Which is a factor of the polynomial f x )= 6x 4 21x 3 4x 2?

The final step is x < 3

What is an inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

Less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and not equal (≠) are the five inequality symbols.

Given inequality is

-2(5 - 4x) < 6x - 4

The inequality sign is less than.

Applying distributive property on the left side

-10 + 8x < 6x -4

Subtract 6x from both sides

-10 + 8x - 6x < 6x -6x - 4

-10 + 2x < - 4

Add 10 on both sides:

-10 + 2x + 10 < - 4 + 10

2x < 6

Divide both sides by 2:

2x/3 < 6/3

x < 3

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Answer: 2³

Step-by-step explanation:

    We will use the order of operations to help us solve. This means, in this case, starting with exponents and then multiplying. We will also use the exponent rules.

    Given:

[tex]\displaystyle (2^2)^4\;*\;2^{-5}[/tex]

    Power rule of exponents:

[tex]\displaystyle (2^2)^4\;*\;2^{-5}=(2^{2*4})\;*\;2^{-5}[/tex]

[tex](2^{8})\;*\;2^{-5}[/tex]

    Product rule of exponents:

[tex]\displaystyle (2^{8})\;*\;2^{-5} = (2^{8+-5})= (2^{8-5})[/tex]

[tex](2^{3})[/tex]

      The simplified form of the expression, from the given options, is 2³.

Parallel lines are two straight lines that never cross. For this to happen, the lines have to have the same slope.

In this case, the equation given is in what's called "slope-intersect" form. The general form of the slope intercept formula is y=mx + b where m is the slope of the line and b is the point on the Y-axis where the line crosses.

The equation given is y=5x+3 and since the 5 is in the place of m from the general equation, 5 is the slope. Since parallel lines have the same slope, 5 is the answer.

Slope-Intercept Form:

When we're given a linear equation we can immediately see if it's in the slope-intercept form if it follows the format  y=mx+b. As long as y does not have a coefficient the slope and y-intercept are the values of m and b.

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No, the biconditional statement isn't true because It's not necessary that if a polygon has four sides, then It will be a square.

What is Biconditional statement?

A statement that combines a conditional statement with its opposite is known as a biconditional statement. So, if and only if the other conditional is also true, the first conditional is true.

Let's elaborate the statement, “If a polygon is a square, then it has four sides.”

We know that a square has four equal sides and So, if a polygon is a square, it must have four equal sides which states that the given statement is true.

But, if we see its converse, "If a polygon has four sides, then it is a square". It is not necessary that the polygon will be a square.

eg. A parallelogram and  rectangle also have four sides, So it could either be a parallelogram, rectangle or a square.

Hence, The given statement is correct but the converse of it, is not correct.

So, It can't be called a biconditional statement.

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Answer:

Let,

length of rectangle ( L) =9cm

breadth of rectangle (b) =4cm

Area of rectangle=L×b

=9×4

=36cm^2

By combining the mother's as well as father's heights in inches, you may determine the midparental height. For boys, measure 5 inches longer; for girls, measure 5 inches shorter. multiply by two.

However, a number of calculations can offer a reliable approximation of a child's growth. Here is a common illustration:

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The value of radius of the merry-go-round will be 6 feet.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circular objects for example our bike wheel.

The longest line which can be drawn inside the circle will be the diameter.

The perimeter of the circle = 2πr where r is the radius of the circle.

The Merry cover on the round in 3 seconds thus, to cover the 2πr path it takes 3 seconds.

2πr/3 = 12.56

2πr = 37.68

r = 5.996 ≈ 6 feet.

Hence "The value of the radius of the merry-go-round will be 6 feet".

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To answer, let's use the exponent rules to solve the power of 1.

Exponents, often known as powers, specify how many times the base number must be multiplied.

Exponent rules are principles that are used to simplify expressions using exponents. These principles are also useful in simplifying formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.

