Find the distance between the pair of points.
(3, 3) and (3,-4)

One of the factor of the given polynomial 6x^4 - 21x^3 - 4x^2 + 24x - 35 is (2x-7).

According to Rational Root Theorem,

Leading coefficient = 6

Trailing constant = 35

Factors of leading coefficient = 1, 2, 3, 6

Factors of trailing constant = 1, 5, 7, 35

Check for the rational roots

Let P = 7, Q = 2, then

P/Q = 3.5

F(P/Q) = 0

Apply Factor theorem which means the given polynomial must be divisible by P/Q, that is (2x-7)

Divide the polynomial into two groups

Group 1  6x^4 - 21x^3

Take 3x^3 common, we get

3x^3(2x - 7)

Group 2  - 4x^2 + 24x - 35

When we divide it by (2x - 7) we get (-2x + 5)

⇒ - 4x^2 + 24x - 35 = (-2x + 5)(2x - 7)

⇒ 6x^4 - 21x^3 - 4x^2 + 24x - 35 = (2x - 7)(3x^3 - 2x + 5)

Hence the correct option is A.

-- The given question is incomplete, the complete question is

"Which is a factor of the polynomial f(x) = 6x^4 - 21x^3 - 4x^2 + 24x - 35? A) 2x - 7 B) 2x + 7 C) 3x - 7 D) 3x + 7" --

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Answer:

m∠DFE = 69°

Step-by-step explanation:

The tangent of a circle is always perpendicular to the radius.

Therefore, as ABC is the tangent to the circle, and OB is the radius of the circle:

⇒ m∠CBO = 90°

Interior angles of a triangle sum to 180°.  Therefore:

⇒ m∠COB + m∠CBO + m∠BCO = 180°

⇒ m∠COB = 180° - m∠CBO - m∠BCO

⇒ m∠COB = 180° - 90° - 48°

⇒ m∠COB = 42°

Angles on a straight line sum to 180°.  Therefore:

⇒ m∠DOE + m∠COB = 180°

⇒ m∠DOE = 180° - m∠COB

⇒ m∠DOE = 180° - 42°

⇒ m∠DOE = 138°

The angle at the center is twice the angle at the circumference.

Therefore:

⇒ m∠DOE = 2 × m∠DFE

⇒ m∠DFE = m∠DOE ÷ 2

⇒ m∠DFE = 138° ÷ 2

⇒ m∠DFE = 69°

Answer:

Slope: - 1/9

Equation: [tex]y=-\frac{1}{9}x +8\frac{1}{9}[/tex]

Step-by-step explanation:

[tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]

[tex]\frac{8-7}{1-10}[/tex]

[tex]\frac{1}{-9}[/tex]

[tex]y=-\frac{1}{9}x +b[/tex]

[tex]8=-\frac{1}{9}(1) +b[/tex]

[tex]8=-\frac{1}{9}+b[/tex]

[tex]b=8\frac{1}{9}[/tex]

[tex]y=-\frac{1}{9}x +8\frac{1}{9}[/tex]

Answer:

The digit 5 in the number 357 is in the tens so it represents 50 whereas the digit in the number 465 is in the ones/units so it represents 5.

The probability that the upward face shows a number that is a multiple of 3 is p = 1/3 .

Given :

When a dodecahedral die is rolled the possible outcomes are:

s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }

The total numbers of possible outcomes is 12.

The numbers of outcomes whose upward face is multiple of 3 .

= { 3 , 6 , 9 , 12 }

so Number of favorable outcomes = 4

What is probability ?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Probability = number of favorable outcomes / number of possible outcomes

= 4 / 12

= 1 / 3

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By referring to the table that summarizes service times of dinners at a fast food restaurant, we can see that there are 49 individuals who are included in the summary.

We may calculate the total number of people by simply adding the frequencies:

9 + 20 + 13 + 4 + 3 = 49 people

A measure of an event's frequency is how often it occurs within a specific time frame. For clarity, it is sometimes referred to as temporal frequency and is distinct from angular frequency. The class interval is the distance between the top and lower class bounds of a frequency distribution table. Data are discrete pieces of factual information that are logged and used for analysis. Raw data is the foundation from which statistics are derived. Statistics are the results of data analysis, including its interpretation and presentation. The outcomes of data analysis, including its interpretation and presentation, are statistics. It includes techniques for data collection, evaluation, analysis, and interpretation, is the study and manipulation of data.

Note that the full question is:

Refer to the table summarizing service times (seconds) of dinners at a fast food restaurant. How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times?

