Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon.

K = 1/3

The graph of the inequality: 3x + y > 7

Can be seen in the image below.

We want to see which graph represents the inequality:

3x + y > 7

We can rewrite the inequality in slope-intercept form as:

y > -3x + 7

So we just need to graph the line:

y = -3x + 7

With a dashed line, and then shade all the region above the line.

To graph the line, you need to find two points that lie on the line.

if we evaluate the line in x = 0 we wll get:

y = -3*0 + 7

y = 7

if x = 1

y = -3*1 + 7

y = -4

Then we have the points (0, -7) and (1, -4), now we can graph these two points and connect them with a dashed line, then shade the region above.

The graph of the inequality is the one below.

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For the given equation of the line 2x + 3y = 6 , the slope = -2 /3,

the x-intercept = 3 and the y-intercept = 2.

As given in the question,

Given equation of the line is :

2x + 3y = 6

Standard equation of the line with slope 'm' and y -intercept = c

y = mx + c

Convert the given equation into standard form we get,

2x + 3y = 6

⇒ y = (-2/3)x + 6/3

⇒y = (-2/3)x + 2

Slope of the line = -2/3

y - intercept when x = 0

y = 2

x - intercept when y = 0

x = 3

Therefore, for the given equation of the line the slope , x- intercept ,and y-intercept is equal to (-2/3) , 3 , and 2 respectively.

The above question is incomplete, the complete question is:

Determine the slope, x-intercept and y-intercept of the line given by the equation 2x + 3y = 6?

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Answer:

M = (36.5-8)/5

[M = 5.7 miles/day]

Step-by-step explanation:

The goal is 36.5 miles.  The remaining miles needed to achieve this goal is reduced by the miles already ridden, 8 miles.

(36.5 - 8) = 28.5 miles remaining.

We are asked to find a value for M, which is the average number of miles Ian would have to ride to reach his goal.  By average, we can assume it is the average miles/days remaining.  The days remaining are 5, so we have:

(28.5 miles remaining)/5 days = 5.7 miles/day

An equation for M using these steps would be:

M = (36.5-8)/5

A digital clock will show that the number of the hour is less than the number of the minute for 12 different displays, starting at 10:00 AM and ending at 4:00 PM.

These displays are:

10:01 AM, 10:12 AM, 10:23 AM, 10:34 AM, 10:45 AM, 11:02 AM, 11:13 AM, 11:24 AM, 11:35 AM, 12:03 PM, 12:14 PM, and 12:25 PM.

For example, 10:01 AM and 11:23 AM.

From 10:00 AM to 12:59 PM, the hour will always be a single digit, so we can check the minutes to see if they are double digit.

From 10:00 AM to 10:59 AM, the minute has to be greater than the hour. So, we can pick the minutes starting from 01 to 59 and check whether the hour is less than the minute which gives us 12 such displays

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The right angle, 99, 171, and 159 are four of the angles. It follows that the x and y angles, which are also equal, must both equal 201/2.

A place where two lines converge creates an angle. They are quantified in degrees and are denoted by the symbol °. Four essential types are reflex, acute, right, and obtuse angles. A circle has 360 degrees. One terminal exists when two rays (half-lines) are merged form an angle. The rays are referred to as the angle's sides, occasionally as its legs, and occasionally as its arms, while the latter is referred to as the angle's vertex. The place where all points of an angle converge is known as the vertex.

given

A polygon's internal angle measurements are equal to (n-2) * 180, where n is the number of sides.

Therefore, 4 * 180 = 720 is the total of the internal angles of this 6-sided object.

The remaining two equal angles are 720 - 90 - 99 - 171 - 159 = 201 .

The right angle, 99, 171, and 159 are four of the angles. It follows that the x and y angles, which are also equal, must both equal 201/2.

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The measure of the interior non-adjacent angle as required in the task content is; 95°.

Recall; It follows from the triangle exterior angle theorem that the measure of exterior angle of a triangle is equal to the sum of the two opposite interiors angles.

