the item to the trashcan. Click the trashcan to cle Solve this equation by completing the square. 3x^(2)-4x=-2

The polynomial 2x² - 10x + 15 will have a quotient 2x and remainder of 15 when divided by x - 5 and the result can be written in the form 2x + 15/(x - 5).

Using the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder

We shall divide the polynomial 2x² - 10x + 15 by x - 5 as follows;

2x² divided by x equals 2x

x - 5 multiplied by 2x

2x(x - 5) = 2x² - 10x

subtract 2x² - 10x from 2x² - 10x + 15

2x² - 10x + 15 - (2x² - 10x)

2x² - 10x + 15 - 2x² + 10x = 15.

Therefore, the polynomial 2x² - 10x + 15 will have a quotient 2x and remainder of 15 when divided by x - 5 and the result can be written in the form 2x + 15/(x - 5).

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By answering the above question, we may state that Hence, the equation nonagon's last seven angles are all around 140.57 degrees.

When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.

S = (n - 2) × 180°

where n is the total number of sides, which in this instance is 9.

The internal angles of a nonagon's sum are as follows:

S = (9 - 2) × 180° = 1260°

Let x represent the dimensions of the nonagon's two equal angles. The nonagon's total angles may therefore be represented as follows:

1000° + 5x + 5x + 180° = 1260°

When we simplify the previous equation, we get:

10x = 80°

x = 8°

Each of the nonagon's two equal angles is 8°, and the total of the remaining seven angles is as follows:

1000° - 2x = 1000° - 2(8°) = 984°

984° ÷ 7 = 140.57° (rounded to two decimal places) (rounded to two decimal places)

Hence, the nonagon's last seven angles are all around 140.57 degrees.

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The options which satisfy the given diagram are

m∠5 + m∠6 = 180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

The sum of the interior angles of a triangle is 180°.

The exterior angle of a triangle is equal to the sum of its interior opposite angles.

Let the Triangle be ABC and the exterior angle be ∠D , then

∠A + ∠B + ∠C =  180°

∠A + ∠B = ∠D , ∠A and ∠B are interior opposite angles of the triangle

So, the Options that satisfied

m∠5 + m∠6 = 180° { linear pair}

m∠2 + m∠3 = m∠6 {exterior angle theorem}

m∠2 + m∠3 + m∠5 = 180° {Angle Sum Property}

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The estimated quotient of the given dividend 2 1 / 2 divided by the divisor 1 7/9 is equal to 1.41 ( round off up to the two decimals ).

Divisor = 1 7/9

Convert the divisor (mixed fraction ) into improper fraction,

1 7 /9

= [( 9× 1 ) + 7]/ 9

= 16/9

Dividend = 2 1 / 2

Convert the dividend (mixed fraction ) into improper fraction,

2 1 / 2

=[ ( 2 ×2 ) + 1] /2

= 5 /2

Divide the 5 / 2 by 16 /9 to get the estimated quotient ,

( 5 / 2 ) ÷ ( 16 / 9)

= ( 5 / 2 ) × ( 9 / 16 )

= ( 5 × 9 ) / ( 2 × 16 )

= 45 / 32

= 1.40625

= 1.41 ( round off up to the two decimals )

Therefore, the estimated quotient of the division is equal to 1.41( round off up to the two decimals ).

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Answer: its all 3

Step-by-step explanation: https://socratic.org/questions/is-12-an-integer-rational-or-real-number#:~:text=Reals%3A%20any%20number%20that%20is%20rational%20or%20irrational,be%20found%20on%20the%20number%20line.%20Answer%20link

Answer:

12/36 ÷ 2/2 = 6/18

12/36 ÷ 3/3 = 4/12

12/36 ÷  4/4 = 3/9

All of these equations are equal to one another since they are all being divided by a whole, they are all just being expressed differently.

I hope this helped & Good Luck <3 !!!

Answer:

12/36 ÷ 1 = 0.0333333.......