Time (sec) Frequency

60 to 119 9

120 to 179 20

180 to 239 13

240 to 299 3

300 to 359 4

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The ordered pair of D is(2,6) by the given graph co-ordinates.

What is ordered pair?

By the given graph Point D has x-axis as 2 and y axis as 6.

Hence, the ordered pair is (2,6) by the given graph co-ordinates.

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Answer:

2+3=5

Step-by-step explanation:

2+

3=

5

answer 2+3=5

The equation of line passing through the points (3,-2) and (-2,3) in

(a) point slope form is  y + 2 = -(x - 3) ;

(b) slope intercept form is y = -x + 1   ;

(c) standard form is  x + y = 1 .

The Standard Form of equation of line is written as ⇒ " Ax + By = C " .

it is given that the line is passing through the points (3,-2) and (-2,3) ;

So , the slope(m) is = (3+2)/(-2-3) = 5/(-5) = -1 .

(a) the point slope form is (y - y₁) = m(x - x₁) ;

substituting x₁ = 3 and y₁ = -2 ;

we get ;

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

y + 2 = -(x - 3) .

(b) the slope intercept form is ⇒ y = mx + c ,

-2 = (-1)3 + c ;

-2 = -3 + c ,

c = -2 + 3 ;

c = 1 ; the equation is ⇒  y = -x + 1 .

(c) the standard form is :

arranging the equation y = -x + 1  ,

we get ;

x + y = 1 .

Therefore , the required equations of line are mentioned above .

The given question is incomplete , the complete question is  

How do you write the equation of the line in point slope form , slope intercept form and standard form given that it passes through (3, -2) , (-2, 3) ?

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Answer:

x = -10

Step-by-step explanation:

Solve means to get the x all by itself on one side of the equation.

40 = -3x + 10

Subtract 10 from both sides.

30 = -3x

Divide both sides by -3.

30/-3 = x

-10 = x

x = -10

You can check your answer by putting it back into the equation and seeing if you get a true statement.

40 = -3x + 10

x = -10

Substitute.

40 = -3(-10) + 10

Multiply.

40 = 30 + 10

Add.

40 = 40

True! This means

x = -10 is correct.

Answer: 470,000

My last answer for the day :)

Explanation: When rounding to the nearest ten thousand, look at the number right after it (the thousand value).

Since the number is 8, round the 6 up by one, so 7.

The solution for [tex]11^{\frac{1}{4} }[/tex] in radical form is 1.82116028... .

Radical form is pretty straight-forward. It refers to the form of a number or algebraic expression in which the number or algebraic expression is under a radical. However, we can better that by manipulating a number or algebraic expression in radical form to put it in a form called simplest radical form.

Apply the rule [tex]x^{\frac{m}{n} }[/tex]=[tex]\sqrt[n]{x^{m} }[/tex] to rewrite the exponential as a radical .

[tex]\sqrt[4]{11^{1} }[/tex]

Anything raised to 1 is the base itself.

[tex]\sqrt[4]{11}[/tex]

So the result can be shown in multiple forms like

Exact form: [tex]\sqrt[4]{11}[/tex]

Decimal form: 1.82116...

So the result for the expression in radical form is 1.82116...

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Refer to the photos taken.

Answer: n= -1

Step-by-step explanation:

6n+8=1-n

6n+n=1-8

7n=-7

n=-1

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

Volume of A /Volume of B =  ( a / b )^3

a is the radius of solid A and b is the radius of solid B.

solid figures

In Geometry, the shape or the figure that has three dimensions (length, breadth and height), are known as solids or three-dimensional shapes. Example:-Cube, Cuboid and Sphere. The major types of solid shapes are: cubes, cuboids, prisms, pyramids, platonic solids, torus, cone, cylinder, and sphere.

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Answer:

Divide both sides by -3.

Step-by-step explanation:

This question is asking you how to get from step 1: [tex]-3(p-7) = -15[/tex] to step 2: [tex]p - 7 = 5[/tex].

We can see that the expression inside of the parentheses (p - 7) didn't go away from step 1 to step 2, and the term that was being multiplied by (p-7) had gone away. The only way you can "get rid" of a multiplied term is by doing the inverse of multiplication, which is division. Thus, you have to divide both sides by -3 to get to step 2.

Answer:

x = 2

Step-by-step explanation:

5 / 2-2

5 / 0 = 0

0 is undefined

The sum of two or more numbers that results in a third number is called a factor.

The factor of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex] exists 2x + 1.

