Graph this line using the slope and y-intercept:
y = x + 2
Click to select points on the graph.

The number of polygons that can be formed are

Points (0, 1) and (2, 3)

The set of points (0, 1) and (2, 3) cannot form a polygon as they are collinear (i.e., lie on the same straight line) and do not enclose an area.

Points  (4, 5), (6, 7), and (8, 9)

These are three different points.

Because a triangle has three sides, one triangle can be formed by the set of points (4,5), (6,7), and (8,9). i.e. One polygon

Points (3, 5) and the x-axis.

One polygon can be formed by the set of points (3,5) and the x-axis: a triangle with vertices at (3,5), (0,0), and (6,0).

Polygon (4)

This is a rectangle with the dimension:

6 units by 5 units

So, we have

Perimeter = 2 * (6 + 5) = 22 units

Area = 6 * 5 = 30 squared units

Polygon (5)

This is a composite figure with the following dimensions:

Square of 4 units

Rectangle: 6 units by 2 units

So, we have

Perimeter = 4 * 4 + 2 * (6 + 2) = 32 units

Area = 4 * 4 + 6 * 2 = 28 squared units

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I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.

II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.

III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.

IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.

I. Gaussian Elimination Method:

To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:

| 6 2 -1 | 4 |

| 1 5 1 | 3 |

| 2 1 4 |27 |

We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.

After performing the necessary row operations, we obtain the following reduced row-echelon form:

| 6 2 -1 | 4 |

| 0 4 2 | -1 |

| 0 0 3 | 6 |

From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.

II. LU-Decomposition Method:

LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.

III. Gauss-Jacobi Method:

The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.

IV. Gauss-Seidel Method:

Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.

Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.

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Answer:

86.53

Step-by-step explanation:

Area of Triangle Formula: A = 1/2bh

Pythagorean Theorem: a² + b² = c²

Step 1: Draw altitude and label numbers

If we draw a line down the middle, we can see that we get a perpendicular bisector and that we get 2 right triangles with a hypotenuse of 29 and a leg of 3. We need to find h using Pythagorean Theorem in order to use area formula:

3² + b² = 29²

b² = 29² - 3²

b = √832 = h

Step 2: Plug in known variables into area formula:

A = 1/2(√832)(6)

A = 3√832

A = 86.5332

Answer:

A

Step-by-step explanation:

consider the coordinates of points C and A

C (4, - 1 ) and A (- 3, 2 )

4 → - 3 in the x- direction is - 7

- 1 → 2 in the y- direction is + 3

then the translation rule is

(x, y ) → (x - 7, y + 3 )

If the total height between two floors is 9'0 1/2" and 14 risers are to be used in a set of stairs, the height of each riser would be approximately 7.75 inches.

To find the height of each riser in a set of stairs given the total height between two floors, we need to divide the total height by the number of risers.

First, let's convert the total height to a consistent unit. The distance between two floors is given as 9'0 1/2". We can convert this to inches by multiplying the feet by 12 and adding the remaining inches:

9 feet = 9 * 12 = 108 inches

0 1/2 inch = 0.5 inch

Total height = 108 + 0.5 = 108.5 inches

Next, we divide the total height by the number of risers (14) to find the height of each riser:

Height of each riser = Total height / Number of risers

Height of each riser = 108.5 inches / 14

Using a calculator, we can compute:

Height of each riser ≈ 7.75 inches

Therefore, the height of each riser in the set of stairs would be approximately 7.75 inches.

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A number that is divided by another, like 1 divided by 2 is one half, it is a fraction of a number.

Answer:

2b+8 is the simplify expression

Answer:

b + 4 + 4 + b=

= +b +b +4 +4

= 2b + 8

__________________________

another way

b + 4 + 4 + b=

= +b +b +4 +4

= 2b + 8

= b = \(\frac{8}{2} \\\\\)

= b= 4

Ans: b= 4

Answer:-2, 0, 2, 3, 4

Step-by-step explanation:

-2 is smaller than 0, 0 is smaller than 2, 2 is smaller than 3, and 3 is smaller than 4.

Answer:

4, 3, 2, 0, -2

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Answer:

Yen, Hana, Tyrell

Step-by-step explanation:

took on edge 2020

The probability that Jack wins the race, and Martina finishes last, is 1/9.

The study of random events or phenomena falls under the category of probability, which is a branch of mathematics. It is concerned with calculating the probability or likelihood of an event happening. A number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event, is used to express the likelihood of an event. An occurrence is more likely to occur the higher its probability. Several disciplines, including statistics, physics, economics, and engineering, employ probability theory to study and forecast unpredictable events.

As there are three equally plausible outcomes and only one of them corresponds to Jack winning, the likelihood that Jack will win the race is 1/3.