Step-by-step explanation:

36/12 ÷ 1 =3

12 divided by 36 gives 0.333...... and the result divided by 1 gives the same answer. The same process applies to 36 divided by 12, which gives 3. The result which is three is divided by 1 which gives the same three.

NB: Any number divided by 1 is still the same number. Example: 1200/1 = 1200

Hope it helps.

The value of x is -11

The sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.

represent the other two base angles as z and y

z= 80(opposite angles)

y = 60( opposite angles)

z+y +x+51 = 180

80+60 +x +51 = 180

140+51+x = 180

x+191 = 180

x = 180-191

x = -11

therefore the value of x is -11

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So, the inverse of \(A\) is:
\[A^{-1} = \left[\begin{array}{ccc}
a^{-1}_{11} & a^{-1}_{12} & a^{-1}_{13} \\
a^{-1}_{21} & a^{-1}_{22} & a^{-1}_{23} \\
a^{-1}_{31} & a^{-1}_{32} & a^{-1}_{33} \\
\end{array}\right]\]

This is how we can compute the inverse of a matrix using the row reduction method.

To compute \(A^{-1}\) using the row reduction method, we need to first set up an augmented matrix with \(A\) on the left and the identity matrix on the right. Then, we will use elementary row operations to reduce the left side of the matrix to the identity matrix, which will result in the inverse of \(A\) on the right side. Here are the steps:

1. Set up the augmented matrix:
\[\left[\begin{array}{ccc|ccc}
a_{11} & a_{12} & a_{13} & 1 & 0 & 0 \\
a_{21} & a_{22} & a_{23} & 0 & 1 & 0 \\
a_{31} & a_{32} & a_{33} & 0 & 0 & 1 \\
\end{array}\right]\]

2. Use elementary row operations to reduce the left side of the matrix to the identity matrix. For example, we can use the following operations:
- Multiply the first row by a constant to make the first element 1
- Subtract a multiple of the first row from the second and third rows to make the first element of those rows 0
- Repeat these steps for the second and third columns until the left side of the matrix is the identity matrix

3. Once the left side of the matrix is the identity matrix, the right side of the matrix will be the inverse of \(A\):
\[\left[\begin{array}{ccc|ccc}
1 & 0 & 0 & a^{-1}_{11} & a^{-1}_{12} & a^{-1}_{13} \\
0 & 1 & 0 & a^{-1}_{21} & a^{-1}_{22} & a^{-1}_{23} \\
0 & 0 & 1 & a^{-1}_{31} & a^{-1}_{32} & a^{-1}_{33} \\
\end{array}\right]\]

So, the inverse of \(A\) is:
\[A^{-1} = \left[\begin{array}{ccc}
a^{-1}_{11} & a^{-1}_{12} & a^{-1}_{13} \\
a^{-1}_{21} & a^{-1}_{22} & a^{-1}_{23} \\
a^{-1}_{31} & a^{-1}_{32} & a^{-1}_{33} \\
\end{array}\right]\]

This is how we can compute the inverse of a matrix using the row reduction method.

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To factor a trinomial, you need to find two binomials that, when multiplied together, give you the original trinomial.

The key to finding binomials is to identify the factors of the quadratic term and the constant term, and then use those factors to construct the binomials.

Here's a step-by-step process for factoring a trinomial:

It's important to note that not all trinomials can be factored using this method.

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A dilation with a scale factor of 8:7 creates an image that is eight times larger than the original.

A scale factor is a numerical value which is used to multiply or divide a given measurement. It is used to compare the sizes of two different objects, or to enlarge or reduce the size of an object. The scale factor can be used to calculate the area, perimeter, and volume of an object. For example, if an object is enlarged by a scale factor of 2, its area will increase by a factor of 4. Similarly, if an object is reduced by a scale factor of 0.5, its area will be reduced by a factor of 0.25.

This means that all of the points in the original image are moved away from the center of the dilation by a factor of eight. This creates an image that is eight times wider and seven times taller than the original. This type of dilation is also known as an enlargement. By enlarging the image, it is possible to see more detail and make the image easier to see. Additionally, it may also be possible to see features that were previously too small to be seen.