On this note, if the sculpture’s opposite interior angle is 32 less than the interior non-adjacent angle, the sum of the two angle measures is therefore;

x + x - 32.

where, x is the measure of the interior non-adjacent angle.

Hence, x + x - 32 = 158

2x = 158 + 32

2x = 190

x = 95°.

Ultimately, the measure of the interior non-adjacent angle is; 95°.

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Answer:

12

Step-by-step explanation:

Answer:

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

Solve in below steps, using log and exponent rules:

The event with the largest probability is rolling a number higher than 2, so the correct option is B.

First, the fact that a 2 was rolled before does not affect the next rolls of the dice, so that information is extra.

Now we just need to see which option has the largest probability.

A) There are only one number lower than 2, then the probability of this event is p = 1/6

B) There are 3 numbers higher than 2, then the probability is p = 3/6 = 1/2

C) The probability of get another 2 is 1/6

We can see that the event with the largest probability is B, so that one is the most likely to occur.

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Answer:

7/10

Step-by-step explanation:

How do you add a fraction?

First you have to check if they have common denominator. If so, add the numerators and keep the denominator. If Not, you have to find common denominator before added. After that,  check if your fraction need to be simplify.

Solve:

Least common multiplier of 10 and 5 is 10

[tex]\frac{3}{10}+\frac{2}{5}[/tex]

Since [tex]\frac{3}{10}[/tex] already have a denominator of 10 we keep it.

[tex]\frac{2}{5}=[/tex] [tex]\frac{2\times2}{5\times2}[/tex] [tex]=\frac{4}{10}[/tex]

Now we have;

[tex]\frac{3}{10}+\frac{4}{10}[/tex]

Apply fraction Rule which is; [tex]\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}[/tex]

[tex]=\frac{3+4}{10}[/tex]

3 + 4 = 7

[tex]=\frac{7}{10}[/tex]

Hence, [tex]\frac{3}{10}+\frac{2}{5}=\frac{7}{10}[/tex]

RevyBreeze

Answer:

Infinitely many solutions.

Step-by-step explanation:

y=5x+2

2y-4=10x

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

2(5x+2)-4=10x

10x+4-4=10x

10x=10x

There are 0.16 gallon is used to paint each chair.

What is gallon?

A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters.

as given, Four gallon of paint are used to paint 25 chair.

i.e. 4 gallon ⇒ 25 chairs

and If each chair used the same amount of paint then how many gallon are used to paint each?

i.e. how many gallons ? ⇒ 1 chair

∴ 4 gallon ⇒ 25 chairs

∴ 25 chairs ⇒ 4 gallon

∴ 1 chairs ⇒ 4 / 25 gallon

∴ 1 chairs ⇒ 0.16 gallon

Therefore, there are 0.16 gallon is used to paint each chair.

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If the rate of the change in the input to the change in the output is the same for every point in the table, then the table represents a linear function.

If a table of values shows a constant rate of change, it is linear.

A non-vertical graph that is a straight line is linear. An equation that can be written in the form y=mx+b is linear. If a table of values shows a constant rate of change, it is linear.

Linear relationships can be modeled using the slope-intercept form y=mx+b, As x increases, y increases by a proportional amount.

A linear function is a linear relationship that obeys the rules of a function and has a graph that forms a straight line. Function notation is used to express a linear relationship when there are clearly defined inputs and outputs.

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Answer:

a^m + a^n = a^m+n

Step-by-step explanation:

This is true for any value of a and n except 0.

