What is the importance of roots of polynomial equation?

Answer:

3x - 5y = - 18

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x - 5y = 10 ( subtract 3x from both sides )

- 5y = - 3x + 10 ( divide through by - 5 )

y = [tex]\frac{3}{5}[/tex] x - 2 ← in slope- intercept form

with slope m = [tex]\frac{3}{5}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{3}{5}[/tex] x + c ← is the partial equation of the parallel line

to find c substitute (- 1, 3 ) into the partial equation

3 = - [tex]\frac{3}{5}[/tex] + c ⇒ c = 3 + [tex]\frac{3}{5}[/tex] = [tex]\frac{18}{5}[/tex]

y = [tex]\frac{3}{5}[/tex] x + [tex]\frac{18}{5}[/tex] ← equation of parallel line in slope- intercept form

multiply through by 5 to clear the fractions

5y = 3x + 18 ( subtract 5y from both sides )

0 = 3x - 5y + 18 ( subtract 18 from both sides )

- 18 = 3x - 5y , that is

3x - 5y = - 18 ← in standard form

Therefore , the solution of the given problem of triangle comes out to be  angle is 58°  is third angle.

Since a triangle has four or even more sections, it is a polygon. It has an easy geometric form. Triangle ABC refers to a square with edges A, B, and C. A single plane or square are produced by Euclidean geometry when the edges are not collinear. A triangle is a polygon if it has three sides & three corners. Where a triangle's three sides come together are known as the corners. A triangle's angles add up to 180 degrees.

Here,

Given :

A triangle has given angles ,

To find the angle :

=> x + 98° + 24° = 180°

=> x = 180° - 122°

=> x = 58°

Thus , angle is 58° .

Therefore , the solution of the given problem of triangle comes out to be  angle is 58°  is third angle.

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The correct answer is B.

The two types of longitude are the Prime Meridian and the International Date Line.

The Prime Meridian is the imaginary line of 0° longitude that divides the earth into the Eastern and Western hemispheres. It passes through Greenwich, England and is the reference point for all other longitudes on the Earth’s surface.

The International Date Line is an imaginary line located on the opposite side of the Earth from the Prime Meridian at 180° longitude. It is the reference point from which we measure the date change when traveling from one side of the world to the other.

The calculation for longitude is fairly simple. Longitude is measured in degrees, with a full circle being 360°. Each degree can be divided into 60 minutes and each minute into 60 seconds. To calculate the longitude, the degree and minutes are added together and converted into decimal form. For example, if a point has a longitude of 15° 22’ 30”, the calculation would be 15 + (22/60) + (30/3600) = 15.375°.

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Answer:

23.9

Step-by-step explanation:

Cartesian equation for x=t2,y=2+3t, x=Ay2+By+C, Where

A=1, B=0, and C=0

To eliminate the parameter t and find a Cartesian equation for the given equation, we need to solve for t in terms of x and substitute it into the equation for y.

We start by solving for t in terms of x:

t = √x

Now, we substitute this into the equation for y:

y = 2 + 3√x

Therefore, the equation for x and y becomes:

x = x

y = 2 + 3√x

Which can be represented as a Cartesian equation:

Ay2 + By + C = 0

where A=1, B=0, and C=0.

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Therefore , the leading term 1 and constant 0 in the above function make it a polynomial function.

A polynomial function can be defined in an equation that uses only real number exponents or non-negative integer powers of a variable. Examples of such equations include cubic and quadratic equations. The exponent of the polynomial 2x+5 is 1, for instance.

Here,

For the following polynomial function, exponents all positive integers in this case.

Exponent 1 applies to the positive number 2x.

, 1 where is an integer with positive exponent and and.

Among the coefficients of the function are real values like 5 and 1.

Thus, a polynomial characterizes the function.

It is a polynomials with a degree of five.

When writing a polynomial in standard form, the word with the largest exponent is used as the starting point, and the other terms are written in order of importance of expressions with lesser exponents.

The polynomial is expressed in standard form as f(x)=2x+1.

containing the leading word 1, the constant 0, and

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Therefore , the magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.

