q5 ANSWER FOR 30 POINTS

Three types of rigid transformations are Reflection, Rotation, and Translation. Rigid transformation, also called isometry.

A rigid transformation, also called isometry,  is a transformation that doesn't change the size or shape of a geometric figure. The following are 3 types of rigid transformation:

1. Reflection

→  is the act of shifting an object's coordinates that flip it across a line without changing its shape or size. Horizontal (draw a figure to the left or right) or vertical (draw a figure to the up or down) reflections are possible. The result of reflection is a mirror image of the figure itself.  

The figure is reflected across [tex]x-[/tex] or [tex]y-[/tex] axis, and then change [tex]x-[/tex] or [tex]y-[/tex] coordinate.

2. Rotation

→ is the non-modification of an object's size or shape by rotating it around an fixed point. A center of rotation is required to rotate an object. And the rotation did by using a degree.

The figure is rotated by a degree (ex: 90°), and then change [tex]x-[/tex] or [tex]y-[/tex] coordinate. Meanwhile, a point's center rotation stays at the same.

3. Translation

→ is sliding a figure in any direction without changing its size, shape, or orientation. Translation could be horizontal (make a figure left or right),  or vertical reflections (make a figure up or down).

Vertical translation is shifting the graph along  [tex]y-[/tex] axis

Horizontal translation is shifting the graph along  [tex]x-[/tex] axis.

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Leala writes essay in 10 minutes contains roughly 83 words.We can find by unitary method.

The unitary method is a technique for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.We can find multiplying by other values.

Multiplication is one of the basic mathematical operations. When two or more numbers are multiplied together the answer obtained is called the product. In the case of the multiplication of two numbers the first number in which the other is being multiplied is called the multiplicand.

Now

Number of word=500

Number of minutes=10

she writes in 60 minute= 500

she writes in 10 minute= 500/60 *10

                                       =500/6

                                        =83.33 words

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The length of AE will be;

⇒ 12 units

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In the diagram,

⇒ CE = 12 units

⇒ BE = 5 units

Now,

Since, Triangle CBE is an right triangle.

And, We have;

⇒ CB = AB

⇒ ∠DBC = 90°

⇒ ∠ABE  = ∠DBC = 90° (opposite angles formed by the intersection of  AC and DE.)

As, ∠CBE and  ∠ABE are supplementary angles and form a straight line.

So, We get;

⇒ ∠CBE + ∠ABE =180°

⇒∠CBE =  180° - ∠ABE  

            = 180°- 90°

            = 90°

And, Between triangle ΔCBE  & ΔABE;

⇒ ∠CBE = ∠ABE = 90°

⇒ CB = AB (given)

⇒ BE = BE  (common side)

Hence, The triangles Δ CBE  & ΔABE are congruent.

⇒ Δ CBE  ≅ ΔABE( by S-A-S Congruency)

⇒ CE = AE ( as triangle Δ CBE  & ΔABE are congruent then the sides are same.)

⇒  AE = 12 units

Thus, The length of AE = 12 units

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The complete question is shown in figure.

Answer:

AE = 12 units

Step-by-step explanation:

Answer:

Step-by-step explanation:

x² = 8² + 1²

x² = 64 + 1

x² = 65

x = √65

or

x = 8.06

The extension or reduction of the line takes place when a line segment is dilated from a point on the line.

When a line segment is dilated from a point on the line, the line segment is extended or reduced in size, depending on the dilation factor.

This dilation can be done by either shrinking the line, making it longer or using a combination of both.

When the dilation is done, the original line and the resulting line will be the same length, but their position will be different. The line segment will be moved or rotated around the point of dilation, so the original line will be in a different position than the resulting line.

The point of dilation will be the same distance from both the original and the resulting line.

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The least number of comparisons needed to sort (order) five elements is 8.