Negative exponents Rule: [tex]a^{-m} = 1/a^m[/tex]

Product Rule: [tex]a^m * a^n = a^{(m+n)}[/tex]

Quotient Rule: [tex]a^m/a^n = a^{(m-n)}[/tex]  

Power of a Power Rule: [tex](a^m)^n = a^{mn}[/tex]

Here, given that, 3 to the power of 1

The number 3¹ may be expressed as 3 to the power of 1, according to the exponent rule.

The base number in this formula is 3, while the power number is 1, and we know that any integer increased to that same power of that one equals the original number.

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Using the ratio we know that before the weekend started, she could have won as many as 164 games.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

A proportion is an equation that sets two ratios at the same value.

For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

So, let n be the number of victories so that:

n/2n = 1/2 and n+3/2n+4 > 503/1000

Now, cross multiply as follows:

1000n + 3000 > 1006n + 2012

n < 988/6 = 164 4/6 = 164 2/3

Therefore, using the ratio we know that before the weekend started, she could have won as many as 164 games.

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“6 more than twice m” can be written in the mathematical form as 2m+6.

The question is saying that we have to write “6 more than twice m” as an algebraic expression or into a mathematical expression.

As in the question, it is mentioned that we have to take the number m as a variable.

So, we are going to use this ‘m’ for solving this question.

Let the number be m.

Then, twice of m will be similar to 2 times m or m multiplied by 2.

Therefore, twice m will be 2m.

Now, the question is saying that 6 more than twice m.

“6 more than” means 6 is added to that specific number.

Hence, 6 more than that number which is twice of m will be 2m+6.

Hence, “6 more than twice m” can be written in the mathematical form as 2m+6.

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Answer:

$6,232.89 or $6,232.90

Step-by-step explanation:

A=P(1+(r/n))^nt

A= 3000(1+(.075/12))^12*10

A= 3,232.89

3,232.89+3000= 6,232.89

Step-by-step explanation:

draw a rectangle with width 98 and height 55 there are two of each side, so 98 + 98 + 55 +55 = 306

Answer:

306m

Step-by-step explanation:

You need to find the perimeter of the rectangle. To do that, you just add the side lenghts. So, this is your lawn with the side lengths:

                      55m
           _____________
           |                           |
           |                           |
           |                           |
98m    |                           |     98m
           |                           |
           |                           |
           |                           |
           _____________
                      55m

You just add them together!

55 + 55 + 98 + 98 = 306

so you need 306 meters of fencing

The three methods to find the mean are arithmetic, geometric and harmonic .

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The given type of effect is called predictive.

What is linear regression?

When predicting a variable's value based on the value of another variable, linear regression analysis is used. The dependent variable is the one you're trying to forecast. The independent variable is the one that you are utilizing to forecast the value of the other variable.

Given:

A variable with a value of x1 x2 is added to the general linear regression model to account for two predictive variables, x1 and x2 and the effect on the response variable.

Linear regression is one of the most generally utilized predictive displaying methods.

It is spoken to by a condition = + + , where an is the catch, b is the slant of the line and e is the blunder term.

This condition can be utilized to predict the estimation of an objective variable dependent on a given predictor variable(s).

The predictor variable is the name given to an autonomous variable utilized in regression examinations.

The predictor variable gives data on a related ward variable concerning a specific result.

Hence, the given type of effect is called predictive.

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The correct answer is e) approximately normal with a mean 122 and standard deviation 0.35.

In this case, the distribution of the sample mean of IQ scores will be approximately normal because the sample size of 200 is sufficiently large. This is known as the Central Limit Theorem, which states that the distribution of the sample mean will be approximately normal as long as the sample size is large enough, regardless of the shape of the distribution of the population.

The mean of the sample mean distribution will be 122, which is the same as the mean of the population. The standard deviation of the sample mean distribution will be smaller than the standard deviation of the population because it is calculated using the sample size rather than the population size.

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Answer:

SB = 4

Step-by-step explanation:

The figure is the intersection of the medians of this triangle. The medians of a triangle bisect the sides of the triangle. The intersection of the medians is called the centroid. In this case, the centroid of this figure would be S.

