Find the distance between point k and point L.

The solutions of the quadratic equation 3x² − x + 8 = 0 are as follows;

x = 0.1667 + 1.6245i

x = 0.1667 - 1.6245i

In Mathematics, the standard form of a quadratic equation is given by this mathematical expression;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

From the information provided above, we can logically deduce the following data values (parameters);

3x² − x + 8 = 0

Where:

Substituting the data values (parameters) into the quadratic formula, we have the following;

[tex]x = \frac{-(-1)\; \pm \;\sqrt{(-1)^2 - 4(3)(8)}}{2(3)}\\\\x = \frac{1\; \pm \;\sqrt{1\; - \;4(3)(8)}}{2(3)}\\\\x = \frac{1\; \pm \;\sqrt{1\; - \;96}}{6}[/tex]

x = (1 ± √95)/6

x = (1 + √95)/6 = 0.1667 + 1.6245i

or

x = (1 - √71)/6 = 0.1667 - 1.6245i

In conclusion, i represents a complex number.

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Complete Question:

Find the solutions of the quadratic equation 3x² − x + 8 = 0.

So, by fraction, number of times he will have to fill the smaller measuring cup to equal 1 3/4 cups is 7 times.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Glass holds = 1(3/4) cups of water

One cup holds = 1/4 cup of water

number of 1/4 cups needed to fill the 1(3/4) cups of water glass.

[tex]\frac{1}{4xC}=1(\frac{3}{4})\\\\\frac{C}{4} = \frac{7}{4} \\\\C=\frac{7}{4x4}\\ \\C= 4[/tex]

number of times the smaller cup fills the glass is 7.

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Complete Question: Quentin is filling a glass that holds 1 3/4 cups of water. he is using 1/4 cup measuring cup. how many times will he have to fill the smaller measuring cup to equal 1 3/4 cups?

Answer:The answer to your question is 9

The sum of 8.8 and 5.5 is 14.3

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

To find the sum of 8.8 and 5.5 without using pen and pencil:

First, we break the term in simple manner.

8.8 = 8 + 0.3 + 0.5

And 5.5 = 5 + 0.5

And now adding the terms one by one,

0.5 + 0.5 = 1.0

0.3 = 0.3

8 + 5 = 13

Addition,

13 + 1 + 0.3 = 14.3

Therefore, the value is 14.3

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The correct choice will be 74 - 90m

the x & y angles are alternate angles.

The alternate exterior angle theorem states that if two lines are parallel and are intersected by a transversal, then the alternate exterior angles are considered as congruent angles or angles of equal measure.

Here, we have,

from the given figure , we get,

the x & y angles are alternate angles.

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In class 7, adjacent angles are defined as two angles that share a common vertex and a common side but do not have any common interior points. They are angles that are next to each other.

Adjacent angles are often used in geometry to describe the angles formed by intersecting lines or figures. The adjacent angles can be classified into two types, namely:

Interior adjacent angles: They are formed by two lines that intersect inside a closed figure, such as in a parallelogram.

Exterior adjacent angles: They are formed by two lines that intersect outside a closed figure, such as in a straight line.

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5 is not an algebraic expression.

Since it is obvious that 5 is a constant, even if constants constitute a component of the algebraic equation, they do not finish it. A variable and an operator are also necessary for an expression to qualify as an algebraic expression. Any unknown term, such as x, y, or z, can be a variable, and the operators + and - can be used. Terms with no associated variables are known as constants. A variable and an operator are also necessary for an expression to qualify as an algebraic expression.

It follows that 5 cannot be an algebraic expression.

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The value of x using Pythagorean theorem is 14.05 units

An equation shows how two or more numbers and variables are related to each other.

Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:

hypotenuse² = adjacent² + opposite²

In the diagram, using Pythagoras theorem:

22² = (x + 1)² + (x + 2)²

484 = x² + 2x + 1 + (x² + 4x + 4)

2x² + 6x + 5 = 484

2x² + 6x - 479 = 0

x = 14.05

The value of x is 14.05 units

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The distance between the girl and her bike is 25.00 ft.