Insertion sort is a simple sorting algorithm that works similar to the way you sort playing cards in your hands. The array is virtually split into a sorted and an unsorted part. Values from the unsorted part are picked and placed at the correct position in the sorted part.

Characteristics of Insertion Sort:

This algorithm is one of the simplest algorithm with simple implementation

Basically, Insertion sort is efficient for small data values

Insertion sort is adaptive in nature, i.e. it is appropriate for data sets which are already partially sorted.

There are 5! = 120 possible outcomes.

Therefore a binary tree for the sorting procedure will have at least 7 levels.

Indeed, 2h ≥ 120 implies h ≥ 7.

But 7 comparisons is not enough.

The least number of comparisons needed to sort (order) five elements is 8.

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The triangle given here, using distance formula, is found to be isosceles.

First, let's calculate the length of the sides of the triangle, by calculating the distance between the given points.

Use the following formula:

[tex]d = \sqrt{(x_{2} - x_{1}) ^2 + (y_{2} - y_{1}) ^2}[/tex] (the distance formula)

where (x1,y1) and (x2,y2) are the limits of a segment with length d.

Then, the distance between points X and Y is:

[tex]d_{XY} = \sqrt{(-5-2)^2 + (-4-(-1))^2} = \sqrt{49+9} = \sqrt{58}[/tex]

The distance between points Y and Z is:

[tex]d_{YZ} = \sqrt{(-2-(-5))^2 + (3-(-4))^2} = \sqrt{9+49} = \sqrt{58}[/tex]

and the distance between points Z and X is:

[tex]d_{ZX} = \sqrt{(2-(-2))^2 + (-1-3)^2} = \sqrt{16+16} = \sqrt{32}[/tex]

Then, you have two sides with the same length, which are sides XY and YZ and another side with a different length. When a triangle has two sides with the same length, such a triangle is isosceles.

Thus, the triangle given here, using distance formula, is found to be isosceles.

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The required equation of the line in slope-intercept form is: y = (1/2)x + (3/2)

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The graph is given in the question, as shown

As per the given graph, we take two points (-3, -4) and (5, 0).

The slope formula is:

[tex]m = (y_2 - y_1) / (x_2 - x_1)[/tex]

where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the coordinates of two points on the line.

Plugging in the coordinates of the given points:

m = (0 - (-4)) / (5 - (-3)) = 4/8 = 1/2

The point-slope form of a line is:

y - y₁ = m(x - x1)

Plugging in the coordinates of the first point and the slope:

y - (-4) = (1/2)(x - (-3))

Simplifying:

y + 4 = (1/2)x + (3/2)

This is the required equation of the line.

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The cheaper drink between the drink is the 12 ounces drink.

The cheaper drink between the 8 ounce drink and the 12 ounces drink, would be the one that cost less per ounce.

To find the cheaper drink, the formula is:

= Cost of drink / Number of ounces

The cost of the 8 ounce drink is:

= 1. 28 / 8

= $ 0. 16 per ounce

The cost of the 12 ounces drink is:

= 1. 68 / 12

= $ 0.14 per ounce

The 12 ounces drink is therefore cheaper.

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The question is:

Which drink is cheaper per ounce ?

The first step in creating parallel lines is to use a straightedge to draw a line that intersects the first line.

How do parallel lines work?

In a plane, two lines are said to be parallel if they do not cross, even when extended in both directions indefinitely.

To create a parallel line with a ruler and compass, follow these steps:

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A graph which represents the system of equations and its solution include the following: graph D.

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs or data points on both the horizontal and vertical lines of a cartesian coordinate, which are generally referred to as the x-coordinate and y-coordinate respectively.

In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x - y = 2         ........equation 1.

x + y = -2       ........equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of the system of equations, which is given by the ordered pair (0, -2).

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The expression that represents the net yardage for these plays is given as follows:

19.8x - 11.1y.

The net yardage is given by the sum of all yards gained for the sum of all yards lost.