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Answer:

$456

Step-by-step explanation:

12% = 0.12

3800 x 0.12 = $456

So, the down payment is  $456

The range of the data is 328. The 1st quartile, median and 3rd quartile is 147, 182, and 197, respectively. The IQR is 50. There is only one outlier in the data, which is 439.

i) The range of the data is the difference between the highest and lowest values. In this case, the range is 439 - 111 = 328.

ii) The 1st quartile is the 25th percentile of the data, the median is the 50th percentile, and the 3rd quartile is the 75th percentile. To find these values, we need to first sort the data in ascending order:
111, 131, 147, 151, 151, 182, 190, 197, 201, 209, 439
Then we can find the quartiles:
1st quartile = 147
Median = 182
3rd quartile = 197

iii) The interquartile range (IQR) is the difference between the 3rd and 1st quartiles. In this case, the IQR is 197 - 147 = 50.

v) Outliers are values that are more than 1.5 times the IQR above the 3rd quartile or below the 1st quartile. In this case, the upper bound for outliers is 197 + (1.5 * 50) = 272.5 and the lower bound is 147 - (1.5 * 50) = 71.5. The only value that falls outside of these bounds is 439, so there is one outlier in the data.

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a. The explicit formula for the sequence is: an = a + (n - 1)d

b. There are 56 tiles in the 13th row.

What is arithmetic sequence?

An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k.

a. Let's denote the number of tiles in the first row as a, and the common difference between consecutive rows as d. Then, the number of tiles in the second row would be a + d, the third row would be a + 2d, and so on. Since the second row has 12 tiles and the first row has 8 tiles, we have:

a + d = 12

a = 8

We can solve this system of equations to find the value of d:

a + d = 12

8 + d = 12

d = 4

Therefore, the explicit formula for the sequence is:

an = a + (n - 1)d

where a = 8 and d = 4.

b. To find the number of tiles in the 13th row, we can plug in n = 13 into the formula:

a13 = 8 + (13 - 1)4

a13 = 8 + 48

a13 = 56

Therefore, there are 56 tiles in the 13th row.

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Answer: a. an= 8+4(n-1)

b. a13=60

Step-by-step explanation:

There are 60 tiles in the 13th row.

a13=4(13)+8

52+8

The both triangles are not similar.

Similar triangles are triangles that have the same shape but may have different sizes. Two triangles are considered similar if their corresponding angles are equal, and their corresponding sides are in proportion or have the same ratio.

In other words, if two triangles have the same angles, then they are similar. The ratio of the lengths of the corresponding sides of similar triangles is the same, and this ratio is called the scale factor.

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Answer:

write relation between work and power

The sum of the two vectors is a vector with length 26.56 and an angle of 12.72°.

The vector ü can be represented in Cartesian coordinates as (16cos5°, 16sin5°) and the vector ü can be represented as (11cos25°, 11sin25°).

To find the sum of these two vectors, we add their corresponding coordinates:
(16cos5° + 11cos25°, 16sin5° + 11sin25°)

Using a calculator, we can approximate these values:
(25.82, 5.81)

Therefore, the sum of the two vectors is approximately (25.82, 5.81) in Cartesian coordinates. To find the length and angle of this vector, we can use the Pythagorean theorem and the inverse tangent function:

Length = √(25.82² + 5.81²)

≈ 26.56

Angle = tan⁻¹(5.81/25.82)

≈ 12.72°

So the sum of the two vectors is a vector with length 26.56 and an angle of 12.72°.