The length and width of the rectangle are 16 cm and 90 cm respectively

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

Let the perimeter of the rectangle be P = 212 cm

Now , the equation will be

The length of the rectangle be = L

And , length is an even integer and the width is 5 times the next consecutive even integer

So , the width of the rectangle W = 5 ( L + 2 )

Substituting the values in the equation , we get

Perimeter of rectangle P = 2 ( Length + Width )

212 = 2 ( L + 5 ( L + 2 ) )

On simplifying the equation , we get

106 = L + 5L + 10

6L = 96

Divide by 6 on both sides of the equation , we get

L = 16 cm

So , W = 5 ( L + 2 )

W = 5 x 18

W = 90 cm

Hence , the length and width of rectangle is 16 and 90 respectively

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on solving 6th term in the binomial expansion of (4x + 1)^8 in simplest form is 3584.

A binomial is an algebraic expression with two terms. For example, a + b, x - y, etc are binomials. We have a set of algebraic identities to find the expansion when a binomial is raised to exponents 2 and 3.

A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.

we know ,

So the 6th term in the equation

is ,8c5 -4x^8-5 = 8c34x^3 is , = 3584

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The angles are congruent and the ratios of sides are equal, then the polygons are similar.

What is the similarity of polygons?

The similarity of polygons refers to the relationship between two or more polygons in which the corresponding angles are congruent (equal in measure) and the corresponding side lengths are in proportion.

We have,

Polygon 1:

Opposite Sides 24 = 24, 12=12,

Angles = 90°

Polygon 1:

Opposite Sides 16 = 16, 8=8,

Angles = 90°

This means that if two polygons are similar, their corresponding angles will have the same measure, and their corresponding side lengths will be in the same ratio. In other words, the ratio of any pair of corresponding sides of similar polygons will be the same.

For example, two triangles are similar if the ratio of their corresponding sides is the same, and their corresponding angles are equal. Similarly, two quadrilaterals are similar if the ratio of their corresponding sides is the same and their corresponding angles are equal.

It's important to note that similarity is a stronger relationship than congruence, because in congruence all the sides and angles must have the same measure, while in similarity only the angles and ratios of sides are the same.

Additionally, the similarity of a polygon can be determined by measuring the angles of the polygon, and comparing the ratios of the corresponding sides.

If the angles are congruent and the ratios are equal, then the polygons are similar.

Hence, the angles are congruent and the ratios of sides are equal, then the polygons are similar.

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The inverse function of f(x) = (x - 5)/3 is f^-1(x) = 3x + 5.

Solution:

To find the inverse of a function, we need to switch the x and y variables, and then solve for y.

Starting with f(x) = (x - 5)/3, we can switch the x and y variables to get y = (x - 5)/3.

We can then solve for x by multiplying both sides by 3, giving us 3y = x - 5.

We can then add 5 to both sides to get 3y + 5 = x, which is the inverse of our original function.

Therefore, the inverse of f(x) = (x - 5)/3 is f^-1(x) = 3x + 5.

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Answer: $20.95

Due to credit rating being fair:

Secured APR = 7.00%

Loan amount = sale price + tax - down payment

New car  =  [tex]19027 + (19072 x 0.045) - 1200 = 18730.24[/tex]

Used car = [tex]15635 + (15635 x 0.045) - 1200 = 15138.575[/tex]

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

Monthly interest = loan amount [tex]x 0.07 x 1/12[/tex]

New car = [tex]18730.24 x 0.07 x 1/12 = 109.26[/tex]

Used car = [tex]15138.575 x 0.07 x 1/12 = 88.31[/tex]

Thus, the difference is [tex]109.26 - 88.31 = $20.95[/tex]

The equation of the polynomial function is (a)  h(x) = x^3 - 2x^2 - 5x - 6

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

x –2 0 1 2 3

h(x) 0 –12 0 8 0

The x-intercepts are where y = 0

So, we have

x = -2, x = 1 and x = 3

The multiplicity is 1

So, we have

h(x) = (x + 2)(x - 1)(x - 3)

Expand

= (x + 2)(x^2 - 4x + 3)

This gives

= x(x^2 - 4x + 3) + 2(x^2 - 4x + 3)

So, we have

= x^3 - 4x^2 + 3x + 2x^2 - 8x + 6

Evaluate the like terms

= x^3 - 2x^2 - 5x - 6

So the equation is h(x) = x^3 - 2x^2 - 5x - 6

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The first and second expressions are equal. The second expression is not synonymous. The third expression is interchangeable. The fourth expression is incorrect.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

According to image,

First expression is equivalent. Second expression is not equivalent. Third expression is equivalent. Forth expression is not equivalent.

