and the measure of angle YZX is 22 degrees.

Task 1: a) What is the measure of angle Y’Z’X’? Explain your reasoning.

Task 2: b) What is the measure of angle X’Y’Z’? Explain your reasoning."

Answer: Deep inside Earth, between the molten iron core and the thin crust at the surface, there is a solid body of rock called the mantle. When rock from the mantle melts, moves to the surface through the crust, and releases pent-up gases, volcanoes erupt. Extremely high temperatures and pressure cause the rock to melt and become liquid rock or magma. When a large body of magma has formed, it rises through the denser rock layers toward Earth's surface.  Magma that has reached the surface is called lava.

Step-by-step explanation:

The height of the candy cane is 11.4024 feet when the man is looking at the top of the candy cane at an angle of 35°.

We have the following information:

A 3 foot Gingerbread man is standing 12 feet from the base of the tall candy cane he has ever seen. He is looking at the top of the candy cane at an angle of 35⁰.

Now, we can find the height of the candy cane using the trigonometric function of tan.

Now, the base will be 12 feet and the height of the candy cane will be added to 3 feet to find the real height of the cane.

Tan 35 = height of the cane/base

0.7002 = Height of the cane/12

Height of the cane = 12*0.7002

Height of the cane = 8.4024 feet

Real height of the cane = 3+8.4024 feet

Real height = 11.4024 feet

Hence, the candy cane is 11.4024 feet when the man is looking at the top of the candy cane at an angle of 35°.

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The graph for system of the equation y = x + 2 and y = 3x - 2 are shown below and solution for the equations is x = 2 and y = 4.

When any equation is represented in the y = mx +c form, it is called the slope intercept form of the equation.

Here m is slope and c is constant.

The given system of equations is,

y = x + 2                (1)

and y = 3x - 2       (2)

The given equations are already in slope intercept form and the slope of the equations are, m₁ = 1 and m₂ = 3.

The graph of the equations y = x + 2 and y = 3x - 2 are represented below.

To find the solutions, solve the equations (1) and (2),

x = 2 and y = 4.

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The large cube has a length of 7 inches each side and it's volume is 343 cubic inches.

Given,

The length of the small cube, a = 3.5 inch

The length of large cube = 2a = 2 × 3.5 = 7 inches

Now,

We have to find the volume of large cube

Volume;-

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Here,

Volume of cube = a³

Volume = 7³ = 343 cubic inches

That is,

The length of side of the large cube is 7 inches and the volume of large cube is 343 cubic inches.

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Given question is incomplete. The completed question is;

A small cube has a length of 3.5 inch. The length of large cube is twice the small cube. Find the volume of the large cube.

Answer:

Option D delta is correcto

Mary is capable of making 4 batches of brownies.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

divide 8/10 by 1/5

4

Hence, Mary is capable of making 4 batches of brownies.

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We can conclude that each one of them will get a fraction of 11/20 chocolate.

An element of a whole is a fraction.

The number is represented mathematically as a quotient, where the numerator and denominator are split.

Both are integers in a simple fraction.

A fraction appears in the numerator or denominator of a complex fraction.

So, the fraction of chocolate each friend gets is:

We know that Landen has: 2¾ of chocolate

She shares it with his 4 more friends.

So, we easily know that there will be 5 pieces of chocolate that are 4 friends, and 1 Landen.

Fraction of choclta eecah gets:

2¾ ÷ 5

8+3/4 ÷ 5

11/4 ÷ 5/1

11/4 * 1/5

11/20

Therefore, we can conclude that each one of them will get a fraction of 11/20 chocolate.

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Answer: y = 45

Step-by-step explanation:

225/5 = 45

45·5 = 45

For the given triangle abc, g is the centroid of  and the length of line segment d g is 9 x 2 so the length of line segment gf is 133 units.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. The specified object is a triangle having vertices A, B, and C. triangle with equal sides.

There are three sides and three angles in every triangle, some of which may be the same. In the case of a right triangle, the three sides are given unique names: the hypotenuse, which is the side that faces the right angle, and the legs, which are the other two sides.

from given information;

2x = 19 * 14

Solving for value of x,

x = 19 * 14 / 2

x = 19 * 7

x = 133.

as both lines are same,

now we found that the length of line segment gf is 133 units.

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Let the tens digit of the original number be x and the ones digit be y. The original number is 10x + y, and the new number formed by reversing the digits is 10y + x.

