Triangle GFH has vertices G(2, –3), F(4, –1), and H(1, 1). The triangle is rotated 270° clockwise using the origin as the center of rotation. Which graph shows the rotated image?
On a coordinate plane, triangle G prime H prime F prime has points (negative 3, negative 2), (1, negative 1), (negative 1, negative 4).
On a coordinate plane, triangle G prime H prime F prime has points (3, 2), (negative 1, 1), (1, 4).
On a coordinate plane, triangle G prime H prime F prime has points (2, negative 3), (1, 1), (4, negative 1).
On a coordinate plane, triangle G prime H prime F prime has points (2, 3), (4, 1), (1, negative 1).

Answers

Answer 1

Check the picture below.

Triangle GFH Has Vertices G(2, 3), F(4, 1), And H(1, 1). The Triangle Is Rotated 270 Clockwise Using
Answer 2

Answer:

b

Step-by-step explanation:

edge 2023


Related Questions

Which function equation is represented by the graph?

ANSWER: f(x)=40(2.25)x

just took the test

Answers

40(2.25)ˣ function equation is represented by the graph transformation.

What do graph transformations mean?

Changes to the graph of a parent function are referred to as transformations. Transformations may be divided into three categories: translations, reflections, and dilations. There are two types of transformations that may be done to a function: vertical (which affects the y-values) and horizontal.

                               (affects the x-values). The following guidelines apply to the function translation and transformation: The function is moved up b units by f (x) + b. The function is moved downward by the notation f (x) b. The function is moved left by the value of f (x + b).

Let the function be of the form

  f(X ) = a(b)ˣ

Then the point (0,40) lies on the graph of this function. This point must satisfy the equation of the function.

We substitute the point to get,

  40 = a(b)⁰

This implies that,

   40 = a(1)

    40 = a

We substitute a=40 into the function equation to get,

         f(x) = 40(b)ˣ

The point (1,90) also lies on the graph of the function. This gives us,

       90 = 40(b)¹

       90 = 40b

      b = 90/40

       b = 2.25

We substitute the value of b also into function to get,

    f(X) = 40(2.25)ˣ

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Choose yes or no to tell whether the equation has the given solution 1/4×+3=3=4×+ 1,x=8

Answers

Answer:

[tex]\large\boxed{\tt No.}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to determine if the equation has a solution given a value.}[/tex]

[tex]\textsf{Since x is given to us, we can use the \underline{Substitution Property of Equality} to evaluate}[/tex]

[tex]\textsf{the equation.}[/tex]

[tex]\large\underline{\textsf{What is the Substitution Property of Equality?}}[/tex]

[tex]\textsf{The Substitution Property of Equality is a Property that allows us to substitute}[/tex]

[tex]\textsf{a known term, or expression for an unknown variable, or some kind of placeholder.}[/tex]

[tex]\textsf{After Substitution, we can prove that the expressions are still equal with this}[/tex]

[tex]\textsf{property.}[/tex]

[tex]\large\underline{\textsf{Solving;}}[/tex]

[tex]\tt \frac{1}{4} x + 3 = " 3 = " 4x+1[/tex]

[tex]\textsf{There's likely a typo in your equation given, hence I will fix it.}[/tex]

[tex]\tt \frac{1}{4} x + 3 = 4x+1[/tex]

[tex]\textsf{Substitute 8 for x in both sides of the equation using our property.}[/tex]

[tex]\underline{\textsf{Use the Substitution Property of Equality;}}[/tex]

[tex]\tt \frac{1}{4} (8) + 3 = 4(8)+1[/tex]

[tex]\underline{\textsf{Follow PEMDAS, multiply first;}}[/tex]

[tex]\tt 2 + 3 = 32+1[/tex]

[tex]\underline{\textsf{Evaluate;}}[/tex]

[tex]\tt 5 \neq 33[/tex]

[tex]\textsf{If the "typo" was the actual equation;}[/tex]

[tex]\tt 5 \neq 3 \neq 33[/tex]

[tex]\large\boxed{\tt No.}[/tex]

The times to run a mile are 7,
9, 10, 11, 11, and 12.
What is the mean?