For example, if Josh Allen passes for 350 yards but loses 20 yards on sacks, his net yardage is given as follows:

350 - 20 = 330 yards.

Then the expression that gives the total net yardage for this problem is given as follows:

25x + 0.9y - 12y - 5.2x.

The expression can be simplified combining the like terms, as follows:

25x - 5.2x + 0.9y - 12y.

(25 - 5.2)x + (0.9 - 12)y

19.8x - 11.1y.

(as combining the like terms means that all the terms with the same letter  and same exponent are added/subtracted).

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Sample is used more often than a population as B. It is usually impossible to count the entire population

In many cases, it is not practical or possible to gather data from every member of a population. For example, imagine trying to survey the purchasing habits of every single adult in the United States. It would be incredibly time-consuming, costly, and difficult to reach everyone.

Instead, researchers use a sample, which is a smaller group of individuals chosen from the population. By analyzing the data from a sample, researchers can make inferences about the population as a whole.

Therefore, the correct option is B.

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Her claims are wrong as per my studied when Your statistics instructor claims that 60 percent of the students who take her elementary statistics class go through life feeling more enriched

She says that 60% of the students are more enriched.

total number of students = 64

if 34 people feel more enriched, the ratio of the students that feel enriched to the total number of students then is ? \frac{34}{64} = 0.53125.

converting .53125 to percentage we'd multiply by 100%.

and hence have .53125*100% =53.125%

since 53.125% is less that the 60% claimed by the instructor, then i infer that her claims are wrong

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On solving the provided question, we can say that- in the triangle UB = UG so, <UBG = <UGB, x+ 10 + x+ 10 + 3x = 180 => x = 32

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

here,

UB = UG

so, <UBG = <UGB

x+ 10 + x+ 10 + 3x = 180

5x + 20 = 180

5x = 160

x = 32

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The response will be;

''The vertical line test is used to determine if each input has exactly one output.''

A relation between a set of inputs having one output each is called a function.

Given that;

The sample answer is,

''The vertical line test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function.''

Now,

Since, The sample answer is,

''The vertical line test determines if one input has exactly one output on the graph. If any vertical line passes through more than one point on the graph, then the relation is not a function.''

Hence, The correct response for the sample answer is,

''The vertical line test is used to determine if each input has exactly one output.''

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A condition that is impossible to satisfy has no solution.

Mathematics can be a powerful tool for solving many problems, but there are some issues that can't be solved.

In particular, any condition that is impossible to satisfy, such as the logical statement ‘this statement is false’, has no solution in mathematics. This is because the statement can’t be proven true or false, and so it can’t be solved.

An unsolvable condition is one that cannot be solved using any combination of logical and mathematical steps.

This means that no matter how much time and effort is put in, a solution to the problem cannot be discovered.

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Answer:

$64.36 or 63.63

Step-by-step explanation:

[tex]22.9+27.6 = 50.5[/tex]

To find tax multiply by .08 and then add to the total

[tex]50.5*.08 = 4.04[/tex]

[tex]50.5 + 4.04 = 54.54[/tex]

I'm not sure of the tip is including the tax or not. However, with tax, multiply the total after tax by .18. Without tax multiply the total beforehand by .18. Then add to the total.

Tip after tax:

[tex]54.54*.18 = 9.82[/tex]

[tex]54.54+ 9.82 = 64.36[/tex]

Tip without tax:

[tex]50.5*.18 = 9.09[/tex]

[tex]54.54+9.09 = 63.63[/tex]

The number of times that the heart beat in one year is 4.20 x 10^7.

Scientific notation is used to compress large numbers in smaller numbers. It is used to transform large numbers into smaller number.

In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, the notation 7 x 10² is equivalent to 700

The number of heart beat in one year = average heart beat per day  number of days in a year

(1.15 x 10^5 x (3.65 x 10^2)

= (1.15 x 3.65) x (10^5 + 2)

= 4.20 x 10^7

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Answer:

Step-by-step explanation:

You want the sums of various geometric series.