As there are three equally possible outcomes and only one of them corresponds to Martina placing last, the likelihood that she does so is also 1/3.

P(Jack wins and Martina finishes last) = P(Jack wins) x P(Martina finishes last) = (1/3) x (1/3) = 1/9

Hence, the probability that Jack wins the race and Martina finishes last is 1/9.

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The complete question is:

a. It represents the spread of the middle 50% of the data.

b. At least 50% of the students scored between 80 and 86.

c. Overall, we can say that the Math 6 class had a range of test scores, with some students performing very well and others performing less well.

How evenly distributed the middle 50% of the data is is determined by the interquartile range. In order to calculate it, the first quartile is subtracted from the third quartile.

A. The interquartile range (IQR) in a box-and-whisker plot is the distance between the first quartile (Q1) and the third quartile (Q3) of the data. It represents the spread of the middle 50% of the data.

B. To determine what percent of the students got 80% or higher, we need to find the upper fence, which is defined as 1.5 times the IQR above Q3. From the box-and-whisker plot, we can see that Q3 is approximately 86 and Q1 is approximately 71. Therefore, the IQR is 86 - 71 = 15. The upper fence is 1.5 * 15 + 86 = 108.5.

Looking at the plot, we can see that there are no data points above 100, so we can safely assume that no students scored above 100%. The highest score is 94, which is within the whiskers of the box-and-whisker plot. Therefore, we know that the percent of students who scored 80% or higher is between the percent of students who scored 80% or higher and the percent of students who scored 94% or higher.

From the plot, we can see that the median is approximately 80 and the third quartile (Q3) is approximately 86. This means that at least 50% of the students scored between 80 and 86. Additionally, we know that the maximum score is 94, so we can say that at least some students scored higher than 86. However, we don't know how many students scored between 86 and 94.

C. Based on the interquartile range, we can say that the middle 50% of the students scored between approximately 71 and 86. This suggests that there is a significant amount of variability in the test scores, as the range is quite wide. Additionally, we know that at least some students scored above 86, but we don't have enough information to determine how many or how high their scores were. Overall, we can say that the Math 6 class had a range of test scores, with some students performing very well and others performing less well.

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What is fractional equivalent?

Equivalent fractions are fractions with distinct numerators and denominators but the same value.

1. The number represented by n has two repeating digits, 15.

2. To convert the repeating decimal to a fraction, we need to identify the place value of the repeating digits. In this case, the repeating digits start immediately after the decimal point, so we need to multiply by a power of 10 that is equal to the number of repeating digits, which is 2.

3. Power of 10 times n = 10^2 x 0.1515... = 15.15...

        \(0.1515... x 10^2 = 15.15...\\\\\)

4.

       \(10^2n = 15.15...\\\\n = 0.1515...\\\\99n = 15\)

To obtain the equation, we multiplied the original bby 100 to eliminate the decimal, which gives 100n = 15.1515... We then subtracted the original equation from the multiplied equation to eliminate the repeating digits, which gives 99n = 15.

5. 99n = 15

n = 15/99

To obtain the fraction, we divided both sides of the equation by 99.

Therefore, the fractional equivalent of the repeating decimal n = 0.1515... is 15/99, which can be simplified to 5/33 in simplest form.

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Answer:

x = 7/3.

Step-by-step explanation:

DE is parallel to BC and AD= DB and AD = EC.

So, AD/DB = (x+1)/(4x-6)

(x + 1)/(4x - 6) = 1

x + 1 = 4x - 6

1 + 6 = 4x - x

3x = 7

x = 7/3.

Answer:

true

Step-by-step explanation:

3n3n3p0mdo98rueu33

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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It takes 10 minutes for the number of bacteria in the population to double.

To determine the time it takes for the number of bacteria in a population to double, we need to find the value of t when the function f(t) equals twice the initial number of bacteria.

The given function is f(t) = 60,000 * 2^(t/10).

To find the time it takes for the number of bacteria to double, we set f(t) equal to twice the initial number of bacteria, which is 2 * 60,000 = 120,000:

120,000 = 60,000 * 2^(t/10).

Next, we can simplify the equation by dividing both sides by 60,000:

2 = 2^(t/10).

Since both sides of the equation have the same base (2), we can equate the exponents:

t/10 = 1.

To solve for t, we multiply both sides by 10:

t = 10.

Therefore, it takes 10 minutes for the number of bacteria in the population to double.

This result is obtained by setting the growth rate of the bacteria population in the given function. The exponent t/10 determines the rate of growth, and when t is equal to 10, the exponent becomes 1, resulting in a doubling of the initial number of bacteria.

