Determine whether the following statements are sometimes, always, or never true. Explain.
How can triangle classifications help you prove triangle congruence?

The translation from A to B is described as-

In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to be the exact size as that of the original shape, therefore the shapes are congruent.

Now, according to the question.

Consider the equation for the shifting from A to B  as y = k x+b

The coordinates of the location A and B are-(see the diagram)

A(-3,-1) and  B(0,1)

Thus, A, B into y = k x+b

Substitute the value of A in the equation;

-1 = -3k + b

b = 1  

So, k = 2/ 3

Put value of k in 'y'.

Hence, AB ; y = (2/3)x + 1

Thus, the coin moves thought y = (2/3)x + 1 from x = -3 to x = 0.

In words; Shifting from A to B, the coin moves 3 spaces to the right after that moves 2 space up.

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I bought 2 pens and 4 pencils from given amount.

Let us represent the number of pens and pencils as x and y respectively. Forming the equation as per the given information -

Equation representing total number of pens and pencils bought

x + y = 6 - Equation 1

Rearranging the equation 1 as per the variable x

x = 6 - y - Equation 2

Equation representing cost of bought pens and pencils

1x + 0.5y = 4 - Equation 3

Keep the value of x from Equation 2 in Equation 3

1 (6 - y) + 0.5y = 4

6 - y + 0.5y = 4

Rearranging the equation for positive sign on each side -

y - 0.5y = 6 - 4

Performing subtraction on Right Hand Side of the equation to find the value of y

0.5y = 2

Shifting 0.5 to Right Hand Side of the equation and performing division

y = 2 ÷ 0.5

y = 4

Calculating the value of x by keeping the value of y in Equation 2

x = 6 - 4

x = 2

Hence, I bought 2 pens and 4 pencils from given amount.

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Answer:

∠ 1 = 131° , ∠ 2 = 49°

Step-by-step explanation:

∠ 1 and ∠ 4 are a linear pair and sum to 180° , that is

∠ 1 + ∠ 4 = 180°

∠ 1 + 49° = 180° ( subtract 49° from both sides )

∠ 1 = 131°

∠ 2 and ∠ 4 are vertically opposite angles and are congruent , so

∠ 2 = 49°

36 is 17th term of sequence a₁₈ = 32, d=-4

Given the 18th term and the common difference, we subtract the common difference from the 18th term to determine the 17th term:

a₁₇ = a₁₈ - d

     = 32 - (-4)

     =  36

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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A proportion exists in an equation in which two ratios stand set equivalent to each other. 367 students in his school have at least one sibling.

A proportion exists an equation that sets two ratios at the same value. A mathematical comparison of two numbers is called a proportion. In terms of proportion, two sets of given numbers are said to rise or decrease in the same ratio if they are directly proportionate to one another.

Let the number of students be x, then

25/32 = x/470

simplifying the above equation, we get

25(470) = 32x

32x = 11750

Dividing both sides of the equation by 32, we get

32x / 32 = 11750 / 32

x = 367

The value of x = 367.

Therefore, 367 students in his school have at least one sibling.

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Answer:

Choice 4

Step-by-step explanation:

A one to one function has every domain with only one range as their individual output. Choice 4 has the output 6 mentioned twice for both 2 and 4 so therefore it's not a one to one function because the range 6 has two outputs 2 and 4.

On a number line, the possible coordinates of point E are: 10 or -12.

Given that point E on a number line has a coordinate of -1, and also, we know that the distance from point E to point G is 11 units, we would determine the possible coordinates of point G as explained below:

11 units from point E is: -1 + 11 = 10

11 units towards point E is: -1 - 11 = -12

Therefore, on a number line, the possible coordinates of point E are: 10 or -12.

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The quadratic opens upwards, so the minimum is at the vertex.

We can see that the minimum value of g is y = -1.

By looking at the given graph, can see that g(x) is a quadratic equation.

If the quadratic equation has a positive leading coefficient (it opens upwards) the minimum of the quadratic is on the vertex, and there is no maximum (as the function end behavior tends to infinity)

If the quadratic equation has a negative leading coefficient (it opens downwards). The maximum is at the vertex, and there is no minimum (similar like the case above).

Here we can see that the quadratic opens upwards, thus, the minimum is at the vertex, which we can see is located at x = 3 and y = -1, then the minimum value of the function g(x) is y = -1

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Answer:

-7

Step-by-step explanation:

-3x-6>15

-3x/-3>21/-3=-7

x<-1+3

x<2.

Answer:

=====================

The distance between points (x₁, y₁) and (x₂, y₂) is:

So we have both segments with same length of 5 units

According to the question, the model has linear relationship between the temperatures which are in degree Fahrenheit and in Celsius.

