factorise completely:
1. 3xy - x
2. 4a² - 9​

For example, if the ratio of one triangle's two sides to that of another triangle is the same and the angles that the two sides of both triangles inscribe are equal, then two triangles are said to be similar. In light of this, if ∠A = ∠X and AB/XY = AC/XZ, then △ABC ≠ △XYZ.

The acronym for the SAS similarity theorem is sided angle side.

We may demonstrate that two triangles are similar when two of their side ratios are the same, plus one of their angles is also equal.

Two triangles are said to be comparable if, for instance, the ratio of one triangle's two sides to those of another triangle is the same, and the angles that the two sides of both triangles inscribe are equal.

Consequently, if ∠A = ∠X and AB/XY = AC/XZ then ΔABC ~ΔXYZ.

Therefore, for example, if the ratio of one triangle's two sides to that of another triangle is the same and the angles that the two sides of both triangles inscribe are equal, then two triangles are said to be similar. In light of this, if ∠A = ∠X and AB/XY = AC/XZ, then △ABC ≠ △XYZ.

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The graph of a slope of 3 is a  straight line.

        Let us assume the co-ordinates

              [tex](x _1, y_1) = (2,1)\\(x _2, y_2) = (5,10)\\\\\text{We know} ,\\\\m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\\\m = \frac{10-1}{5-2} \\[/tex]

              m = 9/ 3

              m = 3 (Refer image for graph)

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The median of the first 10 natural numbers is 5.5.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

x = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10/10

 x = 55/10

 x = 5.5

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The complete question is-

How do you find the mean of first 10 natural numbers ?

On observing the provided question, we can say that - In Korea, 7th grades = 13 or 14 year old, 10th grade is = 16 or 17 year old ,  11th grade is = 17 or 18 and  12th grade is = 18 or 19.

Grading may be done using letters, numbers, percentages, points, or descriptions. The most prevalent grades are in the form of letters, and they usually correspond to a variety of percentages or points. Many people consider "A" and "B" grades to be "good." D and F grades are referred to as "poor grades." Commonly regarded as average is a "C."

We can say that

In Korea,

7th grades =  13 or 14 year old

10th grades = 16 or 17 year old ,

11th grade is = 17 or 18 and  12th grade is = 18 or 19.

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The gradient of y =  3x - 1 is 3.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes.

Given

Equation

y = 3x - 1

Using slope intercept form,

y = mx + b

m = slope

Slope = 3

The gradient of y =  3x - 1 is 3.

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Answer:

b

Step-by-step explanation:

To convert the car's speed from miles per hour to miles per minute, we need to divide its speed in miles per hour by the number of minutes per hour. Since there are 60 minutes per hour, we can divide the car's speed of 39 miles per hour by 60 to get 39 miles/hour / 60 minutes/hour = 0.65 miles/minute. So, the car's speed in miles per minute is 0.65 miles/minute.

To find the number of miles the car will travel in 20 minutes, we need to multiply the car's speed in miles/minute by the number of minutes it will travel for. Since the car will travel for 20 minutes, we can multiply its speed of 0.65 miles/minute by 20 to get 0.65 miles/minute * 20 minutes = 13 miles. Therefore, the car will travel approximately 13 miles in 20 minutes.

When a 180kg man is standing at 1m distance and a boy is standing 4m away from a fulcrum at opposite ends, the mass of boy so that it is balanced is 45kg.

Therefore the answer is 45kg.

Let the mass of the boy be Wb, the mass of the man is Wm = 180kg. The distance of boy from fulcrum is Xb = 4m and the distance of the man from fulcrum is Xm = 1m.

For balancing, the moment about the fulcrum should be zero. That is,

Wb × g × Xb = Wm × g × Xm

Wb × 4 = 180 × 1

Wb = 180/ 4

Wb = 45

--The question is incomplete without figure, answer to the attached figure--

"An 180-kg man balances the boy teeter-totter as shown: Note: Ignore the weight of the board. What is the approximate mass of the boy?"

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The 10 percent rule is used to approximate the independence of trials where sampling is taken without replacement.

Why do we check the 10% condition in stats?

It's important to check the 10% condition before calculating probabilities involving x because we want to ensure that the observations in the sample are close to independent.

According to the premise of independence, your data are not related in any manner (at least not in a way that your model hasn't taken into consideration). Actually, there are two assumptions: Since the groups should have diverse compositions, independent observations should be performed between them.