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21. tan^2 t/sec t = sec t-cos t
First, we can simplify the left-hand side of the equation by dividing tan^2 t by sec t. Remember that tan t = sin t/cos t and sec t = 1/cos t:
tan^2 t/sec t = (sin^2 t/cos^2 t)/(1/cos t) = sin^2 t/cos t
Now we can subtract cos t from both sides of the equation:
sin^2 t/cos t - cos t = sec t - cos t
Next, we can multiply both sides of the equation by cos t to get rid of the fraction:
sin^2 t - cos^2 t = sec t*cos t - cos^2 t
Finally, we can use the Pythagorean identity sin^2 t + cos^2 t = 1 to simplify the left-hand side of the equation:
1 - cos^2 t - cos^2 t = sec t*cos t - cos^2 t
0 = sec t*cos t - 2*cos^2 t
22. cot^2 t/csc t = csc t-sin t
First, we can simplify the left-hand side of the equation by dividing cot^2 t by csc t. Remember that cot t = cos t/sin t and csc t = 1/sin t:
cot^2 t/csc t = (cos^2 t/sin^2 t)/(1/sin t) = cos^2 t/sin t
Now we can subtract sin t from both sides of the equation:
cos^2 t/sin t - sin t = csc t - sin t
Next, we can multiply both sides of the equation by sin t to get rid of the fraction:
cos^2 t - sin^2 t = csc t*sin t - sin^2 t
Finally, we can use the Pythagorean identity sin^2 t + cos^2 t = 1 to simplify the left-hand side of the equation:
1 - sin^2 t - sin^2 t = csc t*sin t - sin^2 t
0 = csc t*sin t - 2*sin^2 t
24. (1−sin θ)/cos θ = sec θ−tan θ
First, we can simplify the left-hand side of the equation by dividing 1-sin θ by cos θ:
(1−sin θ)/cos θ = (1/cos θ) - (sin θ/cos θ) = sec θ - tan θ
So the equation is already simplified and both sides are equal.
25. (sin t/csc t) + (cos t/sec t) = 1
First, we can simplify the left-hand side of the equation by dividing sin t by csc t and cos t by sec t. Remember that csc t = 1/sin t and sec t = 1/cos t:
(sin t/csc t) + (cos t/sec t) = (sin t/(1/sin t)) + (cos t/(1/cos t)) = sin^2 t + cos^2 t
Now we can use the Pythagorean identity sin^2 t + cos^2 t = 1 to simplify the left-hand side of the equation:
1 = 1
So the equation is already simplified and both sides are equal.

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Claim: The current education system should be reformed to ensure that students of all backgrounds are able to pursue education and reach their full potential.

A claim is a statement made by an individual or organization that seeks to establish a legal right or entitlement to something. It is similar to a demand or request but is used in a legal context.

Points in support of the claim:

1. The current education system is not equitable and fails to provide equal opportunities to all students regardless of their background.

2. Students from low-income families are more likely to attend schools with fewer resources and less rigorous curriculums.

3. These students are often at a disadvantage when it comes to competing for college admissions and other opportunities.

4. Education reform can help to bridge the gap between different socioeconomic backgrounds and ensure that all students have access to quality education.

5. Reforms should focus on providing equal resources and opportunities to all students, regardless of their financial or social backgrounds.

6. This can help to create a more equitable education system, which will benefit all students, regardless of their background.

Conclusion:

Education reform is essential for ensuring that all students, regardless of their background, have access to quality education and the opportunities to reach their full potential. The current education system is not equitable and fails to provide equal opportunities to all students, leaving some at a disadvantage. Therefore, steps must be taken to reform the education system and bridge the gap between different socioeconomic backgrounds. This will help to create a more equitable education system that benefits all students, regardless of their backgrounds.

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The result obtained from the long division of the polynomial is n² + 2n - 1 + 3/(n - 9).

The quotient of the polynomial is obtained by applying long division method as shown below.

        n²   +   2n   -   1

   ________________________

n - 9 √ (n³ - 11n² + 21n - 24)

            (n³ -  9n²)  

       ____________

               -2n² + 21n

               -2n² + 18n

               __________

                       3n - 24

                       3n - 27

                       ______

                            3

Therefore, the quotient is n² + 2n - 1 and the remainder is 3.

n³ - 11n² + 21n - 24 =  (n - 9)(n² + 2n - 1) + 3.

So when we divide the polynomial using long division method we would obtain the following result.