Distance is the measure of how far apart two objects, places, or points are. It can be measured in a variety of units, such as miles, kilometers, inches, centimeters, or other units.

The distance between the girl and her bike can be found using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.

In this case, the girl is 20 ft. east of the school and 21 ft. south of the school. Therefore, the two sides of the triangle are 20 ft. and 21 ft. and the hypotenuse is the distance between the girl and her bike.

Using the Pythagorean Theorem, the hypotenuse is equal to the square root of (20^2 + 21^2) = 25.00 ft.

Therefore, the distance between the girl and her bike is 25.00 ft.

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The polynomial 5x³ 4x² 7x has three terms, with the highest degree being 3, which makes the degree of the polynomial 3. The polynomial can be written as 5x³ + 4x² + 7x.

1. Identify the polynomial: 5x³ + 4x² + 7x

2. Count the number of terms: 3

3. Find the highest degree (the largest exponent): 3

4. The degree of the polynomial is 3.

The degree of a polynomial is the highest degree of its terms. A polynomial is a mathematical expression consisting of one or more terms with coefficients and exponents. In this case, the polynomial is 5x³ + 4x² + 7x. This polynomial has three terms, and the highest degree is 3, which makes the degree of the polynomial 3. This means that the largest exponent of the terms is 3. To calculate the degree of a polynomial, simply count the number of terms and identify the highest degree, which is the largest exponent. If the polynomial has only one term, then the degree is the exponent of that term

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Using long division convert 1/4 to a decimal

To convert a fraction into a decimal, we'll just divide the numerator by the denominator:

4√1

we'll divide 1 by 4.

1 divided by 4 equals 0

0

4√1

To keep dividing, we'll add a decimal point and a zero after the 1, we'll also add a decimal point after the 0 on top

0.

4√1.0

Now we can divide 10 by 4, 10 divided by 4 equals 2.

0.2

4√1.0

Now we'll multiply 4 by 2, 4 times 2 equals 8. So we'll subtract 8 from 10.

0.2

4√1.0

-8

______

2

Since 2 is greater than 0, we're not finished dividing yet. We'll add another 0 after the decimal point and bring it down.

0.2

4√1.00

-8

________

20

20 divided by 4 equals 5.

0.25

4√1.00

-8

______

20

Now we'll multiply. 4 times 5 equals 20. When we subtract 20 from 20, we get 0. The 0 means we're done dividing.

0.25

4√1.00

-8

______

20

20

________

0

So 1/4 is equal to 0.25.

The system of equations y = 3x - 7 and 6x - 2y = 12 has no solution. That is the lines of the equation is parallel.

To solve a system of equations, you can use substitution or elimination.

One method to find the solution for this system of equations is substitution. To use this method, you can solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation.

Solving for y in the first equation:

y = 3x - 7

Then substitute the result in the second equation:

6x - 2(3x - 7) = 12

6x - 6x + 14 = 12

14 = 12

That clearly is not true and this system of equations has no solution.

--The question is incomplete, answering to the question below--

"What is the solution to the system y = 3x - 7 and 6x - 2y = 12?

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Step-by-step explanation:

please see the attachment

An equation to find the discount price, y dollars, of the pendant is y=2d.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The original price of the pendant was $200.

Let d represent the percent discount, written as a decimal.

The discount price, y dollars, of the pendant.

y=d% of 200

y=d/100 ×200

y=2d

Therefore, an equation to find the discount price, y dollars, of the pendant is y=2d.

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The range of possible perimeters of the square=10.583

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

A rectangle has a perimeter of 16 centimeters.

The lengths of the sides of the rectangle are between 1 centimeter and 7 centimeters.

let, x represents the length of a side of the rectangle,

then the rectangle's area is represented by x(8-x) square centimeters.

i.e. area of square = 8x-x^2

the side = √x(8-x)

perimeter= 4×√x(8-x)

Hence, the range of possible perimeters of the square=10.583

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The given algebraic equation can be written in many ways as shown.

The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.

Solution:-

-5x-15+25x-30

it can be written as

-5(x+3-5x+6)

20x-45

5(4x-9)

and also

-5(9-4x)

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Find the equation that is equivalent to [tex]-5x-15+25x-30[/tex].