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Answer: If you're asking for the answer if 16,000 divided by 4, it would be 4000, don't know for sure if that's what you were asking for! Hope I helped!

A rectangle is a closed 2-D shape with four sides, four corners, and four right angles (90°).

Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side.

A rectangle has four vertices since it has four sides, four angles, and four corners. The intersection of two sides forms the "vertices" of a polygon. They are corners, to put it another way.

Rectangles' basic characteristics include:

Four-sided shapes include rectangles.

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Answer: Yes, after 7 weeks, they will have the same amount of money

Step-by-step explanation: So let’s say Joyce will be equation 1, so it would be - T = 13 + 6x, where T represents the total money, and x represents the number of weeks. And let’s say Enrique will be equation 2, which will be - T = 80 - 5x, where once again, T represents the total money, and x represents the number of weeks.

So, let’s start going off numbers, we will start at 5 weeks, when we put that in, Joyce will have $43 and Enrique will have $65, so we know it will be more than 5 weeks, so let’s try 8 weeks, Joyce will have $61 and Enrique will have $40, so it’s below 8, so how about we try 7, at 7 weeks, Joyce will have $55, and Enrique will have $55 too. So this means, after 7 weeks, Joyce and Enrique will have the same amount of money

The date Mr. Remy Osta will resume duty after his 50 days leave which lasted from February 10, 2008 is March 31, 2008

A leap year is a year which has 366 days, that is, the days in February are 29 days.

So,

From February 10, 2008

The days remaining in February is 19 more days

The days of march is 31 days

Hence,

19 days + 31 days

= 50 days

Therefore, Mr. Remy Osta will resume duty on March 31, 2008

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Answer:

Here are two data points that can be used to represent this relationship:

(x1, y1) = (8, $320) - this data point represents that when Susan works 8 hours, she gets paid $320.

(x2, y2) = (12, $440) - this data point represents that when Susan works 12 hours, she gets paid $440.

Step-by-step explanation:

In this situation, the independent variable is the number of hours that Susan works, and the dependent variable is the amount of money that she gets paid.

Here are two data points that can be used to represent this relationship:

(x1, y1) = (8, $320) - this data point represents that when Susan works 8 hours, she gets paid $320.

(x2, y2) = (12, $440) - this data point represents that when Susan works 12 hours, she gets paid $440.

We can use these two data points to represent the relationship between the number of hours that Susan works and the amount of money that she gets paid. It shows that, As her work hours increase, her pay increases as well.

Answer:rotational

Step-by-step explanation:

it would not be a line because a line is a line and other make no sense

Answer:

Taylor

Step-by-step explanation:

2.5km in 17 mins time 2=5km in 34mins 3km in 20 mins times 2=6km in 40 mins

As per the following diagram, the angle measures of triangle EFC is 118°

The term angle in math is known as a figure which is formed by two rays or lines that shares a common endpoint.

Here we have given that an artist uses colored tape to divide sections of a mural and she needs to cut a piece of paper to cover triangle EFC while she works on other sections.

According to the diagram, here we know that the value of

=> DE = EF

And the value of

=> EB = FB

Here we know that the value of the angles,

=> ∠EDB = ∠EFB = 90°

Thus implies that the angles,

=> ∠DFB = ∠FEB = 31°

Then the value of the angle is calculated as,

=> ∠EDB =∠EFB = 90° - 31°

=> ∠EDB = ∠EFB = 59°

Then the value of the angle ABC is calculated by sum the values of the angles, then we get,

=> ∠ABC = ∠EDB + ∠EFB = 59 + 59 = 118°

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