Answers

Answer:

10

Step-by-step explanation:

When you think of the mean of a data set, think of the word average. 'Mean' and 'average' are the same thing when you're talking about a set of data.

To find the mean, you have to divide the sum of all values in your data set, by the number of values.

7 + 9 + 10 + 11 + 11 + 12 = 60

60/6 = 10

Therefore, the mean of this data set would be 10.

What integer is closest to the radius of a circle with a circumference of 50.27?

Answers

The integer which is closest to the radius of a circle with a circumference of 50.27 as required is; Choice A; 8.

Which answer choice is closest to the radius of the circle?

It follows from the task content that the integer which is closest to the radius of the circle whose circumference is; 50.27 is to be determined.

Recall; Circumference, C = 2πr

r = C / 2π

r = 50.27 / 2π

r = 8.000718989

Ultimately, the integer which is closest to the radius is; Choice A; 8.

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What is the equation through the points: (6, 10), (5, -6)

ASAP please

Answers

Answer: y=16x - 86

Step-by-step explanation:

A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.8 in. The slant height of the pyramid is 89.8 in. What is the height of the​ pyramid?

Answers

The height of the pyramid formed by the patio heater is 89.07 inches

What is an equation?

An equation is an expression that shows how numbers and variables using mathematical operators.

Pythagoras theorem shows the relationship between the sides of a right angled triangle.

To find the height (h) of the pyramid. A right angled is form with base (b) = side of square / 2 = 22.8 / 2 = 11.4 in

Slant height (S) = 89.8 in

Using Pythagoras:

S² = h² + b²

89.8² = h² + 11.4²

h = 89.07 inches

The height of the pyramid is 89.07 inches

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What is the surface area of this composite solid?

Answers

The surface area of the given composite solid is calculated as: 200.24 square units.

How to Find the Surface Area of the Composite Solid?

Surface area of the composite solid = surface area of rectangular prism + surface area of cylinder - 2(area of the base of the cylinder)

Surface area of rectangular prism = length * width * height = 10 * 3 * 5

= 150 square units.

Surface area of cylinder = 2πr(h + r)

height (h) = 4

Radius (r) = 2

Plug in the values:

Surface area of cylinder = 2 * 3.14 * 2(4 + 2) = 75.36 square units

Area of the base of the cylinder = πr² = 3.14 * 2²

= 12.56 square units

Thus, we have:

Surface area of the composite solid = 150 + 75.36 - 2(12.56) = 200.24 square units.

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Create a bar graph from the results of the following survey question: "On average, how much time do you spend using your cell phone each week?"

Answers

The bar graph from the results of the following survey question titled "Hours spent using your cell phone each week" is found in the attachment.

What is a bar graph?

A bar chart, also called a bar graph, is a visual representation of categorical data that uses rectangular bars with heights or lengths that correspond to the measure of the values they represent.

The bars in a bar chart can be plotted either vertically or horizontally.

Vertical bars, horizontal bars, grouped bars, or stacked bars can all be used to make bar graphs.

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Given this unit circle what is the value of x

Answers

Answer:

  [tex]x=-\dfrac{\sqrt{51}}{10}[/tex]

Step-by-step explanation:

You want the value of x in the third quadrant of a unit circle where y = -7/10.

Pythagorean theorem

The radius of a unit circle is 1, so the Pythagorean theorem tells you the magnitude of the value of x is ...

  1² = x² +(7/10)²

  x = -√(1 -49/100) = -√(51/100) . . . . . . x < 0 in the third quadrant

  x = (-√51)/10

he table of values represents a quadratic function.



Write an equation of the function in standard form.

Answers

The equation of the quadratic function in standard form is f(x) = 5x² - 3x - 7

To write an equation for a quadratic function in standard form, we need to use the general form of the equation, which is: f(x) = ax² + bx + c where a, b, and c are constants that determine the shape and position of the graph of the function.