First, complete arithmetic operations on linear equations [tex]-5x-15+25x-30[/tex]

*Remember : how to complete arithmetic operations on linear equations, grouping terms with the same variable and then adding them up

[tex]-5x-15+25x-30 = -5x+25x-15-30=20x-45[/tex]

Then, find the common factors of [tex]20x[/tex] and [tex]-45[/tex].

Both have the same factor is [tex]-5[/tex].

Use the distributive property to find the equation that is equivalent.

[tex]20x-45=-5(\frac{20x}{-5}-\frac{45}{-5} )=-5(-4x-(-9))=-5(-4x+9)[/tex]

So, [tex]-5x-15+25x-30[/tex] equivalent to [tex]-5(-4x+9)[/tex]

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Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.

A linear equation is one that satisfies the algebraic formula y=mx+b. m is the y-intercept, while B is the slope. The foregoing sentence is sometimes referred to as a "linear equation with two variables" because y and x are variables. Bivariate linear equations are two-variable linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. An equation is said to be linear if its formula is y=mx+b, where m denotes the slope and b the y-intercept.

Here,

Given : (X-5)-1

Thus,

after substituting the value of x with 9

We get,

=> (X-5) -1

=>(9-5)-1

=> 4 -1

=> 3

Therefore , the solution of the problem of linear equation comes out to be the value after substituting is 3.

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The required function that gives [tex]f(g(x))[/tex] that represents the total amount of money Raul earned is

                [tex]f(g(x)) = 10x^{3}+16[/tex]

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Mostly functions are written as f(x) where x is the input of the function.

Given,

[tex]f(x) = 2x^{2}+16[/tex]

[tex]g(x)[/tex] = [tex]\sqrt{5x^{3} }[/tex]

If [tex]f(x)[/tex] represents amount of money Raul earns per ticket and [tex]g(x)[/tex] represents number of tickets Raul sells per hour, where x is the number of hours he works, then,

[tex]f(g(x))[/tex] represents the total amount of money Raul earned in a day.

To find [tex]f(g(x))[/tex], substitute value of [tex]g(x)[/tex] in the place of x in function [tex]f(x)[/tex] .

[tex]f(g(x))[/tex] = [tex]f[/tex]([tex]\sqrt{5x^{3} }[/tex])

          = 2(    [tex]\sqrt{5x^{3} }[/tex])² +16

          = 10x³ + 16

Therefore the required function is [tex]f(g(x)) = 10x^{3}+16[/tex].

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There is a relationship between the numbers of strawberries gathered and the amount of rainfall that can be found in a model (function).

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.1 is valid based on the provided scatter plot.

Part B:

The independent variable (the explanatory variable) is the cause of the dependent variable in a causal connection.

As a result, you need to identify a plausible factor that can influence the number of strawberries collected.

The week before harvest, I could picture how much it would rain.

Hence, There is a relationship between the number of strawberries gathered and the amount of rainfall that can be found in a model (function).

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There are three solutions to the congruence x+13=55 (mod 34).

Two figures are considered to be 'congruent' if they can be put exactly over each other. When you set one slice of bread on top of the other, you'll see that they're both the same shape and size. The phrase "congruent" refers to having exactly the same form and dimension. When two things or forms superimpose on each other, they are said to be congruent. Their shapes and sizes are identical. Line segments with the same length and angles of the same measure are congruent in the case of geometric forms.

Here,

something equaling 55 (mod 34) is unusual to say the least as 55 mod 34 = 21

do you mean x+13=21 (mod 34) ?

clearly x = 8 + 34k which gives 8, 42, 76 begin less than 100

The congruence x+13=55 (mod 34) has three solutions.

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Answer:Yes

?=6



Step-by-step explanation:

they sare the same angle 55 and angle

Answer:

Triangle ABC is similar to triangle CDE

?=8

Step-by-step explanation:

We can set up a proportion: x/12=8/12. We can use cross multiplication to get 12x=96 which would x=8.

The triangles are similar since both of them have 55 degrees as one of the angle measures.

The percentage of increase in the number of points is 16 %

What Does Percent Mean?