(n³ - 11n² + 21n - 24) ÷ (n - 9) = n² + 2n - 1 + 3/(n - 9)

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Find the quotient of this long division; (n³ - 11n² +21n-24)÷(n-9)

The solution of the system of equation is

1) The solution to the system of equations is x = -7 and y = -2.

2) The solution to the system of equations is x = -7 and y = -2.

3) The solution to the system of equations is any point on the line 2x + 5y = 0

4) The solution to the system of equations is x = -2 and y = 1.

5) The solution to the system of equations is x = 1 and y = -16.

In mathematics, a system of equations refers to a set of two or more equations that must be solved simultaneously. Solving a system of equations involves finding the values of the variables that satisfy all the given equations. In this response, we will go through the process of solving five different systems of equations.

−2x−8y=10 and 2x−6y=18, in order to solve this system of equations, we need to eliminate one of the variables, x or y. One way to do this is to add the two equations together. When we add them, the x term cancels out, leaving us with -14y = 28. Solving for y, we get y = -2. Substituting this value of y into either equation, we get x = -7.

And then the equations, −2x+9y=−4 and 2x+3y=−20, to solve this system of equations, we can use the method of elimination again. If we add the two equations, the x term cancels out, leaving us with 12y = -24. Solving for y, we get y = -2. Substituting this value of y into either equation, we get x = -7.

Then the third one 2x+5y=0 and x + 5y = −10 is in this system of equations, we notice that the second equation is just the first equation with a constant term added. Therefore, these equations are dependent, meaning that they represent the same line. Any point that satisfies one equation will also satisfy the other equation.

And the fourth one has −4x+y=9 and −4x+9y=17, to solve this system of equations, we can use the method of substitution. We can solve the first equation for y, getting y = 4x + 9. Substituting this expression for y into the second equation, we get -4x + 9(4x + 9) = 17. Simplifying, we get 25x + 72 = 17. Solving for x, we get x = -2. Substituting this value of x into the first equation, we get y = 1.

−6x − y = 10 and −16x + 6y = −24,  To solve this system of equations, we can use the method of elimination. If we multiply the first equation by -6 and the second equation by -1, we can add the two equations to eliminate y. Doing so, we get 80x = 80. Solving for x, we get x = 1. Substituting this value of x into either equation, we get y = -16.

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Complete Question:

Solve the system of equations

1) −2x−8y=10 and 2x−6y=18

2) −2x+9y=−4 and 2x+3y=−20

3) 2x+5y=0 and x + 5y = −10

4) −4x+y=9 and −4x+9y=17

5) −6x − y = 10 and −16x + 6y = −24

Using the definition of the tangent function, we will get that:

5√(6)/12 = sin(θ)

Here you need to remember how the tangent function is defined, we know that:

tan(θ) = sin(θ)/cos(θ)

Here we know that:

tan(θ) = √15/3

cos(θ) = √10/4

Replacing that we can write:

√15/3 = sin(θ)*(4/√10)

Solving for the sine, we will get:

(√15/3)*(√10/4) = sin(θ)

(√15*√10)/(3*4) = sin(θ)

(√150)/(12) = sin(θ)

(√(25*6))/(12) = sin(θ)

5√(6)/12 = sin(θ)

That is the answer.

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Answer:

To find the slope of the line passing through (-3, 1) and (2, -3), we can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-3, 1) and (x2, y2) = (2, -3).

slope = (-3 - 1) / (2 - (-3))

= -4 / 5

So, the slope of the line passing through (-3, 1) and (2, -3) is -4/5.

To find the slope of a line parallel to this line, we need to remember that parallel lines have the same slope. Therefore, the slope of the parallel line is also -4/5.

The expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].

What is expression?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are arranged in a particular way. Expressions can represent various mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and can be used to calculate a value or to represent a relationship between quantities.

The given expression is:

[tex]y^6 * y^3[/tex]

We can simplify this expression by adding the exponents of y:

[tex]y^6 * y^3 = y^(6+3) = y^9[/tex]

Therefore, the expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].