Let's choose the points (-2, -16), (-1, -15), and (0, -12) from the table. Substituting these values into the equation above, we get:

-16 = 4a - 2b + c -15 = a - b + c -12 = c

We can use the third equation to solve for c, which is -12 in this case. Substituting this value into the first two equations, we get:

-16 = 4a - 2b - 12 => 4a - 2b = 4 -15 = a - b - 12 => a - b = 3

Now we have two equations in two unknowns, which we can solve by substitution or elimination. Let's use substitution to solve for b first:

a - b = 3 => b = a - 3

Substituting this into the first equation, we get:

4a - 2(a - 3) = 4 => 2a = 10 => a = 5

Now we can substitute the values of a and b into one of the original equations to find c:

-15 = 5 - b + c => -15 = 5 - (5 - 3) + c => c = -7

Therefore, the equation of the quadratic function in standard form is:

f(x) = 5x² - 3x - 7

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The ratio of children: teenagers: adults in a survey sample are 2: 11:17. a) Which is the largest group represented? b) If there are 180 people surveyed how many are:​

Answers

The solution is,

there are children = 12, teenagers= 66, adults = 102,

so, adults = 102 is the largest group represented

Here, we have,

given that,

The ratio of children: teenagers: adults in a survey sample are 2: 11:17.

now, we have,

If there are 180 people surveyed

now, let , we have,

children = 2x

teenagers= 11x

adults = 17x

now, we have,

2x + 11x + 17x = 180

or, 30x = 180

or. x = 6

Hence, The solution is,

there are children = 12, teenagers= 66, adults = 102,

so, adults = 102 is the largest group represented.

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Which of the following is not a run-on sentence?
O The average length for a feature film is between 80 and 100 minutes but there are some films that exceed 14 hours in length and one film that was 85
hours long.
O According to data collected throughout film history, the average length for a feature film is between 80 and 100 minutes, although some far exceed the
standard running time.
O There are some movies that clock in at over 14 hours long even though the average movie is around 80 minutes but can run up to 120 minutes.
O With an average film length of 80 to 100 minutes it can be surprising to discover that some movies have been 14 hours long and even 85 hours long.

Answers

The option that is not a run-on sentence is this: According to data collected throughout film history, the average length for a feature film is between 80 and 100 minutes, although some far exceed the standard running time.

What is a run-on sentence?

A run-on sentence is a sentence that continues without using appropriate punctuation to join independent clauses. In the sentence above, the comma is used in the right place to join the independent clause, so we may not refer to this as a run-on sentence.

The other three options continue on end without appropriate punctuation to break off the independent clauses.

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The nine members of a coed intramural volleyball team are to be randomly selected from nine college men and ten college women. To be classified as coed the team must include at least one player of each gender. What is the probability the selected team includes more women than men?

Answers

The probability that selected team includes more women then men is [tex]\frac{Σ^{8} _{n=5} (^{10} _{n} )(^{9} _{9-n} )}{(^{19} _{9} ) - (^{10} _{9} ) - (^{9} _{9} )}[/tex]

The likelihood that the selected team contains more women than males matches the probability that the team contains 5, 6, 7, or 8 women (there would therefore be 4, 3, 2, or 1 man in the squad, respectively).

The likelihood of there being 5 women on the team is equal to

[tex]\frac{(^{10} _{5} )(^{9} _{4} )}{(^{19} _{9} ) - (^{10} _{9} ) - (^{9} _{9} )}[/tex]

Since, we can choose 5 women out of 10 in [tex](^{10} _{5} )[/tex] ways, 4 men out of 9 in [tex](^{9} _{4} )[/tex] ways, and 9 persons out of 19 in [tex](^{19} _{9})[/tex] - [tex](^{10} _{9})[/tex] - [tex](^{9} _{9})[/tex] ways (we must reject the possibility of having all men ( [tex](^{9} _{9})[/tex] ways) or all women ( [tex](^{10} _{9})[/tex] ways) because it is a must).

Similarly, we compute the odds of having 6, 7, or 8 women on the team, and because these are disjoint alternatives, the final result is the total of their probabilities, which is

[tex]\frac{Σ^{8} _{n=5} (^{10} _{n} )(^{9} _{9-n} )}{(^{19} _{9} ) - (^{10} _{9} ) - (^{9} _{9} )}[/tex]

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Time (minutes) Jumping Jacks
1 50
2 100
3 150
4 200


Considering the jumping jacks: 50, 100, 150, 200, what is the common difference?
50

Now, think of this table as a set of ordered pairs. This means that the first row can be placed in an ordered pair as (1, 50). The second row can be written as (2, 100). Using this, what is the slope of the line that connects the first two points?
50

What is the slope of the line that connects the 3rd and 4th point?
50

What is the slope of the line that connects the 1st and the 4th point?
150

Is the common difference (aka slope aka rate of change) constant?
Yes

Why is it or is it not constant?
It is constant because it is a linear function.