The frequency with which students ask to leave the room during crucial informative periods is reduced thanks to this technique. The 10/10 rule, which prohibits pupils from leaving the classroom during the beginning or last ten minutes of class, is used to achieve this.

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Assuming a 10% rate of orders that are incorrect. The accuracy rate seems to be satisfactory.

Definition of accuracy-The accuracy formula provides accuracy as a difference of error rate from 100%. To find accuracy we first need to calculate the error rate. And the error rate is the percentage value of the difference of the observed and the actual value, divided by the actual value.

Given: A study of the accuracy of fast food drive-through orders, one restaurant had 37 orders that were not accurate among 333 orders observed. Significance level-0.05

Explanation: Assuming a 10% rate of orders that are incorrect. The accuracy rate seems to be satisfactory.

Let a be the population proportion of the orders that were not accurate.

Then according to the claim we have,

[tex]H_{o} :[/tex]  [tex]p[/tex] = [tex]0.10[/tex]

[tex]H{a} :p[/tex] ≠ [tex]0.10[/tex]

Since the alternative hypothesis is two-tailed so the hypothesis test is a  two-tailed test.

For example,

n = 333

The proportion of the orders that were not accurate =  [tex]p{'}[/tex][tex]=\frac{37}{333}[/tex] ≈[tex]0.112[/tex]

Test statistics for population proportion:-

Assuming a 10% rate of orders that are incorrect. The accuracy rate seems to be satisfactory.

Let a be the population proportion of the orders that were not accurate.

Then according to the claim we have,

[tex]H_{o} :p=0.10[/tex]

[tex]H_{a} :p[/tex] ≠ [tex]0.10[/tex]

Since the alternative hypothesis is two-tailed so the hypothesis test is a  two-tailed test.

For example,

n = 333

The proportion of the orders that were not accurate =  [tex]p^{'} =\frac{37}{333}[/tex] ≈ [tex]0.112[/tex]

Test statistics for population proportion:-

[tex]z=\frac{p-p'}\sqrt{p(1-p)/\sqrt{n}[/tex][tex]=\frac{0.112-0.10}\sqrt{0.10(0.90)}/ {333}[/tex] ≈ [tex]0.75[/tex]

By using the standard normal distribution table,

The p-value : [tex]2(z > 0.75)=2.55[/tex]

Since the p-value is greater than the significance level (0.05), so we do not reject the null hypothesis.

Hence, we conclude that the accuracy rate appears to be​ acceptable and satisfactory.

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We come to the conclusion that there are three different kinds of parameters that can be used with functions in Python. Default, keyword, and arbitrary arguments are these.

a number that can be any number it is defined to be, but for which no particular value is chosen. Since it may represent any number while also having the value of any number, it is frequently employed in proofs since it allows the proof to be applied to several scenarios.

here

Python parameters are variables that serve as stand-ins for the real values a function needs.

They are supplied as arguments when the function is called.

An illustration would be the function's arguments.

Default, keyword, and arbitrary arguments are these.

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Answer:

A = 6

B = 4

C = 8

D = 10

surface area ❀

leftmost rectangle : 8 x 4 = 32

middle rectangle : 10 x 4 = 40

rightmost rectangle : 6 x 4 = 24

top and bottom triangles : (8 x 6) = 48

total = 32 + 40 + 24 + 48 = 144cm²

Step-by-step explanation:

not sure if its correct. but i tried.

The solution is

The measure of A = 6 cm

The measure of B = 4 cm

The measure of C = 8 cm

The measure of D = 10 cm

b) The net surface area of the triangular prism = 144 cm²

What is the surface area of the prism?

The surface area of the prism is calculated as

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

The area of the triangular prism is A = ph + ( 1/2 ) bh

Given data ,

Let the measure of the side A = 6 cm

The measure of side B = 4 cm

The measure of side C = 8 cm

The measure of side D = 10 cm

The surface area of the triangular prism is = 2B + ph

The surface area A = ( 6 x 8 ) + ( 6 x 4 ) + ( 10 x 4 ) + ( 8 x 4 )

The surface area A = 48 + 24 + 32 + 40

The surface area A = 144 cm²

Therefore , the value of A is 144 cm²

Hence , the area of the triangular prism is 144 cm²

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Assuming a 10% rate of orders that are incorrect. The accuracy rate seems to be satisfactory.

Let a be the population proportion of the orders that were not accurate.

