In the diagram, the ratios of two pairs of corresponding
sides are equal.
N
3
M
X 6 Z
9
To prove that ALMN-AXYZ by the SAS similarity
theorem, it also needs to be shown that
O O ZN ZX
O ZL ZZ
O ZL ZY

Answer:    (x,y)=(3,-1)

Step-by-step explanation:

Olivia could have used a translation and a rotation to move ABCDE onto A'B'C'DE".

Distance in numerical measurement of how far apart to 16 places in point are in space age is often measured in unit like came miles with as for free system also can be conceptualized in the term of time as Indian distance between two points in the time.

A translation would involve shifting the figure ABCDE along some axis by a certain distance, while a rotation would involve rotating the figure ABCDE around a fixed point. By combining the two transformations, Olivia could move ABCDE onto A'B'C'DE".

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Answer:

Part A: 23

Part B: n < 77

Step-by-step explanation:

Answer: The constants in the expression are -3 and 2.

In the expression:

2 y

x−3+²7 - 12/2

X-3+

The term -3 is a constant and does not change its value regardless of the values of any variables. The term 2/2 can also be simplified to 1, which is another constant. Hence, the constants in the expression are -3 and 2.

Step-by-step explanation:

A is directed along negative X and Y axes respectively having magnitudes 3.214 and 3.83 units respectively.

A vector is an object that, as we all know, possesses both magnitude and direction. We must determine a vector's length in order to determine its magnitude. Vector quantities include things like velocity, displacement, force, momentum, etc. However, scalar quantities like as speed, mass, distance, volume, temperature, etc. exist. In contrast to vectors, which

have both magnitude and direction, scalars only have magnitude.

Magnitude of vector A = |A| = 5 units

We know, the negative Y-axis is an angle of 270° counterclockwise with a positive X-axis.

θ = Angle of vector A with positive X-axis = (270° - 40°) = 230°

So, x component of vector A = Ax = |A| * cos 230° = |A| * cos (180° + 50°) = |A| * (- cos 50°) = 5 * (-0.6428) = -3.214

And, y component of vector A = Ay = |A| * sin 230° = |A| * sin (180° + 50°) = |A| * (- sin 50°) = 5 * (-0.766) = -3.83

Since Ax and Ay both are negative relative to positive X and Y axes respectively; so, the x and y components of vector A are directed along negative X and Y axes respectively having magnitudes 3.214 and 3.83 units respectively.

the complete question is -

Vector img has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis.What are the x and y components of vector img .

A)Ax = 3.83 and Ay = 3.21

B)Ax = 3.83 and Ay = -3.21

C)Ax = -3.21 and Ay = -3.83

D)Ax = -3.21 and Ay = 3.83

E)Ax = 4.29 and Ay = 2.16

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The answer to question of trail mix in ascending order would be, 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, 2/3 cup peanuts.

The order of ingredients from least to greatest for Juan's trail mix recipe is: 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, and 2/3 cup peanuts. Juan's mother provided the recipe which consists of a combination of dried fruits, nuts, and cereal. The recipe calls for 1/2 cup of cereal, which is the least amount of any of the ingredients. The next ingredient is 3/4 cup of raisins, followed by 1/3 cup of almonds, and finally 2/3 cup of peanuts, which is the greatest amount of any of the ingredients. These ingredients can be combined and enjoyed as a snack.

Hence the answer is, 1/2 cup cereal, 3/4 cup raisins, 1/3 cup almonds, 2/3 cup peanuts.

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The number of different ways that the letters of "recommend" can be arranged is 90720.

What is arrangement?

Generally speaking, an arrangement of objects is just a collection of them. A combination (order is ignored) or permutation is used to determine the number of "arrangements" of the components (order is significant). An arrangement is a group of hyperplanes that divides a space into cells.

If there are n different objects in the system then the number of different ways of arrangement of n objects is n!

If the repetition of the objects are allowed in the system the number of different ways of arrangement is -

n! / (no. of repetition of object 1)! .... (no. of repetition of object r)!

Total number of letters in the word "recommend is 9.

The number of different ways of arangement of the 9 letters is 91

The repetition of letter "e" is 2 and repetition of letter "m" is 2.

The number of different ways that the letters of "recommend" can be arranged is -

9! / 2! × 2!

(9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (2 × 1) × (2 × 1)

(9 × 8 × 7 × 6 × 5 × 3 × 2 × 1)

90720

Therefore, the number of different ways is 90720.

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Answer:

Step-by-step explanation:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Triangles PQR and ZQX are similar!

Square side => a

XZ / (PQ - PZ) = PR / PQ

a / (12 - a) = 8 / 12

a = 4.8

The side length of the square PZXY is sqrt(2).