Now, to calculate the rate of change of the temperature which is defined in the ratio of y-axis and x-axis. Therefore, the expression can be written as:

Rate of change of the temperature = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

From the graph model, the coordinate values are (0,32) and (30,86)

[tex]x_{2} = 30; x_{1}=0; y_{2}=86; y_{1}=32[/tex]

Substituting the given values in the standard expression to calculate the rate of change of the temperature:

Rate of change of the temperature = [tex]\frac{86-32}{30-0}=\frac{54}{30} =\frac{9}{5}[/tex]

Hence, the rate of change of the temperature is 9/5.

What is rate of change in the graph?

In the graph, the rate of change of a quantity defines the relationship between the two quantities. The calculated values are either positive, negative or zero. It is a slope of a line in the form of ratio of vertical to horizontal axis.

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Answer:

1: P = -3

2: X = -60

3: N = 5

Step-by-step explanation:

Ok, for number one you are going to add 4 on the -4 canceling that out, and adding 4 on the -7 making that -3.

Number 2 you times 10 on the x/10 to cancel out the 10 (making it x) then you do -6 times 10, and then you get -60

Last one is a little tricky here's the equations I used to get the last one

-3 x 8n = -24x

New equation: 4-24x=-104

                        +4         +  4

___________________________

                        -24x = -100

                         ___     ___

                         -24      -24

                                                   _

so the answer would be x = 5

The value of x in equation is 8

To find the value of x, we will solve the given mathematical expression based on the sequence of signs and placement of bracket. Firstly bracket will be solved followed by subtraction or addition.

Rewriting the equation -

6(x - 4) = 3x

Performing multiplication on Left Hand Side of the equation to find the value of x

6x - 24 = 3x

Shifting 3x and 24 to other side of equation

6x - 3x = 24

Performing subtraction on Left Hand Side of the equation

3x = 24

Shifting 3 to other side of equation as denominator

x = 24 ÷ 3

Performing division on Right Hand Side of the equation

x = 8

Hence, the value of x is 8.

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The total surface area of the closed milk tin is 528 cm²

The shape of the closed tin of milk is cylinder.

The formula for calculating the total surface area of cylinder is the curved surface area of the cylinder + the area of the two circles(on the top and the bottom) which equals to 2πr(r+h), where r is the radius of the cylinder and h represents the height of the cylinder.

The diameter of the cylinder is 12cm and the height of the cylinder is 8cm.

The radius of the cylinder is half of the diameter of the cylinder which is 12/2=6cm

By putting the values, we get = 2×22/7×6(6+8)

    = 264/7(14)

    = 264(2)

    = 528 cm²

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Answer:

System C

Step-by-step explanation:

When we multiply both sides of the equation 4x - 3y = 9 by -2, we obtain

-8x + 6y = -18. So system C has infinitely many solutions.

The salary after 6 years is $83,000.

The salary after tt years is 53,000 + 5000tt.

The equation that can be used to determine Aisha's salary after a period of time can be represented by a linear equation. This is because that her salary increases by a constant rate each year.

A linear function represents a straight line when drawn on a coordinate plane. A linear function is a function that has a single variable raised to the power of 1. An example is y + 2. The variable y is raised to the power of 1. 2 is the constant term.

Total salary = beginning salary + (rate of increase x number of years)

Salary after 6 years: 53,000 + (5,000 x 6)

= 53,000 + 30,000 = $83,000

Salary after tt years: 53,000 + (5,000 x tt)

53,000 + 5000tt

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The factored form of the expression 16x² + 9y² over the complex numbers is; (4x + 3iy)(4x − 3iy)

We want to find the factored form of the expression 16x² + 9y² over the complex numbers.

We can rewrite the given expression 16x² + 9y² as perfect squares;

= (4x)² + (3y)²

Now, from using the difference of squares formula, we know that;

a² - b² = (a + b)(a - b)

Thus;

(4x)² + (3y)² = (4x)² - (√-9)²y²) can be expressed as;

(4x + 3iy)(4x − 3iy)

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x = 73 is the value of x.

To find the value of x:

So,

Then rounding to the nearest tenths gives x = 73.

Therefore, x = 73 is the value of x.

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The geometric mean between pair of numbers √20 and √80 is 6.32

We know that for a sequence of numbers x1, x2,.., xn

The formula of geometric mean is,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have been given two numbers √20 and √80

We need to find the geometric mean between pair of numbers, √20 and √80

Using the formula for the geometric mean,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have two numbers.

So, the value of n is 2.

[tex]\Pi=\sqrt{\sqrt{20}\times \sqrt{80} }\\\\ \Pi=\sqrt{\sqrt{1600} }\\\\ \Pi=\sqrt{40}\\\\ \Pi=6.32[/tex]

Therefore, the geometric mean between pair of numbers √20 and √80 is 6.32

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The slope of the line is 150.