An ordered combination of numbers “ a ” and “ b that is stated as just a / b, where b not greater than zero, is referred to as a ratio. A ratio is the result of equating two ratios. If there were one boy and three girls, the ratio could be shown as 1:3.   1/4 are boys, and 3/4 are girls. A part is a number, a proportion of size, or a difference among two or more things.

Here,

Since: Marco To avoid your batter and bakery items acquiring a purple-blue tinge, wash freeze blueberries multiple times in water it until water becomes lighter in color.

The magic muffin ratio is 2:2:1:1, which equals 1-two cups and 2,8 cups.

With a paper towel, dry them off, and then delicately fold it into the batter. Maintaining the lightness of rapid breads is the aim of this process.

The magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.

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The graph on the bottom left represents the polynomial function

y =  -x⁴ + 6x³ + 11x² - 60x - 100.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

Given:

An equation,

y =  -x⁴ + 6x³ + 11x² - 60x - 100.

And one of the factors of the equation is (x-5).

That means, x = 5 is one of the roots of the equation.

From the given graphs,

we can eliminate top left graph and bottom right graph.

Because, the graphs of the equation do not touch the x-axis at x = 5.

Let x = -2,

Then,

y = -(-2)⁴ + 6(-2)³ + 11(-2)² - 60(-2) - 100.

y = -16 -48 + 44 + 120 - 100

y = 0

That means,

x = -2 is one of the roots of the equation.

And the graph is given in the attached image.

And the graph is the bottom left graph.

Therefore, the graph in the bottom left is the required graph.

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The value of x is 0.

The value of y is 2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

2y = 6x + 4 _____(1)

y = -2x + 2 ______(2)

Substituting (2) in (1).

2 (-2x + 2) = 6x + 4

-4x + 4 = 6x + 4

4 - 4 = 6x + 4x

10x = 0

x = 0

Now,

x = 0 in (2)

y = -2 x 0 + 2

y = 0 + 2

y = 2

Thus,

The value of x and y is 0 and 2.

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The solution of the expression 17n + 8 = 104 + 5n for the variable n is given as follows:

n = 8.

The expression for this problem is defined as follows:

17n + 8 = 104 + 5n

Combining the like terms, the expression is given as follows:

17n - 5n = 104 - 8.

12n = 96.

The inverse operation of the multiplication is the division, hence the value of n is obtained as follows:

n = 96/12

n = 8.

Which is the solution of the expression for the variable n.

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Given that the hypotenuse of the right triangle is as given then;

i. α = 56^o

ii. Adjacent = 2.80

iii. Opposite = 4.15

A right triangle is a type of triangle which has only one of its internal angles equal to 90^o. Thus the hypotenuse is opposite to the greatest angle, while the second long side is opposite to the greater angle, and the shortest side opposite to the measure of the least angle.

Applying the Pythagorean theorem to the triangle, we have;

i. The sum of angles in a triangle is 180^o. So that;

α + 34 + 90 = 180

α + 124 = 180

α = 56^o

ii. Let the length of the opposite side be represented by y;

   Sin θ = opposite/ hypotenuse

   Sin 34 = y/ 5

y = 5 * Sin 34

 = 2.796

The length of its opposite side is 2.80.

iii. Let the length of the adjacent side be represented by x;

Cos θ = adjacent/ hypotenuse

Cos 34 = x/ hypotenuse

            = x/ 5

x = 5 * Cos 34

  = 4.145

The length of its adjacent side is 4.15.

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Answer:

80 boxes of cookies

Step-by-step explanation:

First, we have to find 1% by taking

32 divided by 40 = 0.8

Then we take it times 100%

0.8 x 100 = 80 boxes of cookies

Jean want to sell 80 boxes of cookies

The fraction  12/3+3/4÷(−1/3)−1/2is evaluated to give -114/10

A fraction can be defined as part of a whole element, variable or number

The several  types of fractions in mathematics are;

From the information, we have that;

12/3+3/4÷(−1/3)−1/2

The fraction given is a mixture of proper fractions and improper fractions

Expand the bracket, we get;

12/3 + 3/4 ÷ -1/3 -1/2

Find the lowest common denominator

48 + 9 /12 ÷ -2 - 3 /6

Add the numerators

57/12  ÷ -5/6

Take the inverse of the divisor and multiply

57/12 × 6/-5

-114/10

Hence, the value evaluated from the fraction is -114/10

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Answer: 50 ft

Step-by-step Explanation:

First, subtract the given length from the perimeter:

*268 - (84 x 2) = 100

Then divide this by 2:

100 / 2 = 50

*We multiply the 84 by 2 since the court is assumed to have 4 sides meaning there are two sides with lengths and two sides with widths.