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1241 student tickets were sold. Below, you will learn how to solve the problem.

2566 concert tickets were sold for a total of $10,348, and if students paid $3 and nonstudents paid $5, then the number of student tickets sold can be calculated.

To solve this problem, we can set up an equation using the given information.

X + Y = 2566

3X + 5Y = 10348

Find the value of X:

Y = 2566 - X

3X + 5(2566 - X) = 10348

3X + 12830 - 5X = 10348

2X = 12830 - 10348

2X = 2482

X = 1241

Therefore, 1241 student tickets were sold.

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Tracy's expression makes it easier to see how the areas of the rectangles are related i.e. 1/6 bh.

What is a Rectangle?

The opposite sides of a quadrilateral are equal and parallel, and all the angles are equal. Around us, there are several rectangle-shaped items. Two dimensions, the length and breadth, define each rectangle shape. The width and length of a rectangle are its longer and shorter sides, respectively.

Dimensions of top rectangle :

base = b

height = h

So, area = b × h

Dimensions of bottom rectangle :

base = b/3

height = h/2

So, area = b/3 × h/2 = (b × h) 6

Hence, area of bottom rectangle is  1/6th of that top rectangle.

Devin writes the area of the smaller rectangle as the product 1/3 b • 1/2 h. Tracy rewrites this as 1/6 bh.

Hence, Tracy's expression represents more easier way to see how the rectangle's area is related.

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(3, 5): Point A is located at the coordinates (3, 5) on the Cartesian plane, meaning it is 3 units to the right of the origin and 5 units above the origin.

Coordinates are points on a graph used to determine the position of a particular location. Coordinates can be expressed in two-dimensional (2D) or three-dimensional (3D) formats. In 2D, a point is determined by two numbers—its x and y values—which are the distances from the point to the origin along each axis. In 3D, an additional z-value is needed to indicate the distance from the origin along the third axis. Coordinates are used in a variety of applications, including navigation, mapping, surveying, and astronomy.

B. (2, -3): Point B is located at the coordinates (2, -3) on the Cartesian plane, meaning it is 2 units to the right of the origin and 3 units below the origin.

C. (-4, -2): Point C is located at the coordinates (-4, -2) on the Cartesian plane, meaning it is 4 units to the left of the origin and 2 units below the origin.

D. (0, 0): Point D is located at the coordinates (0, 0) on the Cartesian plane, meaning it is at the origin.

E. (-2, 1): Point E is located at the coordinates (-2, 1) on the Cartesian plane, meaning it is 2 units to the left of the origin and 1 unit above the origin.

F. (5, -4): Point F is located at the coordinates (5, -4) on the Cartesian plane, meaning it is 5 units to the right of the origin and 4 units below the origin.

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The factored form of the polynomial is f(x) = (x + 2)(x + 10)(x - 6) .

The given polynomial is f(x) = x4 + x3 + 2x2 - 22x - 60.

To find the zeros of the polynomial, set f(x) = 0 and solve for x. This gives us the following equation:

x4 + x3 + 2x2 - 22x - 60 = 0

The given zero is -2. To factor the polynomial, use the zero(-2) as one factor. To find the other factors, set (x + 2) = 0 and solve for x. This gives us the following equation:

x3 + 2x2 - 22x - 60 = 0

To solve this equation, use the Quadratic Formula. This gives us two factors, (x + 10) = 0 and (x - 6) = 0. Therefore, the factored form of the polynomial is:

f(x) = (x + 2)(x + 10)(x - 6)

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From the given equation the value of r is 8.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

To solve this equation for r, we need to isolate r on one side of the equation. First, we add 14 to both sides of the equation:

4r-14+14 = (9/4)r+14

4r = (9/4)r+14

Then, we subtract (9/4)r from both sides:

4r - (9/4)r = (9/4)r+14 - (9/4)r

(5/4)r = 14

Finally, divide both sides of the equation by (5/4) to isolate r:

r = 14/(5/4) = 8

Therefore, the value of r is 8.