In fact, the distance from a vertex to the centroid of the triangle is 2/3 of the distance from said vertex to the vertex's opposite side.

Create the equation SB = 2/3(PB).

.....................................SB = 2/3(6)

....................................SB = 12/3

...................................∴SB = 4

Answer:

SB = 4

Step-by-step explanation:

SB = 2/3 BP

SB = 2/3 (6)

SB = 4

Answer:

( x + 6, y + 4)

Step-by-step explanation:

Let's pick point S at ( -9, -4); it changes to point S' at ( -3, 0)

The x increase by 6, and the y increase by so the answer is

( x + 6, y + 4)

Yes, the isosceles triangles are equal to 180 degrees.

We know that isosceles triangles are triangles which have two equal sides. Since the sides are equal, they subtend equal angles as well.

However, the two equal angles subtended by the equal sides and one more angle which is subtended by the third side of the isosceles triangle all add up to a total of 180 degree as we know that the sum of all the angles of a triangle is always equal to 180 degrees.

Hence we can conclude that the isosceles triangles are also equal to 180 degrees like every other triangle.

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The triangles are congruent if all three sets of comparable sides are present. The side-side-side shortcut is a congruence technique (SSS).

Triangles are considered congruent by SAS if their two sides match up with their corresponding two sides on the other triangle, and if their included angles match up in both triangles.

We can prove two triangles, either by SSS or SAS by simply taking two triangles and checking whether the sides and the angles of the corresponding triangles are congruent or not.

By simply comparing it on the basis of their sides and angles we can easily prove the corresponding triangles by SSS or SAS.

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Number of combinations = 56 combinations can be created from the letters in the word "friendly"

Points to remember

nCₐ = n!/(r!(n - r)!)

The given word is "FRIENDLY"

F R I E N D L Y is a 8 letter word.

To find the number of combinations

5 letters can be selected from 8 letter = 8C₅

8C₅ = 8!/(8 - 5)!5!

= 8!/3!5!

= (8 * 7 * 6* 5!)/(1 * 2 * 3 * 5!)

= 8 * 7

=  56

5 letter combinations can be created from the letters in the world “friendly = 56

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Using the concept of percentage, social media budget will cost $425.25

This is the expression of a ratio or fraction in percentage form. This is done by multiplying a ratio by 100.

The original advertising budget is $81,000 and they plan to increase it by 5%.

Let's calculate the 5% increase in the budget.

5% of 81000 =

5 / 100 = x / 81000

0.05 = x / 81000

x = 81000 * 0.05

x = 4050

The budget for next year will 81000 + 4050 = 85050

In the breakdown for the advertising budget, social media budget got 0.5%

Let's find 0.5% of 85050

0.5% * 85050

0.5 / 100 = x / 85050

0.005 = x / 85050

x = 0.005 * 85050

x = 425.25

The social media budget is $425.25

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The positive sign indicates that Gunther pulls to the right.

A force that would result in a balanced force for the game is: 45N

First we define a reference system.

Let's assume the horizontal axis as positive towards the right.

Suppose Kiley and Jermaine pull the rope to the left, while Gunther pulls the rope to the right.

The equilibrium equation is given by:

-20-25+F=0

Where,

F: force with which Gunther pulls the rope.

Clearing F we have:

The positive sign indicates that Gunther pulls to the right.

A force that would result in a balanced force for the game is: 45N

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7.500 (rounded to 4 decimals) sum of the numbers on the balls.