Then according to the claim we have,

[tex]H_{o} : p=0.10\\H_{a} : p\neq 0.10[/tex]

Since the alternative hypothesis is two-tailed so the hypothesis test is a  two-tailed test.

For example,

n = 333

The proportion of the orders that were not accurate = [tex]p'=\frac{37}{333}[/tex] ≈ [tex]0.112[/tex]

Test statistics for population proportion:-

[tex]z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }\\= \frac{0.112-0.10}{\sqrt{\frac{0.10(0.90)}{333} } }[/tex] ≈[tex]0.75[/tex]

By using the standard normal distribution table,

The p-value : [tex]2(z > 0.75)= 2.55[/tex]

Since the p-value is greater than the significance level (0.05), so we do not reject the null hypothesis.

Hence, we conclude that the accuracy rate appears to be​ acceptable.

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The theoretical probability is 0.5

the practical probability is 0.5

Given, A coin is tossed 50 times, and it lands on heads 28 times. Theoretically, when a coin is tossed the probability of getting a head is 0.5 since in this question we tossed the same coin so the theoretical probability of the given question is 0.5. as per the given data, the Practical probability of getting a head is event happen divided by total events.

Practical probability = 28/50 = 0.56

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To simplify the denominator, we can subtract the common terms - x² and x - leaving us with just x. We can then combine our simplifications to form the final answer of x + 2, then the quotient is  x³ + 3x² + 3x + 2 / x² + x = x + 2

x³ + 3x² + 3x + 2

x² + x

Simplifying the numerator:

x³ + 2x² + 3x + 2 - x² - x = x² + 2x + 2

Simplifying the denominator:

x² + x - x = x

Final Answer:

x + 2

The expression x³ 3x² 3x 2 X² x 1 is a fraction, with the numerator being x³ 3x² 3x 2 and the denominator being X² x 1. To solve this expression, we need to simplify both the numerator and the denominator. To simplify the numerator, we can subtract the common terms - x² and x - leaving us with x² + 2x + 2. To simplify the denominator, we can subtract the common terms - x² and x - leaving us with just x. We can then combine our simplifications to form the final answer of x + 2.

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Answer:

(B) In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.

(C) Vertical angles prove that Angle 3 is congruent to Angle 6.

(D) The triangles are similar because alternate interior angles are congruent.

Step-by-step explanation:

Alternate Interior Angles Theorem

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

As line q has intersected the set of parallel lines c and d, angles 1 and 4 are alternate interior angles, and are therefore congruent.

As line p has intersected the set of parallel lines c and d, angles 2 and 5 are alternate interior angles, and are therefore congruent.

Angle-Angle similarity states that if any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.  Therefore, the triangles are similar because alternate interior angles are congruent.

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Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

The intersection of lines p and q created two opposite vertical angles: angle 3 and angle 6 are opposite vertical angles.  Therefore:

----------------------------------------------------------------------------------------

Triangle similarity

Two triangles are similar if their corresponding angles are the same size.

As angles 1 and 4 are alternate interior angles and are therefore congruent, they are corresponding angles.  Similarly, as angles 2 and 5 are alternate interior angles and are therefore congruent, they are corresponding angles

Therefore this proves that the two triangles are similar and Angle 1 and Angle 4 are corresponding angles.

The missing angles and side measures are:

Angle A = 40°

Angle C = 70°

Side AC = 12 cm

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Triangle ABC is an isosceles triangle.

This means,

Two sides of the triangle are equal and the angle opposite to the sides are also equal.

Now,

Angle C and Angle B are equal.

Angle C = Angle B = 70°

The sum of the three angles is 180 degrees.

Angle A + Angle B + Angle C = 180

Angle A + 70 + 70 = 180

Angle A = 180 - 140

Angle A = 40°

Thus,

The angles of the triangle are 70, 70, and 40.

The sides of the triangle are 12 cm, 12 cm, and 8 cm.

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The nature of the roots of the quadratic equation x² - 6x + 9 = 0 are real and equal

Given that :

The quadratic equation x² - 6x + 9 = 0

To find :

The nature of the roots of the quadratic equation x² - 6x + 9 = 0

x² - 6x + 9 = 0

Find discriminant of the equation

Comparing the given Quadratic equation x² - 6x + 9 = 0 with the general equation ax² + bx + c = 0 we get

a = 1 , b = - 6 , c = 9

The discriminant of the quadratic equation

= b² - 4ac

= (-6)² - 4* 1*9

=36 - 36

=0

Find nature of the roots of the quadratic equation

Since the discriminant of the quadratic equation = D = 0

Hence the roots of the quadratic equation x² - 6x + 9 = 0 are real and equal

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Answer:

18 2/3

Step-by-step explanation:

Rigid transformation is a type of geometric transformation in which the shape of an object is preserved. It includes translations, rotations, and reflections, but does not include any scaling, shearing, or any other kind of distortion. In other words, rigid transformations preserve the distances between points in an object.

Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.

A dramatic change in look or form is referred to as a transformation. An important event, such as acquiring your driver's license, starting college, or getting married, may cause your life to alter. A metamorphosis is a significant, abrupt change.

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The number of terms in the algebraic expression 2n + 5 - 3p + 4q is:

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

To know the number of terms in an algebraic expression we only need to identify the number of addition or subtraction operations and add 1 to it.

The expression is 2n + 5 - 3p + 4q

has 3 symbols

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All pairs of an integer array whose sum is equal to a given number in Python using the algorithm based on below three steps:

Step 1: Initialize array and its values

Step 2: Initialize value of sum

Step 3: Call the function find

Programming in Python for all pairs of given number : We will get an array as input from user. We need to find all possible pairs from the given array whose sum is same as given sum. Example:

Array : [5, 2, 0, 4, 1, 8, 7]

Sum = 7

Possible pairs: [5, 2], [0,7],

Algorithm based on below three steps:

Step 1: Initialize array and its values

Step 2: Initialize value of sum

Step 3: Call the function find

Algorithm for function find

Step 1: Iterate on the elements of array with variable i, from 0 to length of array as you want.

Thus, we get the required results.

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Answer:

Vertex = (0,0)

Focus = (0, -1/8)

Axis of symmetry; x = 0

directrix, y = 1/8

Step-by-step explanation:

Answer:

Vertex = (0,0)

Focus = (0, -1/8)

Axis of symmetry; x = 0

directrix, y = 1/8

Step-by-step explanation:

Therefore , the  mathematics make us cry because we aren't able to understand the mathematics .

Numbers, forms, logic, quantity, equation and arrangements are all topics covered in the study of mathematics. Math allows students to identify solutions to problems through numerical  variable computations.

Here,

Anxiety may be indicated by tears or anger, particularly if they only occur during math.

Students who struggle with math anxiety are prone to being very critical of themselves and operating under the damaging and incorrect belief that being strong at arithmetic entails fast obtaining the right answers.

These ideas and attitudes are very restrictive.

Therefore , the  mathematics make us cry because we aren't able to understand the mathematics .

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Answer:

12 is not a prime number.

Step-by-step explanation:

⭐What is a prime number?

12 is not a prime number because it is divisible by numbers other than 1 and itself, such as...

Answer:

1. 38 = 88 - (10 + x + 25)

38 = 88 - 35 - x

x = 53 - 38

x = 15

2. Spanish only = 65 - (5 + 15 + 10)

= 65 - 30

= 35

3. x = 180 - (65 + 25 + 38 + 15 + 5 + 10 + 35)

x = 180 -  193

x = -13

4. 65 + 38 + 35

= 138

Step-by-step explanation:

Answer: If the scale factor is 1, then the original image and the image produced are congruent.

When the scale factor is exactly 1, the copy is the same size as the original.

It is commonly used in maps to represent the actual figures in smaller units. For example, a scale of 1:3 means 1 on the map represents the size of 3 in the real world. The scale factor is a conversion factor - a number that is used to increase or decrease the size of a figure.

The scale factor is the ratio that determines the proportional relationship between the sides of similar figures. For the pairs of sides to be proportional to each other, they must have the same scale factor. In other words, similar figures have congruent angles and sides with the same scale factor

Step-by-step explanation:

Answer: C

Step-by-step explanation:If you use a calculator and you divide 255.6 by 12.5 you’d get 20.448

Answer:20.448

[tex]256.6\div12.5[/tex]

Divide:

[tex]256.6\div12.5\\=20.448[/tex]

[tex]\fbox{Option C}[/tex]

Answer:

There are 6 outcomes: 1, 2, 3, 4, 5, or 6 could appear on the top face of the number cube.

Step-by-step explanation:

How many outcomes does a 6 sided die have? 36 For each of 6 outcomes for the first die the second die may have any of 6 outcomes, so the total is 6+6+6+6+6+6=36, or more compactly, 6⋅6=36. How many possible outcomes are there when a six-sided die is rolled and a coin is flipped at the same time? 6 possible outcomes