The sum of n terms of a geometric sequence with first term a1 and common ratio r is ...

 Sn = a1·(r^n -1)/(r -1)

When the series is infinite, the sum will converge if and only if |r| < 1.

The ratio can be found as the ratio of the first two terms:

  r = a2/a1

The ratio is ...

  r = 16/2 = 2

The magnitude of r is greater than 1, so this series does not converge.

The ratio is ...

  r = 25/5 = 5

The magnitude of r is greater than 1, so this series does not converge.

The ratio is ...

  r = 4/1 = 4

The magnitude of r is greater than 1, so this series does not converge.

The ratio is ...

  r = 12/24 = 1/2

The sum of the first 8 terms is ...

  S8 = 24·((1/2)^8 -1)/(1/2 -1) = 24·(-255/256)/(-1/2) = 24(255/128)

  S8 = 47 13/16

The ratio is ...

  r = -6/3 = -2

The sum of the first 10 terms is ...

  S10 = 3·((-2)^10 -1)/(-2 -1) = 3(1023)/(-3)

  S10 = -1023

__

Additional comment

If you have a number of these, a spreadsheet or graphing calculator can do the math for you.

Answer:

Applying Boadmass

( 1-1/4)^-2

(3/4)^-2

(4/3)^2

(1.333) ^2

1.76

Step-by-step explanation:

Evaluation of the expression gives  1/ 9. Option A

Index form is the power or exponent raised to a number or variable.

In mathematics, an index (or indexes) is the power or exponent that is added to a number or variable. For instance, the index of 2 in the number 24 is 4. Indexes is the plural form of the word. Constants and variables are concepts found in algebra. A constant is a number that cannot be altered. As opposed to a fixed quantity, a variable quantity's value can be altered or assigned any number. In algebra, indices are discussed in terms of numerical values.

From the information given, we have the expression to be.

= (3^(-4) )^(1/2)

Expand the bracket

= (3)^(-4*1/2)

= (3)^(-4*1/2)

= (3)^(-4/2)

= (3)^(-2)

Take the inverse of the square of 3

=1/3^2

=1/9

The expression is simplified to 1/ 9

Thus, evaluation of the expression gives  1/ 9. Option A

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The expression is simplified to 1/ 9

Now, According to the question:

Let's Know:

What is index form?

Index form is the power or exponent raised to a number or variable.

From the information given, we have the expression to be.

[tex]= (3^-^4 )^(^1^/^2^)[/tex]

Multiply the powers:

= [tex](3)^-^4^/^2[/tex]

= [tex](3)^-^2[/tex]

Take the inverse of the square of 3

[tex]=1/3^2[/tex]

=1/9

The expression is simplified to 1/ 9.

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Answer:

Second, Third and fifth options

Step-by-step explanation:

Angle 1 not equal to Angle 2 (Add up to 180 degrees)

Angles 1 and 4 - Vertically opposite angles (Equal)

Angles 3 and 6 - Alternate angles (Equal)

Angle 3 not equal to Angle 5 (Add up to 180 degrees) - angles of a parallelogram

Angles 7 and 2 - Alternate angles and vertically opposite angles (Equal)

Angle 7 not equal to Angle 1 (Same reasoning as angles 3 and 5)

The average rate of change of the function f(x) on the interval [1, 4] is:

R = 3.

After a small search online, I found that the table for the function f(x) is:

x  f(x)

0   1

1    4

2   7

3   10

4   13

5   16

For any function f(x), we define the average rate of change on an interval [a, b] as:

R = ( f(b) - f(a))/(b - a)

In this case we want to find the average rate of change on the interval  1≤x≤4, then we will get:

R = ( f(4) - f(1))/(4 - 1)

Using the table we can see that:

f(4) = 13

f(1) =  4

Then the average rate of change is:

R = ( f(4) - f(1))/(4 - 1)

R = ( 13 - 4)/(4 - 1) = 9/3 = 3

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The application of laws of exponents on the exponential functions gives;

1) ? = -2

2) ? = 4

Some of the laws of exponents are;

- When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.