It is given the number of songs (in million) downloaded from the internet in 2006 and 2004.

We actually need to graph this data which will be a straight line. We try to find two points in this graph using the given data.

Represent the years as x coordinates and the number of songs as y coordinates. Also take 2006 as 6 only and 2004 as 4 only for convenience.

Now we get two points [tex](x_1,y_1)[/tex] = (4, 200) and [tex](x_2,y_2)[/tex] = (6, 500)

Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{500-200}{6-4}[/tex] = 300/2 = 150

Here the slope is positive, which means that the number of downloads are increasing with increase in years. The rate of change in number of downloaded songs from internet is 150 million in two years.

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The equation for the vertical translation of y=f(x). 2 units up is y=f(x)+2.

Using equations of the form y=f(x), you may be able to modify the graph in various ways. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of transformations/modifications to change it to the desired function.

A point on the graph of y=f(x) has the shape (x,f(x)).

The points on the graph of y=f(x)+2 are of the form (x,f(x)+2).

So, the graph for y=f(x) +2 is the same as the graph for y=f(x) shifted up by 2 units.

The new equation is:

y=f(x)+2

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Step-by-step explanation:

i thank the answer is 10.5 thanks for your question

The leg length is 9/ root2

Here we are given a right angle triangle , and in a right triangle , sum of squares of sides is equal to the square of hypotenuse.

[tex]a^{2}+b^{2} =c^{2}[/tex]

This is right angle scalene triangle as the two angles other than right angle are 45° each.

Hence ,

In this case we have

[tex]a^{2}+a^{2} =c^{2}[/tex]

[tex]2a^{2}=c^{2}[/tex]

[tex]a^{2}=\frac{c^{2} }{2}[/tex]

Taking square roots on both sides

[tex]a=\frac{c}{\sqrt{2} }[/tex]

Here we have hypotenuse c given as 9

Hence, the leg length is [tex]a =\frac{9}{\sqrt{2} }[/tex]

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The equation of the line in slope-intercept form is y = (1/2)x + (-5/2) .

The equation of a line in slope-intercept form can be written as follows,

y = mx + c                                                       equation 1

m in the above equation represents slope of the line and c represents the intercept.

The given equation is 2x - 4y = 10 .

To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as

   2x - 4y = 10

⇒ 4y = 2x -10

Now on dividing this equation by 4 on both sides, we will get

y = (1/2)x + (-5/2)                                               equation 2

On equating equation 1  and equation 2, we will get

Slope of the line = m = 1/2.

Intercept = c = -5/2

The equation of the line in slope-intercept form is y = (1/2)x + (-5/2) .      

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According to the question, the homeroom class wants to get a present for a student. From [tex]32[/tex]students, [tex]10[/tex] choose cards, [tex]12[/tex] choose t-shirts, [tex]6[/tex] choose a video and the remaining choose a bracelet.

Now, calculate the probability that the exchange students should get a card or a bracelet.

Let us assume, ‘C’ represents the card and ‘B’ represents the bracelet.

Using standard probability formula:

P (C or B) = P(C)+P(B) = [tex]\frac{10}{32} + \frac{4}{32} = \frac{14}{32} = \frac{7}{16} = 43.8%[/tex]

Therefore, the probability to get a card or a bracelet is [tex]43.8[/tex] percent.

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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The comparison and contrast function notation and vector notation for translations are-

Function notation is a method for writing functions that are simple to comprehend and read.

Whenever a vector is simply a list of numbers, it can be represented by an arrow in space.

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Anna , Bob , Chris weigh 108 pounds , 118 pounds  , 92 pounds respectively .

Let the Anna weigh = x pounds

Let the Bob weigh = y pounds

Let the Chris weigh = z pounds

According to the question Anna and Bob together weigh 226 pounds which can be written as  [tex]x+y=226[/tex]     ..(1)

According to the question Bob and Christ together weigh 210 pounds. which can be written as   [tex]y+z=210[/tex]      ...(2)

According to the question Anna and Chris together weigh 200 pounds. which can be written as  [tex]x+z=200[/tex]      ..(3)

From equation (1) [tex]y=226-x[/tex]  putting this value in equation (2) , we get

      [tex]226-x+z=210\\16=x-z\\16+z=x[/tex]       ..(4)

Putting above value in equation (3) , we get

     [tex]16+z+z=200\\2z=184\\z=92[/tex]

Putting z = 92 in equation (4) , we get

    [tex]x=16+92\\x=108[/tex]

Putting x = 108 in equation (1) , we get

   [tex]y=226-108\\y=118[/tex]

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b ≈ 16.1 is high up on the side of the house, to the nearest tenth of a foot, does the ladder reach.

What are examples of linear equations?

8²  +  b²  = 18²

64 + b² = 324

b² = 260

b ≈ 16.1

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