Suppose we select two distinct balls

Then we have the following possibilities of selecting two balls

(2,2), (2,2) ............, i.e. 2 ways to get a sum of 4...............(2+2 = 4 and 2+2 = 4)    

(2,5), (2,5), (5,2), (5,2), i.e. 4 ways to get a sum of 7...............(5+2 = 7 and 2+5 = 7)    

(2,6), (2,6), (2,6), (2,6), i.e. 4 ways to get a sum of 8...............(2+6 = 8 and 6+2 = 8)    

(6,5), (5,6) , i.e. 2 ways to get a sum of 11...............(5+6 = 11 and 6+5 = 11)    

total number of possible outcomes =  2(for a sum of 4) + 4(for a sum of 7) + 4(for a sum of 8) + 2 (for a sum of 11)

= 2 + 4 + 4+2

= 12

So, P(getting a sum of 4) = (number of ways to get a sum of 4)/total number = 2/12

similarly,

P(getting a sum of 7) = (number of ways to get a sum of 7)/total number = 4/12

P(getting a sum of 8) = (number of ways to get a sum of 8)/total number = 4/12

P(getting a sum of 11) = (number of ways to get a sum of 11)/total number = 2/12

We know that expected value E[x] = sum of all individual sum values by their respective probability

= 4*(2/12) +7*(4/12) +8*(4/12) +11*(2/12)

= 0.6667 + 2.3333 + 2.6667 + 1.8333

= 7.500 (rounded to 4 decimals)

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The three types of set based on the number of elements is empty set, finite set and infinite set.

In mathematics, a set is a collection of unique objects. The number of elements in a set can be finite or infinite.

An empty set is a set with no elements. It is also called a null set. For example, a set of natural numbers less than 0.

Finite set is a set containing finite number of elements, that is the number of elements in the set is countable. For example, a set of natural numbers less than 100.

Whereas infinite set is a set with infinite number of elements, that is the number of elements in the set is not countable. For example, a set of natural numbers.

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Answer:

Aisha mix will be more lemony

Step-by-step explanation:

Find Rahul's percentage of the powdered lemon mix by

Finding the total number of cups

14 + 5 = 19 total cups

Then take

5 divided by 19, times 100% = 26.3%

Find Aisha's percentage of the powdered lemon mix by

Finding the total number of cups

11 + 4 = 15 total cups

Then take

4 divided by 15, times 100% = 26.6% or 27%

Answer: Ariana uses 85% drink mix, and Andres uses 90% drink mix. Therefore, Andres's drink will taste more lemony.

Step-by-step explanation:

Ariana uses 17 cups of mix out of the 20 total cups which is 85%

Andres uses 10 cups of mix out of the 11 total cups which is around 90%

Step-by-step explanation:

f(-4) = -18, f(-2) = -10, f(6) = 12 and f(-1) = -6 using the piecewise function.

A function defined by numerous sub-functions, where each sub-function applies to a distinct interval in the domain, is known in mathematics as a piecewise-defined function (also known as a piecewise function, a hybrid function, or definition by cases).  Instead of being a property of the function itself, piecewise definition is a means to express the function.

When the domain may be divided into intervals on which the property holds, the phrase "property holding piecewise for a function" is used, which is separate but related. This is a characteristic of the function itself, as opposed to the idea mentioned above.

f(-4) = 4(-4)-2 = -18  ∵-4≤-1

f(-2) = 4(-2)-2= -10  ∵-2≤-1

f(6) = [tex]\frac{1}{2}*6 + 9 = 12[/tex] ∵6>-1

f(-1) = 4(-1)-2 = -6 ∵-1≤-1

f(-4) = -18, f(-2) = -10, f(6) = 12 and f(-1) = -6 using the piecewise function.

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We may deduce from the contour map that the estimates of the given functions are;

fx(2, 1) = 10

fy(2, 1) = 3

The geographic mapping used as a form of activism against prevailing power systems is known as counter-mapping.

Contour lines are described as the faint lines drawn on a map that link places of equal height above sea level. This indicates that even if you followed a contour line physically, the elevation (height of the land) would stay constant.

According to the contour map, the contour lines indicate that the coordinate (2, 1) in the x-direction has a value of 10.

Therefore;   fx(2, 1) = 10

Using the same idea, we can deduce from the attached contour map that the coordinate (2, 1) in the y-direction will have a value between 0 and 6. Therefore;

Average = (0 + 6) divided by 2 = 3

Thus;   fy(2, 1) = 3

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