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is given as side².

We have,

Since triangle PQR is a right triangle, we can use the Pythagorean theorem to find the length of QR:

QR² = PQ² + PR²

QR² = 1² + 1²

QR² = 2

QR = √2

Since PZXY is a square, its sides are equal in length.

Let's denote the length of one side of the square as s.

Then, we can write:

PR = PX + RX

1 = s + QY

Since QY = PZ = s and PX = QX = QR - QY = sqrt(2) - s,

we can substitute these values into the equation for PR to get:

1 = s + (√2 - s)

1 = √2

Therefore,

The side length of the square PZXY is √2.

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Answer:

7, 11, 15, 19, 23

Step-by-step explanation:

Since the common difference is 4 each successive term is 4 more than the previous term

If we let aₙ be the nth term,

a₁ = 7

a₂ = 7 + 4 = 11

a₃ = 11 + 4 = 15

a₄ = 15 + 4 = 19

a₅ = 19 + 4 =23

The first five terms are: 7, 11, 15, 19, 23

We can also use the generalized formula for the nth term:

aₙ = a₁ + d(n - 1)

where a₁ = first term

d = common difference

Plugging in the known values we get
aₙ = 7 + 4(n- 1)

aₙ = 7 + 4n - 4

aₙ = 3 + 4n

Substituting n = 1, 2, 3, 4, 5 into the above equation will yield the same values

Maybe your teacher prefers one of the above approach.

Answer:

17%

Step-by-step explanation:

area represents the populations

United States has a radius of 4.2 cm and

India has a radius of 8.7 cm.

If 4% of the world's population is in United States,

what percentage of the world's population is in India

US π r² = π*4.2²

India π r² = π*8.7²

so india/US = 4.29

so india = 4.29 *4% = 17%

Answer: To calculate the simple interest, you can use the formula:

I = Prt

where I is the interest, P is the principal (the amount borrowed), r is the interest rate as a decimal, and t is the time in years.

In this case, P = $4,200, r = 0.03, and t = 6/12 = 0.5 (since the interest is paid over 6 months, which is half of a year). Plugging these values into the formula, we get:

I = Prt = 4,200 * 0.03 * 0.5 = $63

So, Jimena will pay the store $63 in simple interest.

Step-by-step explanation:

The row in the original matrix and the column in the primary matrix must match. Hence, the matrix product has the first matrix's number of rows and the second matrix's number of columns.

Read an overview of this subject. a collection of numbers lined up in rows or columns to form a flat array is called a matrix. The atoms, or units, of the matrix are the integers.

The study of squares is the main focus of the mathematical field known as matrix theory. It started out as a branch of linear algebra but quickly expanded to cover topics in graph theory, algebra, combinatorics, and statistics.

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The equation of the line that is perpendicular to 5x-8y=-6 and passes through (4,-4) is y = (-8/5)x + 16/5.

Parallel lines are two or more lines in a coordinate plane that are equidistant from each other at all coordinates.

The given line can be rewritten in slope-intercept form as y=(5/8)x+(3/4), where the slope is 5/8. So, any parallel line will also have a slope of 5/8.

Using the point-slope form of a line, we can write the equation of the line as:

y - (-4) = (5/8)(x - 4)

Simplifying, we get:

y = (5/8)x - 23/8

Therefore, the equation of the line that is parallel to 5x-8y=-6 and passes through (4,-4) is y = (5/8)x - 23/8.

The slope of the given line is 5/8, so the slope of any line perpendicular to it will be -8/5.

y - (-4) = (-8/5)(x - 4)

Simplifying, we get:

y = (-8/5)x + 16/5

Therefore, the equation of the line that is perpendicular to 5x-8y=-6 and passes through (4,-4) is y = (-8/5)x + 16/5.

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The domain of the linear function shown in the graph is given as follows:

{x | 2 ≤ x ≤ 9}.

The domain of a function is composed by the set containing all the possible input values for the function, hence it is composed by all the values of x assumed by the function.

The bounds of the domain in this problem are given as follows:

Hence the correct option regarding the domain of the function is given by the second option.

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The conversion factor of litre to quarts is 1 litre = 1.057 quarts and its meaning is discussed below.

What is a conversion factor?

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value. The correct conversion factor to convert minutes to hours is 60 minutes = 1 hour.

The metric unit of a volume known as the litre is mostly used to measure liquids.

An English measurement of volume equal to the one-quarter gallon is the quart. There are now three different types of quarts in use: the liquid quart, dry quart, and imperial quart of the British imperial system.

The standard value of converting liquid to quarts is 1 litre = 1.057 quarts.

This means that volume of 1 litre of a substance is equivalent to the volume of 1.057 quarts of the same substance.