Answers

Answer:

Step-by-step explanation:

The common difference between the number of jumping jacks is 50, as you correctly stated. This means that the number of jumping jacks increases by 50 for each additional minute.

The slope of the line that connects any two points on this table represents the rate of change of the number of jumping jacks with respect to time. Since the common difference is constant, the slope of the line that connects any two points on this table will be the same. In this case, the slope is 50.

The slope of the line that connects the first and fourth points is calculated as (200 - 50) / (4 - 1) = 150 / 3 = 50, not 150.

The common difference (aka slope aka rate of change) is constant because the number of jumping jacks increases by the same amount for each additional minute. This means that the relationship between time and the number of jumping jacks is linear.

The table below shows the number of people in an arena t minutes after an event has ended.
T= minutes after event ended: 4 8 12 16 20 24
F(t)= number of people in area: 15221 10649 7375 4859 3468 2285
-Use the regression capability of your graphing calculator to find an exponential equation matching this data. Round values to three decimal places.
F(T)= ___
-use your equation (with values rounded to three decimal places) to help you answer the following questions.
(Note: do not use the data table to answer these questions) Round your answers to the nearest whole number.
- How many people were in the arena 23 minutes after the event ended?
-How many people were in the arena 60 minutes after the event ended?
How many people were in the arena at the exact moment the event ended?

Answers

Approximately 19142 people were in the arena at the exact moment the event ended.

How to solve

To decipher an exponential equation synchronous with the provided data, we will employ the equation of [tex]F(t) = a * b^t.[/tex]

Herein, 'F(t)' stands for the total number of attendees in the stadium at 't' minutes after the stoppage of the event, with 'a' symbolizing the initial value and 'b' being the base.

Exploiting the regression aptitudes of a graphing calculator, the exponential equation that most adequately applies to the listed information is: [tex]F(t) = a * b^t[/tex] with three decimal points specified.

F(t) = 19141.846 * 0.718^t

Using the equation:

[tex]F(23) = 19141.846 * 0.718^2^3 = 2726[/tex]

Answer: Approximately 2726 people were in the arena 23 minutes after the event ended.

How many people were in the arena 60 minutes after the event ended?

[tex]F(60) = 19141.846 * 0.718^6^0 = 123[/tex]

Answer: Around 123 people were in the arena a full hour after the occurrence concluded.

How many people were present precisely when the event wrapped up?

F(0) = 19141.846 * 0.718^0 = 19141.846 * 1 = 19141.846

Answer: Approximately 19142 people were in the arena at the exact moment the event ended.

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Husk takes out a 3200 student loan at 6.7% to help him

Part (a) find the total amount interest that will accrue for loan 1(community college )

Part (b) find the total amount of intrest that will a cure for loan 2 state university
Part (c) find the total amount intrest that accrues until payment begin

Answers

(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.

How to solve

(a) For loan 1, $3200 at 6.7% for 4 years and 7 months (4 years in college + 3 months deferment), the simple interest = 3200 * 0.067 * (55/12) ≈ $1023.33.

(b) For loan 2, $12,000 at 7.3% for 2 years and 7 months (2 years in college + 3 months deferment), simple interest = 12000 * 0.073 * (31/12) ≈ $2362.33.

(c) Total interest accrued until payments begin = $1023.33 (loan 1) + $2362.33 (loan 2) ≈ $3385.66.

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to help open up a restaurant Alonzo borrowed money from his Credit Union.
he took out a personal amortized loan for $49,000 at an interest rate of 6.55% with monthly payments for a term of 6 years. is Alonso pays the monthly payment each month for the full term find his total amount to repay the loan ​

Answers

If Alonso pays the monthly payment each month for the full term. Alonzo will repay a total of $59,389.2 over the 6-year term of the loan if he makes the monthly payment each month.