Since the new number exceeds the original number by 54, we can set up the equation:

10y + x = 10x + y + 54

9x - 9y = 54

x - y = 6

Since x and y are both digits, they must both be integers. The only solution to this equation that satisfies this condition is x = 8 and y = 2.

Therefore, the original number is 82 and the new number formed by reversing the digits is 28. This is the new number.

You are running the concession stand for the basketball game. You sell hot dogs for $1.50 and drinks for $2.

a)  an equation in a standard form that models this situation is

1.5H + 2D = 250

b) Hot dogs sold 104

Generally, a) Let H be the number of hot dogs sold and D be the number of drinks sold. The equation that models this situation is:

1.5H + 2D = 250

b) To find the number of hot dogs sold, we can solve the equation for H:

1.5H = 250 - 2D H = (250 - 2D) / 1.5

Substituting D = 47 into this equation gives us:

H = (250 - 2*47) / 1.5 H = (250 - 94) / 1.5 H = 156 / 1.5 H = 104

Therefore, you sold 104 hot dogs.

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90 minutes before 11:40.

= 10:10 + 90 minutes

= 10:10 + 1 hour + 30 minutes

= 11:40

The latest time the class can start the test to get to lunch on time is 10:10.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Time take to take the test = 1(1/2) hours = 1 hour and 30 minutes

The time the test needs to finished = 11:40

This means,

The test must start 90 minutes before 11:40.

1 hour = 60 minutes

1 hour and 30 minutes = (60 + 30) minutes

1 hour and 30 minutes = 90 minutes

Now,

90 minutes before 11:40.

= 10:10 + 90 minutes

= 10:10 + 1 hour + 30 minutes

= 11:40

Thus,

The latest time the class can start the test to get to lunch on time is 10:10.

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The complete question is:

Mr. Potter's class will take a test for 1 1/2 hours. They need to finish by 11:40 to get to lunch on time.

What is the latest time the class can start the test to get to lunch on time?

You bought 17 pounds of rice for a group lunch at the neighborhood market the last time you went there for $12.75. This week, you'll need 38 pounds of rice to prepare another shared meal.

Step 1: Divide the percent discount by 100% to convert it to a decimal. Step 2: Construct the equation P=(1d)x P = (1 d) x where P is the sale price, d is the discount expressed as a decimal, and x is the original price of the item to get its original price.

A linear demand equation is written as Q = a - bP in standard form. The price is treated as a function of quantity required in the inverse demand equation (also known as the pricing equation): P = f(Q) (Q).

When you most recently visited the neighborhood market, you spent $12.75 on 17 pounds of rice for a communal lunch. You need 38 pounds of rice this week to create another communal supper.

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Answer: 10000

Step-by-step explanation:

((1234568)(198765432)+(98765432)(98765432))^1/4

=(245389441853376+(98765432)(98765432))^1/4

=(245389441853376+9754610558146624)^1/4

=10000000000000000^1/4

=10000

Hope this helps!!! :)

The required matrix is obtained by scalar multiplication as [tex]\left[\begin{array}{ccc}-6&0\\9&15\\\end{array}\right][/tex].

A matrix can be defined as a rectangular array of elements written in the form of rows and columns. For m rows and n columns the order of the matrix can be written as m × n.

The number of rows and columns for a square matrix are always equal.

Two matrix can only be added when their orders are equal.

The given matrix can be written as follows,

N = [tex]\left[\begin{array}{ccc}-2&0\\3&5\\\end{array}\right][/tex]      

Where its elements are a₁₁ = -2, a₁₂ = 0, a₂₁ = 3 and a₂₂ = 5.

Since, the scalar multiplication of a matrix is equivalent to the matrix each of which elements are multiplied by that scalar.

As per the problem the matrix 3N can be evaluated as follows,

3N = [tex]\left[\begin{array}{ccc}-2\times3&0\times3\\3\times3&5\times3\\\end{array}\right][/tex]

     = [tex]\left[\begin{array}{ccc}-6&0\\9&15\\\end{array}\right][/tex]

Hence, the matrix 3N is obtained by multiplying all of the terms of matrix by 3 as [tex]\left[\begin{array}{ccc}-6&0\\9&15\\\end{array}\right][/tex].  

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Answer: The answer is -2

Step-by-step explanation: Common sense