Therefore the conversion factor of litre to quarts is 1 litre = 1.057 quarts.

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The nontrivial solution to the equation Ax = 0 is x = [1, 1, 1]^T.

What is the nontrivial solution?

To find a nontrivial solution to the equation Ax = 0, where A is the given matrix, we need to find a vector x that satisfies the equation and is not the trivial solution x = 0.

We can start by using the observation that the first column plus twice the second column equal the third column:

4x1 - 7x2 + 9x3 = 0

x1 + 2x2 - 3x3 = 0

6x1 + 3x2 + 3x3 = 0

Applying row reduction to the matrix A, we find:

{{4,1,6},{-7,5,3},{9,-3,3}}

{{1,1/2,-3/2},{-7,5,3},{9,-3,3}}

{{1,1/2,-3/2},{0,11/2,15/2},{0,11/2,15/2}}

The rank of the matrix A is 2, which is less than the rank of the matrix of the system of linear equations, which is 3. This means there is a nontrivial solution to the equation Ax = 0.

One such nontrivial solution can be found by setting x3 = 1 and solving for x1 and x2:

x1 + 2x2 - 3(1) = 0

x1 + 2x2 = 3

x1 = 3 - 2x2

Setting x2 = 1, we find:

x1 = 3 - 2(1) = 1

x2 = 1

x3 = 1

Hence, a nontrivial solution to the equation Ax = 0 is x = [1, 1, 1]^T.

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Approximately 99.7% of the vehicles travel between 53 miles per hour and 77 miles per hour.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

The mean and the standard deviation for this problem are given as follows:

Hence:

Meaning that the approximate percentage is of 99.7%.

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The quotient of 2 3/4 divided by 4 1/2 is approximately 0.622222222.

The outcome of dividing two numbers is referred to mathematically as the quotient. It is the amount produced when a numerator is divided by a denominator.

For example, consider the expression "10 ÷ 2". 10 is the numerator, and 2 is the denominator. The quotient of this expression is 5. This has the following notation in mathematics:

10 ÷ 2 = 5

The quotient can also be a fraction, in which case it represents a ratio of two numbers. For instance, the fraction representation of the equation "5 2" is as follows:

5 ÷ 2 = 5/2

In this case, the quotient represents the ratio of 5 to 2.

The quotient is an important concept in mathematics, as it is used in many areas, including arithmetic, algebra, and calculus. It is used to solve problems involving division and ratios, and it is a basic building block for more advanced mathematical concepts.

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Answer:

1.  sin∠EDA is equal to sin∠EBC

2.  sin∠CEB is not equal to sin∠EBC

3.  cos∠BEC is equal to sin∠EBC

4.  cos∠ADE is not equal to sin∠EBC

5.  sin(90 - m∠EBC) is not equal to sin∠EBC

6.  cos(90 - m∠EDA) is equal to sin∠EBC

Step-by-step explanation:

From inspection of the given diagram, ∠EAD = ∠ECB = 90°.

According to the vertical angles theorem, ∠BEC = ∠DEA.

According to AA similarity theorem, ΔADE ~ ΔCBE

Therefore, ∠EDA = ∠EBC.

This means that:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Since  cos∠BEC = CE/BE  and  sin∠EBC = CE/BE  then:

As  ∠BEC ≠ ∠ADE  then:

As  sin(90° - x) = cos(x)  then  sin(90 - m∠EBC) = cos∠EBC.

As  cos∠EBC ≠ sin∠EBC  then:

As  cos(90° - x) = sin(x)  then  cos(90 - m∠EDA) = sin∠EDA.

As  sin∠EDA = sin∠EBC  then  cos(90 - m∠EDA) = sin∠EBC.

Hence:

Answer:

y = 5x

Step-by-step explanation:

It can be observed that as ‘x’ increases, ‘y’ also increases.

It can also be observed that

[tex]\frac{y}{x}[/tex] = the same constant for all four sets of values

k =[tex]\frac{10}{2} = \frac{20}{4} = \frac{30}{6} =\frac{40}{8}[/tex]=5

It can concluded that y is directly proportional to x:

y = kx                      Where k = constant of proportionality

For these four sets of values:

y = 5x

The velocity of the particle v as a function of time t is given by v(t) = 36 - 0.10 * t^2 cm/s and the position x as a function of time t is given by x(t) = 36 * t - 0.05 * t^3 cm.