How to find the total amount?

To calculate the total amount that Alonzo will repay over the 6-year term of the loan, we need to use the formula for the monthly payment on an amortized loan:

M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)

where:

M is the monthly payment

P is the principal amount

r is the monthly interest rate (which is the annual interest rate divided by 12)

n is the total number of payments (which is the number of years multiplied by 12).

Using the values given in the problem, we have:

P = $49,000

r = 6.55% / 12 = 0.005458333 (monthly interest rate)

n = 6 years * 12 months/year = 72

Substituting these values into the formula, we get:

M = $49,000 * 0.005458333 * (1 + 0.005458333)^72 / ((1 + 0.005458333)^72 - 1)

= $824.85 (rounded to the nearest cent)

To find the total amount he will repay, we can simply multiply the monthly payment by the number of payments:

Total amount =$824.85 * 72

Total amount = $59,389.2

Therefore, Alonzo will repay a total of $59,389.2 over the 6-year term of the loan if he makes the monthly payment each month.

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The combined math and verbal scores for females taking the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202 (based on date from the College Board). If a college includes a minimum score of 1025 among its requirements, what percentage of females do not satisfy that requirement?
I have already tried 64.8% as my answer!!

Answers

The percentage of females that do not satisfy the requirement is given as follows:

55.17%.

How to obtain probabilities using the normal distribution?

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.

The mean and the standard deviation are given as follows:

[tex]\mu = 998, \sigma = 202[/tex]

The proportion that does not satisfy the requirement is the p-value of Z when X = 1025, hence:

Z = (1025 - 998)/202

Z = 0.13

Z = 0.13 has a p-value of 0.5517.

Hence the percentage is given as follows:

0.5517 x 100% = 55.17%.

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11. Higher Order Thinking Gabriela lives.
2 miles from school. On her way home,
she runs of the way and walks the rest.
How far does she walk? Explain.

Answers

Gabriela walks 1 mile distance on her way home from school as she is running part of the way.

What is distance?

The distance between two things is measured in distance units like miles, kilometres, or metres. Given that it only possesses magnitude and not direction, distance is a scalar number.

We must ascertain Gabriela's total trip distance before we can respond to this query.

We can get the overall distance by adding the distance she runs to the distance she walks because she runs a portion of the route and walks the other.  

Gabriela commutes two miles to school, so

She needs to travel a total of 2 miles.

We need to figure out how far she runs because she is running a portion of the way.

Since running is typically faster than walking, we can infer that she covers the distance in one mile by running half of it.

She will therefore need to walk the additional mile.  

Gabriela walks a mile on her way home from school, which is the answer to the question.

This is because she walks the remaining mile and runs the first mile.

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The ratio of two numbers is 7 to 3 and the sum of their squares is 232. Find the numbers.

Answers

Let the two numbers be 7x and 3x.

We know that (7x)^2 + (3x)^2 = 232.

Expanding this equation, we get 58x^2 = 232.

Dividing both sides by 58, we get x^2 = 4.

Therefore, x = +/- 2.

Plugging this value of x into the expression for the two numbers, we get that the numbers are 14 and 6, or -14 and -6.
Let's call the two numbers in this problem "x" and "y". We know that the ratio of x to y is 7 to 3, so we can write:

x/y = 7/3

We can use this information to solve for one of the variables in terms of the other. For example, we can solve for y in terms of x:

y = (3/7) x

Now we know that one of the numbers is equal to (3/7) times the other. We also know that the sum of their squares is 232, so we can write:

x^2 + y^2 = 232

Substituting y = (3/7) x, we get:

x^2 + (3/7)^2 x^2 = 232

Simplifying, we get:

(1 + (3/7)^2) x^2 = 232

(1 + 9/49) x^2 = 232

(58/49) x^2 = 232

x^2 = (232 * 49) / 58

x^2 = 196

Taking the square root of both sides, we get:

x = 14

Now we can use the equation y = (3/7) x to find y:

y = (3/7) * 14 = 6

Therefore, the two numbers are 14 and 6.

Help asap!! Please help I don’t get this

Answers

The value of arc CD is 110⁰.

The value of arc AD is 120⁰.

What is the measure of the angle?