The definition of a factor is a number that divides another number by itself with no remainder. In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them.

What can split a number exactly are factors. So there is no residual after division. Factors are the sums of two or more numbers that produce a third number. Consequently, a factor is a number that divides another.

The use of more variable factors—those whose values do fluctuate with output—occurs as production rises and falls. Workforce, energy, and directly used raw materials are examples of typical variable components.

Let the given equation be [tex]$& x^2+\frac{x}{6}-\frac{1}{6} \\[/tex]

[tex]$& =\frac{6 x^2+x-1}{6} \\[/tex]

simplifying the above equation, we get

[tex]$& =\frac{1}{6}\left(6 x^2+x-1\right)[/tex]

We will factorize the polynomial by splitting its middle term.

[tex]$& \frac{1}{6}\left(6 x^2+x-1\right) \\[/tex]

[tex]$& =\frac{1}{6}\left(6 x^2+3 x-2 x-1\right) \\[/tex]

simplifying the above equation, we get

[tex]$& =\frac{1}{6}(3 x(2 x+1)-1(2 x+1)) \\[/tex]

[tex]$& =\frac{1}{6}(3 x-1)(2 x+1)[/tex]

[tex]$\frac{1}{6^{}}(3 x-1)$[/tex] and (2x + 1) are factors of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex]

Therefore, the correct answer is option B. 2x + 1

The complete question is:

Which among the following is a factor of [tex]$x^2+\frac{x}{6}-\frac{1}{6}$[/tex] ?

A. 3x + 1

B. 2x + 1

C. [tex]$x-\frac{1}{5}$[/tex]

D. [tex]$x-\frac{1}{2}$[/tex]

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The slope of the line perpendicular to the given line is equal to -4/1.

The equation is in the form y=mx+b

so, y=(1/4)x -10

First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4

To find the slope perpendicular to the line you must find the negative reciprocal of 1/4. (Which just means change the sign then flip the fraction)

Multiplying 1/4 by -1 which is -1/4

Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1

Thus, the slope of the line perpendicular to the given line is equal to -4/1.

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The equation is in the form y=mx+b

so, y=(1/4)x -10

First, find the slope of the line which is the value being multiplied by x. Therefore m=1/4

Multiplying 1/4 by -1 which is -1/4

Then flip the fraction and keep the sign with the numerator to find the reciprocal. So now it’s -4/1

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "≅" is the congruence symbol.

There are a few rules that check congruency of 2 distinct triangles  are:

1.Side-Angle-Side (SAS) Rule

 The triangles are congruent if the two sides and included angle of one     triangle equal the two sides and included angle of another triangle.

2. Angle-Side-Angle (ASA) Rule

  The triangles are congruent if two angles and the included side of one triangle equal two angles and the included side of another triangle.

and some other but these are the conditions that prove congruency of any traingle

Two triangles are similar if :

There are a few rules that check similarity of 2 distinct triangles  are:

1.Side-Angle-Side (SAS) Rule

  Two triangles are similar if they have two pairs of sides that are in the same ratio and if the included angles are likewise equal.

2. Side - Side -Side (SSS) Rule

    Two triangles are similar if they have three pairs of sides that are in the same ratio.

 and some other but these are the conditions that prove similarity of any traingle

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Distance of 125 feet covered in 5 seconds, so the speed is 25 feet/second.

Any object's distance traveled in a unit of time is referred to as speed.

In mathematical term, Speed is express as S = D/T,

where S=speed, D=distance, T= time.

Given that,

The distance = 125 feet.

The time taken to cover the distance = 5 seconds.

To find the unit rate.

Apply formula,

speed = distance / time

          = 125 / 5

          = 25 feet / second

The required speed is 25 feet / second.

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The name of radicals are cation and anion

A radical is an atom, molecule, or ion that has an unpaired valence electron. A notable example of a radical is the calcium ion

A radical can be electrically stable, positively charged and negatively charged.

Positively charged radicals are called cations and the negatively charged radicals are called anions.

If a balanced atom loses one or more electrons, it will become a positively charged cation.And if a balanced atom gains one or more electrons, it will become negatively charged anions.

Therefore the names of radicals are cations and anions i.e positively charged radicals and negatively charged radicals respectively.

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Answer:

-9z + 72

Step-by-step explanation:

The asymptotes in a given function is a line that the graph of a function approaches as either x or y go to positive or negative infinity.

An asymptote in a function is defined as the a line that the graph of a function approaches as either x or y go to positive or negative infinity.