- When dividing two bases of the same value, keep the base the same, and then subtract the exponent values.

- Where a power is being raised by another power, multiply the exponents together and keep the base the same.

1) (2x^(?)y⁴)⁻³ = 1x⁶/8y¹²

Expanding this gives;

2⁻³x^(-3?)y⁻¹² = ¹/₈x⁶y⁻¹²

¹/₈x^(-3?)y⁻¹² = ¹/₈x⁶y⁻¹²

Equating like terms gives;

-3? = 6

? = 6/-3

? = -2

2) (a^3b^-2)^? = a^12 / b^8

Applying laws of exponents gives;

a^(3?)b^(-2?) = a^(12)b(-8)

Equating like terms gives;

3? = 12

? = 12/3

? = 4

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Rite a partial decay series for At-217 undergoing the following sequential decays,

α decay:

217  At    ​→        4 α  + 213 Bi

85                    2          83

In order to change into a more stable state, a radioactive atom will naturally produce radiation in the form of energy or particles. It is necessary to distinguish between radioactive material and the radiation it produces. Beta, gamma, and alpha decay are the three kinds of radioactivity.

"Alpha decay," a common form of radioactive decay, happens when a nucleus emits an alpha particle (a helium-4 nucleus). During the usual radioactive decay process known as beta decay, a nucleus generates beta particles. The child nucleus will possess a greater atomic mass than the parent nucleus.

α decay:

217  At    ​→        4 α  + 213 Bi

85                    2          83

β decay:

213 Bi     →       0 e  +  213 Po

83                   -1           84

α decay:

213 Po    →        4 α  + 209 Tl

84                    2           82

β decay:

209 Tl     →        0 e  + 209 Pb

82                    -1          83

Therefore,

Rite a partial decay series for At-217 undergoing the following sequential decays,

α decay:

217  At    ​→        4 α  + 213 Bi

85                    2          83

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Use the chain rule to get the derivative (the slope), then use the given point to write the equation.

y = sin(sinx)

dy/dx = cos(sinx) cos(x)

x = 3π

sin(3π) = 0

cos(sin(3π)) = cos(0) = 1

cos(3π) = -1

m = dy/dx|x=3π = -1

y = -x + b

0 = -3π + b

b = 3π

y = -x + 3π

[tex]9w+6=33[/tex]

Subtract 6 from both sides:

[tex]9w+6-6=33-6[/tex]

[tex]9w=27[/tex]

Divide both sides by 9:

[tex]\dfrac{9w}{9} =\dfrac{27}{9}[/tex]

[tex]\fbox{w = 3}[/tex]

Check:

[tex]9(3)+6=33\\27+6=33[/tex]

[tex]\checkmark[/tex]

The two true statements regarding the circle equation are:

"The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9"

"The center of the circle lies on the x-axis."

Remember that the equation for a circle of center (a, b) and radius R is:

(x - a)^2 + (y - b)^2 = R^2

Here we have the equation:

x^2 + y^2 - 2x - 8  =0

First we need to complete squares on x, remember the perfect square trinomial:

(a - b)^2 = a^2 - 2ab + b^2

So we can rewrite:

x^2 + y^2 - 2x - 8  =0

(x^2 - 2x) + y^2 = 8

Now we can add and subtract 1:

(x^2 - 2x) + y^2 + 1 - 1 = 8

(x^2 - 2x + 1) + y^2 - 1 = 8

(x - 1)^2 + y^2 = 8 + 1

(x - 1)^2 + y^2 = 3^2

So, the center is (1, 0) and the radius is 3.

Then the true statements are:

"The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" it is also 3.

"The center of the circle lies on the x-axis." because the center is at (1, 0).

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