The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

angle DEC = ¹/₂ (360 - 2x100) (sum of angle at a point)

angle DEC = ¹/₂ (360 - 200)

angle DEC = 80⁰

The value of arc CD is calculated as follows;

80 = ¹/₂ (CD + 50) (intersecting chord theorem)

2 x 80 = CD + 50

160 = CD + 50

CD = 110⁰

Arc AD = 360 - (50 + 80 + 110) (sum of angles in a circle)

arc AD = 120⁰

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If Duane's income tax bill was $1000, what was his taxable income?

Answers

To determine Duane's taxable income, we need to know his tax rate. Let's assume that his tax rate is a flat 20%.

We can use the formula:

taxable income = tax bill / tax rate

Plugging in the values given, we get:

taxable income = $1000 / 0.20

taxable income = $5000

Therefore, Duane's taxable income was $5000.

Answer:

Without more information, it is not possible to determine Duane's taxable income.

The coordinates of the midpoints of the four sides of a square are S(-4, 11), Q(2, 5), U(-4, -1), and A(-10, 5).
Determine the perimeter and area of the square.
5
O perimeter is 144 units; area is 48 square units
O perimeter is 48 units; area is 144 square units
O perimeter is 24√/2 units; area is 72 square units
O perimeter is 72 units; area is 24√/2 square units

Answers

The perimeter and area of the square are 24√2 units and 12 units² respectively

What is the perimeter and area of the square?

To determine the perimeter and area of the square, we have to find the lengths of the sides.

But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.

SQ = √(x₂ - x₁)² + (y₂ - y₁)²

SQ = √(2 - (-4)² + (5 - 11)²

SQ = 6√2

Let's find for QU

QU = √(-4 - 2)² + (-1 - 5)²

QU = 6√2

Let's find for UA ;

UA = √(-10 - (-4))² - (5 - (-1)²

UA = 6√2

And the distance from AS = 6√2

The perimeter of the square = 4 * (6√2)

Perimeter = 24√2 units

The area of the square is l²

Area of the square = (6√2)²

Area of square = 12 units²

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help please The sum of two even numbers is even. The sum of 6 and another number is even. What conjecture can you make about the other number?

A) The other number is odd.
B) The number is even.
C) Not enough information.
D) The number is 8.

Answers

The conjecture that can be made about the other number is option A: the other number is odd.

Let's assume that the two even numbers are x and y. Then, we can write their sum as x + y = 2a, where a is some even number.

Now, let's consider the sum of 6 and another number, which we can represent as 6 + z, where z is some unknown number. If this sum is even, then we can write it as 2b, where b is some even number.

So, we have the equations:

x + y = 2a (since the sum of two even numbers is even)

6 + z = 2b (since the sum of 6 and another number is even)

We can subtract 6 from both sides of the second equation to get:

z = 2b - 6

Now, we can substitute this expression for z into the first equation:

x + y = 2a

And we get:

x + y + z - 2z = 2a

x + (y + z) - 2z = 2a

x + (2b - 6) - 2z = 2a

x + 2b - 2z - 6 = 2a

This equation tells us that x + 2b - 2z - 6 is an even number (since 2a is even). Since x and 2b are even, the expression -2z - 6 must also be even. Therefore, -2z must be even. This means that z is odd (since an even number minus an even number is even, and -6 is even).

So, we can conclude that the other number (z) is odd. Option A is the correct answer.

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Prove the following this : Let H be a subgroup of a group G . The left cosets of H constitute a partition of G ; the right cosets of H constitute a partition of G ?

Answers

To prove that the left cosets of H constitute a partition of G, we need to show that they satisfy two conditions:

1) Each element of G belongs to some left coset of H.

2) Any two distinct left cosets of H are disjoint.

Let g be any element of G. Then, by definition of a left coset, there exists an element h of H such that g = h·x for some x in G. Therefore, g belongs to the left coset H·x. Since this holds for any element g of G, we have shown that the left cosets of H cover all of G, satisfying the first condition.

Now, let H·x and H·y be two distinct left cosets of H. Suppose there exists an element z in both H·x and H·y.