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Answer:

3/2 or 1.5 inches

Step-by-step explanation:

Because a quarter of six is 1.5

1/4×6=6/4

which when simplified is 1.5

Answer and explanation:

One route goes up and down the hill while the other goes around the edge of the hill, in other words one route goes through a hill to get to the destination while the alternative route has a tunnel that makes it possible to avoid the hill.

Relationship between distance and time is given by the formula:

Distance = Speed × time

For example to find the distance travelled with a speed of 10km/hr and 4 hours travelled, we simply multiply speed 10km/hr by time travelled 4 hrs = 40km

Answer:

16, and 8 are the two common denominators

If you want the answer for the question it's 7/8

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

Looking at the figure, we can say that it is a vertical angle.

5x - 7 = 23

5x - 7 + 7 = 23 + 7

5x = 30

5x / 5 = 30 / 5

x = 6

Since it is a vertical angle, the other side should be 23⁰. You can also plug in the x value to find if it gives you 23⁰ or not.

5x - 7

5(6) - 7

30 - 7

23

Therefore, x = 6. Hope this helps and stay safe, happy, and healthy, thank you :) !!

Hello !

68/17 = 4

=> yes for 68

84/17 = 4.941...

=> no for 84

357/17 = 21

=> yes for 357

1001/17 = 58.882...

=> no for 1001

The resulting graph is a circle with center at (-3,-1) and radius 3.

The graph of the equation (x+3)²+(y+1)²=9

is a circle with center at (-3,-1) and radius 3. The equation of a circle with center (a,b) and radius r is given by the equation (x-a)² + (y-b)² = r². By comparing the given equation with the standard equation of a circle, we can easily see that the center of the circle is (-3,-1) and the radius is 3. To graph a circle, we need to first plot the center of the circle, which is (-3,-1) in this case. Next, we need to mark the radius of the circle, which is 3 units. We can do this by measuring 3 units from the center in any direction and marking the point. Since the radius of the circle is the same in all directions, we can repeat this process for other directions to get points on the circumference of the circle. We can use a compass to make this process easier. After plotting a sufficient number of points, we can draw a smooth curve passing through all the points to obtain the graph of the circle.

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Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

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Given a rectangle of which its length is nine more than triple the width. The width is _10_inches. The length is 39 inches.

Let:

l = length of the rectangle

w = width of the rectangle

"The length of a rectangle is nine more than triple the width" can be translated as:

l = 9 + 3w

perimeter = 2 l + 2w

Substitute perimeter = 98 and  l =  9 + 3w into the perimeter equation:

98 = 2 x (9 + 3w) + 2w

98 = 18 + 8w

8w = 98 - 18

8w = 80

w = 80/8 = 10 inch.

Substitute w = 10 into the length equation:

l = 9 + 3w

l = 9 + 3 x 10

l = 9 + 30 = 39

Therefore the correct answer is:

The width is _10_inches. The length is 39 inches.

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Answer:

I'm pretty sure its A cuz it looks different than the others

Answer:

Step-by-step explanation:

Given function:

This is a quadratic function with positive leading coefficient.

It means the graph of the function opens up and therefore it has minimum value of the function at the vertex.

Correct answer choice is A

Objects commonly found in a locality include residential buildings, commercial establishments, public facilities, transportation infrastructure, landmarks, natural features, utilities, street furniture, and vehicles.

The type of objects that can be found in a locality can vary greatly depending on the specific location and its surroundings. Here are some common types of objects that can be found in a locality:

Residential Buildings: Houses, apartments, condominiums, and other types of residential structures are commonly found in localities where people live.

Commercial Establishments: Localities often have various types of commercial establishments such as stores, shops, restaurants, cafes, banks, offices, and shopping centers.

Public Facilities: Localities typically have public facilities such as schools, libraries, hospitals, community centers, parks, playgrounds, and sports facilities.

Transportation Infrastructure: Localities usually have roads, sidewalks, bridges, and public transportation systems like bus stops or train stations.

Landmarks and Monuments: Some localities may have landmarks, historical sites, monuments, or cultural attractions that represent the area's heritage or significance.

Natural Features: Depending on the locality's geographical characteristics, natural features like parks, lakes, rivers, mountains, forests, or beaches can be present.

Utilities: Localities have infrastructure for utilities such as water supply systems, electrical grids, sewage systems, and telecommunications networks.

Street Furniture: Localities often have street furniture like benches, streetlights, waste bins, traffic signs, and public art installations.

Vehicles: Various types of vehicles can be found in a locality, including cars, bicycles, motorcycles, buses, trucks, and possibly other modes of transportation.

It's important to note that the objects present in a locality can significantly differ based on factors such as urban or rural setting, cultural context, economic development, and geographical location.

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