A triangle's exterior angle is the product of its interior opposing angles.

Exterior angles are those that run parallel to a polygon's exterior angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle.

At each vertex, there are two equivalent exterior angles.

Each vertex often only shows one external angle, though.

A triangle's exterior angles have these three essential qualities:

(1) A triangle's corresponding and exterior angles pair together to form a linear pair of angles. The inner and exterior angles therefore total up to 180 degrees.

(2) The size of a triangle's external angle is equal to the sum of its two diametrically opposed internal angles. The exterior angle theorem is another name for this property.

(3) A triangle's outside angles add up to a total of 360.

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Therefore , the solution of the given problem of table comes out to be we can create a table in form by following below steps.

A mathematical list is a list of numbers that represents the results of a calculation with several inputs. organized in rows and columns, data consists of numbers and descriptions. It is simple to recall the table and the 10 pattern. 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 are the numerals in numerical order. Value mapping are used to illustrate the connections between various data elements.

Here,

Import the layout table by moving the pointer to the desired location on the form template.

Click Insert, followed by Layout Table, in the Tables toolbar.

The number of rows and rows to be included in the table should be entered with in Insert Table dialog box.

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Answer:

x = -175

Step-by-step explanation:

Given:

⇒ [tex]-\frac{x}{7}-8=17[/tex]

Solution:

Work:

[tex]-\frac{x}{7}-8=17[/tex]

[tex]-\frac{x}{7}-8+8=17+8[/tex]    ⇒ Add 8 to both sides

[tex]-\frac{x}{7}=25[/tex]

[tex]7\left(-\frac{x}{7}\right)=25\cdot \:7[/tex] ⇒ Multiply both sides by 7

-x = 175

[tex]\frac{-x}{-1}=\frac{175}{-1}[/tex] ⇒ Divide both sides by -1

x = -175

Check:

Since, x = -175. We can substitute into the equation to check.

[tex]-\frac{-175}{7}-8=17[/tex]

[tex]-\frac{-175}{7}=25[/tex]

[tex]25-8=17[/tex] ⇒ Statement = True (25 minus 8 is 17.

Hence, x = -175

Lenvy~

Answer:

Step-by-step explanation:

The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80… and so on.

Answer: 3

Step-by-step explanation:

Answer:

The perimeter of a rectangle is the total distance around the outside of the rectangle. To find the perimeter of a rectangle, you add the lengths of all four sides.

In this case, the width of the rectangle is 15 cm and the length is 25 cm. To find the perimeter, we add the lengths of all four sides, which are:

15 cm + 15 cm + 25 cm + 25 cm = 75 cm

Therefore, the perimeter of the rectangle is 75 cm. The answer is B. 75 cm.

Step-by-step explanation:

Answer:

-14[tex]k^{2}[/tex] + 5k -6

Step-by-step explanation:

(-8[tex]k^{2}[/tex] -6) - (6[tex]k^{2}[/tex] - 5k)  Distribute the negative sign

-8[tex]k^{2}[/tex] - 6 -6[tex]k^{2}[/tex] + 5k   Combine like terms

-14[tex]k^{2}[/tex] + 5k -6

Answer: -14k^2+15k-6

Step-by-step explanation:

(-8k^2-6)-(6k^2-5k)

-8k^2-6-6k^2+5k

-14k^2-6+5k

-14k^2+15k-6

Answer:

x = 1, x = 5

Step-by-step explanation:

|x−7|=|2x−8|  ==> there are 2 ways to simplify this equation:

1. x - 7 = 2x - 8

2. -(x - 7) = 2x - 8

Let's first solve equation 1:

x - 7 = 2x - 8

-7 = x - 8  ==> subtract x on both sides

x - 8 + 8 = -7 + 8  ==> add 8 on both sides

x = 1  ==> simplify

Now let's solve equation 2:

-(x - 7) = 2x - 8

-x - (-7) = 2x - 8  ==> distribute the negative sign to x and -7

-x + 7 = 2x - 8  ==> subtracting a negative number is equivalent to adding a

                               positive number

7 = 3x - 8  ==> add x on both sides

15 = 3x ==> add 8 on both sides

x = 5 ==> divide 3 on both sides

Hence, the answers are x = 1 and x = 5.

This refers to objects that can be divided into two identical halves. The line that divides the object into its identical halves is known as the line of symmetry.

Line of symmetry is of three types: vertical symmetry, horizontal symmetry, and diagonal symmetry.

Irregular shapes have no equal sides. Thus, they can not be split into two identical halves.

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The variable for the number of wraps and the number of gift bags are x and y.

A linear function can be used to depict a straight line on the coordinate plane. The equation y = 3x - 2 serves as an illustration of a linear function since it represents a straight line in the coordinate plane.

Nonlinear functions are those whose graphs do not follow a straight line. A graph of it can be any curve other than a straight line.

A quadratic function is an illustration of a non-linear function.

Let, The number of wraps be 'x' and the number of gift bags be 'y'.

Therefore, From the given information x + y = 25 and 6x + 2y = 110.

Solving this linear system graphically we have an intersection (x, y)

at (15, 10).

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If the Set A is denoted by the set of elements  {1,2,3}  , then the number of ordered pairs that it can have is 9  .

The Ordered Pair is defined as a pair formed by two elements which are separated by comma and written inside the parentheses .

For Example : the (x,y) represents a ordered pair .

The Ordered Pairs can be obtained by developing a function or by performing the operation which is called as Cartesian product.

The set A is given as : {1,2,3} ;

the ordered pair can be written as : [tex](1,1) , (2,2), (3,3) , (1,2) , (1,3) , (2,1) , (2,3) , (3,1) , (3,2) .[/tex]

Therefore , The number of ordered pairs formed of Set A are 9 .

The given question is incomplete , the complete question is

How many ordered pairs can be formed from the set A = {1,2,3} ?

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If the function g(t) is -4t + 5 then  (g o g)(t) will be 16t - 15.

Here given function,

g(t) = -4t + 5

We have to find (g o g) (t)

(g o g)(t) = g(g(t))

= g(-4t + 5)

= -4(-4t + 5)+ 5

= 16t -20 +5

= 16t - 15

Therefore the function (g o g)(t) is 16t - 15.

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The box will start at 72 and end at 86. At 78.5, a vertical line will be drawn through the box. Arrows will appear at both ends of the box. The one on the left will come to a halt at 65 miles per hour, while the one on the right will come to a halt at 98 miles per hour.

A box plot, often known as a boxplot, is a method in descriptive statistics for graphically displaying the localization, spread, and skewness groups of numerical data through their quartiles. A box plot is a graphical representation of statistical data that uses the lowest, first quartile, median, third quartile, and maximum values. The name "box plot" refers to how the graph resembles a rectangle with lines extending from the top and bottom. Box and whisker plots, often known as box plots, are an excellent graphic for displaying the distribution of data points over a specified metric. These graphs show ranges within variables that have been measured. Outliers, the median, the mean, and where the majority of the data points fall inside the "box" are all included.

Here,

65, 66, 72, 76, 78, 79, 85, 86, 90, 98

Q1 = 72

(78 + 79) / 2 = 78.5 Q2 (median)

Q3 = 86

min = 65

max = 98

So the box plot will look like this:

The box will begin at 72 and conclude at 86. At 78.5, a line will be drawn vertically through the box. Arrows will emerge from both ends of the box. The one on the left will come to a stop at 65, while the one on the right will come to a rest at 98.

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The five steps to solving inequalities are:

To solve an inequality, one must isolate the inequality symbol, simplify the inequality, graph the inequality on a number line, make a sign analysis of the inequality, and find the solution set of the inequality.

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