A ratio or figure stated as a fraction of 100 is called a percentage. The percent marker is frequently used to indicate it,%

given the data,

The basketball team's total point total was 75.

The basketball team's enhanced point total was 87.

The difference between the basketball team's total points scored and its increased points are the increase in points.

The increase in points = 87 - 75

                                     = 12 points

So, the percentage increase in points = ( increase in points/number of points scored by the basketball team ) x 100

The percentage increase in points = ( 12 / 75 ) x 100

                                                         = 0.16 x 100

                                                         = 16 %

Therefore, the percentage increase is 16 %

Hence, the percentage of increase in the number of points is 16 %

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Therefore , the solution to the given problem of inequality comes out to be Part a:where x is the no of apples and y is the no of grapes , Part b:Inequality sign and Part c:  ordered pair (3, −4) isn't solution.

An unbalanced connection between two expressions or values is referred to in mathematics as an inequality. So, inequity results from imbalance. In mathematics, an inequality defines the connection between two non-equal quantities. Egality and inequality do not mean the same thing. Use the not equal sign whenever two values are not equal (). It is possible to compare values of any size using a variety of inequalities. By changing both sides until only the variables are left, it is possible to solve many straightforward inequality problems.

Here,

Given :  3x + 4y ≤ 20.

where x is the no of apples

and y is the no of grapes

Thus,

Part a:

where x is the no of apples

and y is the no of grapes

Part b:

Inequality signs means that 20 will be the maximum amount of the no of apples and no of grapes summation.

Part c: ordered pair (3, −4)

Thus,

putting in the inequality we find:

=> 3(-3)+ 4(-4)

=> -6 -16

=> -22

Thus , it is not a solution for inequality.

Therefore , the solution to the given problem of inequality comes out to be Part a:where x is the no of apples and y is the no of grapes , Part b:Inequality sign and Part c:  ordered pair (3, −4) isn't solution.

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The equation is (5 x 2) - (5 + 5) = 20

The given equation can be solved by performing the operations within the parentheses first.

First, 5 x 2 = 10, then 5 + 5 = 10.

Then, the next step is to subtract the second set of parentheses from the first set, 10 - 10 = 0.

Finally, we can see that 0 + 20 = 20.

In this equation, the operation of multiplication and addition are used and the final value is 20.

The equation is (5 x 2) - (5 + 5) = 20

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Complete Question is -

solve the following mathematical operation that involves parentheses, five numbers, two different operations and has a value of 20?

Answer:

Selecting ball number 25 has no chance of happening.

Probability is only the likelihood that something will occur. When we don't know how something will turn out, we might discuss the likelihood of various outcomes or the potential of one. Statistics is the scientific study of events that conform to a probability distribution.

It is predicated on the likelihood that something will take place. The rationale for probability serves as the theoretical probability's essential tenet. A coin has a 12% chance of landing on its head, for instance, when it is flipped.

Probability is a statistic that is used to indicate the likelihood or potential for an event to occur. Both fractions from 0 to 1 and percentages from 0% to 100% can be used to indicate probabilities.

In 25th Ball it is 0

Because there is no 25th ball

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The equivalent values to the given expressions are -

2/3 and 3/7 respectively.

Given are two expressions as -

1/3 + 1/3

5/7 - 2/7

The given expression are -

1/3 + 1/3

(1 + 1)/3

2/3

5/7 - 2/7

(5 - 2)/7

3/7

Therefore, the equivalent values to the given expressions are -

2/3 and 3/7 respectively.

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Answer: 17

Step-by-step explanation:

Answer:

x = 17°

Step-by-step explanation:

The given angles are,

→ 6x + 8

→ 4x + 2

Now we have to,

→ find the required value of x.

Forming the equation,

→ (6x + 8) + (4x + 2) = 180°

{As two angles in a straight line is 180°}

Then the value of x will be,

→ (6x + 8) + (4x + 2) = 180°

→ 6x + 4x + 8 + 2 = 180°

→ 10x + 10 = 180°

→ 10x = 180° - 10

→ x = 170/10

→ [ x = 17° ]

Hence, the value of x is 17°.