Then, z = [tex]h_{1}[/tex]·x = [tex]h_{2}[/tex]·y for some [tex]h_{1}[/tex], [tex]h_{2}[/tex] in H.

Solving for x,

x = [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] · y.

Since H is a subgroup, [tex]h_{1}^{-1}[/tex]· [tex]h_{2}[/tex] is also in H, and therefore x belongs to H·y.

Thus, H·x is contained entirely in H·y, and the two cosets cannot intersect.

This satisfies the second condition, and hence the left cosets of H constitute a partition of G.

A similar argument can be used to show that the right cosets of H also constitute a partition of G. This completes the proof.

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Hey folks help me out for some points :)

Answers

Answer:

C

Step-by-step explanation:

Positive numbers represent a positive situation. And negative numbers coincide with a negative situation.

 Ex: An increase in temperature corresponds to a positive number, and a decrease in temperature with a negative number.

Correct answer gets brainliest!!!!

Answers

It is a point and point is zero dimensional. Therefore the right options are A and C respectively.

Understanding Point in Mathematics

Point is a basic geometric object that represents a location or a position in space. It is often represented as a dot or a small circle.

Points have no size, shape, or dimension. They are considered to be zero-dimensional objects, and they are often used as a building block for more complex geometric structures.

In addition to representing locations in space, points are also used in other areas of mathematics, such as in coordinate systems and in topology. In geometry, points are used to define lines, planes, and other geometric shapes.

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Select the incorrect phrases in the paragraph.
Given:
is a right angle

is a right angle

Prove:
Four lines M A, M B, M C, and M D that starts from point M are drawn such that angle A M C equals 90 degrees, and angle B M D equals 90 degrees.

1. Angle A M C is a right angle. It leads to angle A M B and angle B M C are complementary 2. Angle B M D is a right angle. It leads to angle B M C and angle C M D are complementary. 1 and 2 lead to Angle A M B which approximately equals angle C M D.

The proof is converted to paragraph form.

Which parts of the paragraph proof are incorrect?
is a right angleis given.
is a right angleis also given.Since
is a right angle,
and
are complementary.Since
is a right angle,
and
are complementary.By the Congruent Complements Theorem,
.

Answers

Note that in the proof stated above, there is no incorrect statement.

How is this so?

The evidence is that when four lines are drawn starting from a point and making two right angles, the two angles between those lines are equal.

The proof begins by stating that when you have a right angle, the two angles that add up to produce the correct angle are referred to as complementary angles.

The Congruent Complements Theorem is then used to demonstrate that the two angles in the centre are equal.

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Polynomial Functions

Answers

a) Yes, the function is in standard form.

  Degree = 2

  Exponent = 2

  Constant term = -1

b) No, the function is not in standard form.

   And it doesn't have the degree, exponent and constant term.

Firstly, let's consider the function f(x) = x(x-1). To determine if it is a polynomial function, we need to check if all of its terms have non-negative integer exponents. In this case, we see that f(x) can be written as x² - x, which has only two terms, and each term has a non-negative integer exponent. Therefore, f(x) is a polynomial function.

In this case, the degree of f(x) is 2 because the highest exponent of x is 2.

In this case, the leading term of f(x) is x², and its leading coefficient is 1.

Finally, the constant term is the term that does not have the variable in it. Here, the constant term of f(x) is -1.

Next, let's consider the function f(x) = 3 - 1/2 x. We can see that f(x) is not a polynomial function because it has a term with a negative exponent.

Polynomial functions must have non-negative integer exponents on all terms.

Therefore, the answer to the first question is 'no.'

Since f(x) is not a polynomial function, it does not have a degree, leading term, or constant term.

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find the probability that a randomly selected point within the large square falls in the red shaded square 6 6 15 15 p= enter as a decimal rounded to the nearest hundredth

Answers

The probability that a randomly selected point within the red-shaded square is 0.16

Finding the probability of a point

From the question, we have the following parameters that can be used in our computation:

Red square of 6 by 6White square of length 15

The areas of the above shapes are

Red square = 6 * 6 = 36

White square = 15^2 = 225

The probability is then calculated as

P = Red square /White square

So, we have

P = 36/225

Evaluate

P = 0.16

Hence, the calculated value of the probability that the point falls in the red square is 0.16

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