The problem states that at time t = 0, the particle has an initial velocity of v = 36 cm/s and is located at x = 0 cm. The particle is accelerating with a=-0.10 V v. This means that the velocity of the particle is changing by -0.10 V v each second. This can be expressed in terms of the time t as v(t) = 36 - 0.10 * t^2 cm/s. The position of the particle at any time t can be expressed as x(t) = x0 + v0 * t + 1/2 * a * t^2, where x0 is the initial position and v0 is the initial velocity. In this case, x0 = 0 and v0 = 36, so the position of the particle at any time t can be expressed as x(t) = 36 * t - 0.05 * t^3 cm. This means that the particle will move away from the origin (x=0) and its velocity will decrease each second.

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The linear expression for 2h - 1 and 3h + 4 is 5h + 3. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

According to mathematicians, the four fundamental operations, also referred to as "arithmetic operations," can be used to describe all real numbers. Division, multiplication, addition, and subtraction are the four mathematical operations that result in the terms quotient, product, sum, and difference, respectively.

We are given two expressions as 2h - 1 and 3h + 4.

On adding both, we get

2h - 1 + 3h + 4 = 5h + 3

Hence, the linear expression for 2h - 1 and 3h + 4 is 5h + 3.

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Answer:

Step-by-step explanation:

Given triangle WXY with sides WX = 7 in and XY = 7 in and angle X = 60°, you want the measure of angle Y and the length of side WY.

The equal given side measures tell you that their opposite angles (W and Y) have equal values. Those values will be such that the total of all angles is 180°:

  W +Y +X = 180°

  Y +Y +60° = 180° . . . . . . . . . . . use given values; substitute Y for W

  Y = (180° -60°)/2 = 60° . . . . . . . subtract 60°, divide by 2

All of the angles in this triangle have the same measure, so it is an equilateral triangle. All of the sides have the same measure, too.

  angle Y = 60°

  WY = 7 inches

__

Additional comment

It is helpful to recognize that an isosceles triangle with a vertex angle of 60° is an equilateral triangle. That recognition lets you write down the answer with no further work.

The solution is, each tour guide have an equal number of 8 students.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

there are 12 students in each class.

Four classes are on a field trip.

There are 6 tour guides.

total students = 12*4

                       = 48

so, each guide have = 48/6

                                  = 8

Hence, The solution is, each tour guide have an equal number of 8 students.

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The x-intercept is -3 and the vertex of the parabola is (-1.5, -13.5).

The intersection of two lines, two line segments, or any other suitable arrangement of rays, segments, and lines that results in two straight "sides" coming together at one location is known as an angle's vertex.

The x coordinate of the vertex is given as:

x = -b/2a= -18/ 2(6)= - 1.5

The y coordinate of the vertex is given as:

y = f(- 1.5)

f(- 1.5) = 6(- 1.5)² + 18(- 1.5) = 13.5 - 27= -13.5

Hence, the vertex of the parabola is (-1.5, -13.5).

The x intercept is found by substituting the value of y = 0 in the function:

0 = 6x² + 18x

0 = 6x (x + 3)

x + 3 = 0

x = -3

Hence, the x-intercept is -3 and the vertex of the parabola is (-1.5, -13.5).

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Answer:

No

Step-by-step explanation:

An isosceles triangle has two sides of equal length.

All interior angles in an isosceles acute triangle are less than 90°.

Therefore, it is not possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100° as two sides are not of equal length and 100° > 90°.

The greatest volume and smallest volume container is of rice and flour.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

Given;

Sugar container radius and height is 2.5in and 8.5inch

Rice container radius and volume is 2.5in and 235.3inch^3

Sugar container area of base and height is 12.26in and 4inch

Now,

1. volume= pi*r*r*h

=3.14*2.5*2.5*8.5

=166.8125

2. volume= pi*r*r*h

235.3=3.14*2.5*2.5*h

h=11.98in

3. volume= base*h

=12.26*4

=49.04in^3

Therefore, the volume of flour container is 49.04in^3.

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The required expression is n/6 +3

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.

Given here: The statement " 3 added to the quotient of a number divided by 6

Let the number be n

Dividing the number by 6 we get the quotient as n/6

Again adding 3 to the quotient we get

3+n/6

Hence, The required expression is n/6 + 3

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If we are to write the following polynomial in descending powers of the variable and with no missing powers 3x^3 -70, it would be 3x^3 - 70 + 0x^2 + 0x + 0

A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.

Hence, it can be seen that descending order is basically when the power of a term decreases for each succeeding term. For example, x3 + x2 + x or 2 x4 + 3 x2 + 7 x are arranged in descending order. Descending order is more commonly used.

The polynomial in descending powers of the variable with no missing powers is:

3x^3 - 70 = 3x^3 - 70 + 0x^2 + 0x^1 + 0x^0

= 3x^3 - 70 + 0x^2 + 0x + 0

Note: The polynomial can also be written as 3x^3 - 70x^0.

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