There are various types of asymptote which include the following:

To determine the asymptote of a function in a graph is a descending curve that approaches but does not reach the horizontal axis is said to be asymptotic to that axis, which is the asymptote of the curve.

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Answer:

£29

Step-by-step explanation:

20% = 0.2

Take 145 times 0.2 = £29

So, he saves £29

A discrete random variable may take on only a countable number of distinct values such as 0,1,2,3,4,...

Definition of discrete random variable-Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, and the number of defective light bulbs in a box of ten.

Explanation-The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.

Example:-

The cumulative distribution function for the above probability distribution is calculated as follows:

The probability that  is less than or equal to is 0.1,

the probability that  is less than or equal to 2 is 0.1+0.3 = 0.4,

the probability that  is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and

the probability that  is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1.

So, finally we can conclude that discrete random variables can only take  a finite number of values.

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Answer:

linear inequation with 1 variable

The probability that all symbols are different is  0.45 and the probability that all all symbols are different and the first number is the largest among the numbers is 0.11.

There are three places for alphabets, which can be filled by any one of the 26 letters. So the total possible ways of selecting 3 letters is 26³.

There are four places for alphabets, which can be filled by any one of the 10 digits. So the total possible ways of selecting 4 numbers is [tex]10^{4}[/tex].

So, the total possible ways of selecting 3 alphabets and 4 numbers for license plates is 26³ × [tex]10^{4}[/tex] = 175760000.

(a) The probability that all symbols are different.

The three letters can be selected in 26! ways = 26 × 25 × 24 = 15600

Similarly, the four numbers can be selected in 10! ways = 10 × 9 × 8 × 7 = 5040

Therefore, the probability that all symbols are different is

= 15600 × 5040 / 175760000

= 0.45 approximately

(b) The probability that all symbols are different and the first number is the largest among the numbers.

The probability that first number is largest among the numbers is = 3!/4! = 1/4

The probability that all symbols are different is  0.45 approximately

Therefore, the required probability is

= 1/4 of 0.45

= 0.11 approximately.

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The production possibilities using at least two data points.

In order to illustrate the proper allocation of resources, a minimum of two data points are required. The first data point represents the production of both goods at the same level, while the second data point shows the production of one good at its maximum level while the other good is at its minimum level. The two data points represent the two different production possibilities available to the economy, and they demonstrate the trade-off between the two goods.

For example, if we have an economy that can produce two goods, A and B, the PPC can be used to illustrate the different combinations of these two goods that can be produced with a given level of resources. If we assume that the economy can produce 10 units of A and 8 units of B, the first data point would be (10,8). This represents the combination of A and B that can be produced using the same level of resources. The second data point would be (10,0), which represents the maximum production of A and the minimum production of B. This data point demonstrates the trade-off between the two goods, as more of A can be produced if fewer of B are produced.

Overall, the production possibility curve is a useful tool for understanding the trade-offs that an economy has to make in order to maximize its production of goods and services. By illustrating the production possibilities using at least two data points, the proper allocation of resources can be better understood

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Answer: The answer is three. 3.

Step-by-step explanation:

Got it right on edge.

The area of rectangular deck with length 8 feet and width 2 feet is 16 ft².

Area can be defined as the amount of space covered by a plane of a particular shape. It is measured in "number" of square units (cm², inch², ft² etc.). In other words, the space occupied around this shape is called the area of the rectangle.

We have, a rectangular deck with

length is 4 times its width and perimeter is 20ft.

Let us assume that "l" and "w" be length and width of a rectangular deck.

so, l = 4 w --(1)

Now, perimeter of rectangular deck = 2 ( l+w)

=> 2(l+w) = 20 --(2)

we have to calculate the area of rectangular deck and for this we have to calculate measure of length and width.

plug the value of "l" in equation (2) from (1)

2(l+w) = 20

=> 2(4w + w) = 20

=> 2× 5w = 20

=> w = 20/10 = 2 feet

from equation (1) , l = 4 × 2 = 8 feet

Area of rectangular deck, A = l× w

=> A = 8× 2 = 16 square feet

So, the required area is 16 square feet.

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By taking the modulus value of both of their balances we obtain that the difference Maria and Charles allowable balance is $10.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

Given, The table shows the allowable balance of several children.

From the given table we can conclude that Maria's allowable balance is

- 15.25 and Charles's allowable balance is - 5.25.

So, The difference of their allowable balance is |- 15.25| - |- 5.25|.

= 15.25 - 5.25.

= 10.

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