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The fraction of cake left with Bobby is 5/8.

Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.

Given that, Bobby has 3/4 of a cake. He shared 1/8 slice with Morgan.

Slice of cake left = 3/4 -1/8

= 6/8 -1/8

= 5/8

Therefore, the fraction of cake left with Bobby is 5/8.

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Answer:

x = -1

y = -8

Step-by-step explanation:

2x+3y= −26

5x+3y= −29

Time the first equation by -1

-2x - 3y = 26

5x + 3y = -29

3x = -3

x = -1

Now put -1 in for x and solve for y

2(-1) + 3y = - 26

-2 + 3y = -26

3y = -24

y = -8

Let's check

2(-1) + 3(-8) = -26

-2 - 24 = -26

-26 = -26

So, x = -1 and y = -8 is the correct answer.

[tex]2x + 3y = - 26 \\ \implies \: 2x + 3y + 26 = 0[/tex]

[tex]5x + 3y = - 29 \\ \implies \: 5x + 3y + 29 = 0[/tex]

For finding what sort of solution the pair of equations give , we need to check the type of equality between

[tex] \frac{ a_{1}}{ a_{2} \: } , \: \frac{ b_{1} }{ b_{2} } , \: \frac{ c_{1}}{ c_{2} } \\ [/tex]

The following results can be obtained ,

[tex]if \: \: \frac{ a_{1} }{a _{2} } \neq \: \frac{ b_{1}}{ b_{2}} \\ \\ \implies \: we \: obtain \: a \: unique \: solution[/tex]

[tex]if \: \: \frac{ a_{1} }{a _{2} } = \: \frac{ b_{1}}{ b_{2}} \: \neq \: \frac{ c_{1}}{ c_{2}} \\ \\ \implies \:we \: obtain \: no \: solution[/tex]

[tex]if \: \: \frac{ a_{1} }{a _{2} } = \: \frac{ b_{1}}{ b_{2}} \: = \: \frac{ c_{1}}{ c_{2}} \\ \\ \implies \:we \: obtain \: infinitely \: many \: \: solutions[/tex]

Considering the equations provided ,

[tex] a_{1} = 2 \: \: , \: \: b_{1} = 3 \: \: , \: \: c_{1} = 26 \\ a_{2} = 5 \: \: , \: \: b_{2} = 3 \: \: , \: \: c_{2} = 29[/tex]

[tex]\therefore \frac{ a_{1}}{ a_{2} } = \frac{2}{5} \: \: \: , \: \: \: \frac{ b_{1}}{ b_{2} } = \frac{3}{3} = \frac{1}{1} \: \: \: , \: \: \: \frac{ c_{1} }{ c_{2} } = \frac{26}{29} \\ [/tex]

Since ,

[tex] \frac{ a_{1} }{ a_{2}} \neq \: \frac{ b_{1} }{ b_{2}} \\ [/tex]

The system of equations has a unique solution .

On further calculations done by elimination method , the solution of the equations comes out to be

[tex]\boxed{x = - 1} \\ \boxed{y = - 8}[/tex]

let's have a look at how it'll be done now.

the equations given in the question are -

[tex]2x + 3y + 26 = 0 \: ...(1) \\ 5x + 3y + 29 = 0...(2) \\ \\ multiplying \: equation \: (1) \: by \: - 1 \\ \implies \: - 2x - 3 - 26 = 0...(3) \\ \\ solving \: eqs. \: (2) \: and \: (3) \\ \\ 5x + \cancel{3y} + 29 = 0 \\ \underline{ - 2x \cancel{- 3y} - 26 = 0} \\ 3x + 3 = 0 \\ \\ \implies \: 3x = - 3 \\ \implies \: \boxed{x = - 1} [/tex]

substiting the value of x in equation 1

[tex]2( - 1) + 3y + 26 = 0 \\ 3y + 26 - 2 = 0 \\ 3y + 24 = 0 \\ 3y = - 24 \\ \implies \: \boxed{y = - 8}[/tex]

hope helpful! :)