How do you solve complex fractions with rational expressions?.

B.  Let (2a + 1) and  (2b + 1) are different odd numbers. sum of these odd number is 2(a+ b +1) is a multiple of 2.

Whole numbers in mathematics can be divided into even and odd numbers. There isn't a single number that can be both even and odd, making odd and even numbers distinct sets of numbers. A number can be even or odd. Odd numbers are ones that are not entirely divisible by two, whereas even numbers are entirely divisible by two.

Let (2a + 1) and  (2b + 1) are different odd numbers. the sum of these odd numbers is 2(a+b+1) is a multiple of 2. furthermore, let 2a and 2b be two even numbers so the sum of those two will also be an even number. Therefore the summation of two odd numbers is always even.

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The complete question is:

Jona is given a test question asking him how that the um of two odd integers is always an even integer. Which choice is the best proof of his conjecture?

A) Every time you add two odd numbers, the sum is an even number.

B) Let a and b both represent odd numbers and a+b be an even number. Therefore, a+b=b+a which shows that the sum of two odd numbers is even.

C) Look at these different examples: 5+3=8, 15+7=22, 21+13=34. So the sum of two odd numbers must be even.

D) Let (2a+1) be one odd number and let (2b+1) be the other odd number. (2a+1)+ (2b+1) = 2a+2b+2 = 2(a+b+1). Because 2(a+b+1) is a multiple of 2,it is an even number.

The larger number could have been before rounding is 4000001.

We know that both numbers were rounded up to the nearest million and added together to get 7000000.

Since one number was less than 3000000 to start with and both numbers were rounded up, the greatest that the smaller number could have been before rounding is 2999999.

We can use the equation:

(x + y) = 7000000

Where x is the smaller number and y is the larger number before rounding.

We know that x < 3000000 and x = 2999999

So we can substitute these values into the equation:

(2999999 + y) = 7000000

Solving for y:

y = 7000000 - 2999999

y = 4000001

So the greatest that the larger number could have been before rounding is 4000001.

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The vertical axis of a relative frequency histogram employs relative or proportional frequency rather than plain frequency, which is the only difference between it and a frequency histogram.

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The equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).

An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two expressions on either side of an equals sign, and it indicates that the expressions have the same value.

The equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis can be expressed in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.
To calculate the slope, we can use the formula m = (y2 - y1)/(x2 - x1). Plugging in the coordinates, we get m = (7 - (-3))/(-9 - (-6)) = 10/3.
To calculate the y-intercept, we can use the formula b = y - mx. Plugging in the coordinates and the slope we just calculated, we get b = 7 - (10/3)(-9) = 61/3.
Therefore, the equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).

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Complete Question:
Complete the equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.

The equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).

A mathematical statement that expresses the equivalence of two expressions is known as an equation. It typically consists of two expressions on either side of an equal sign, and it indicates that the expressions have the same value.

The equation of the line through (-9,7)(−9,7), and (-6,-3)(−6,−3) can be expressed in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.

To calculate the slope, we can use the formula m = (y₂ - y₁)/(x₂ - x₁). Plugging in the coordinates, we get

m = (7 - (-3))/(-9 - (-6))

= 10/3.

To calculate the y-intercept, we can use the formula b = y - mx. Plugging in the coordinates and the slope we just calculated, we get b = 7 - (10/3)(-9) = 61/3.

Therefore, the equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).

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The complete question:

Complete the equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.

The formula for number pattern is an = dn - c.

A series or sequence that frequently repeats itself is referred to as a pattern. In our daily lives, we notice patterns in things like colours, behaviours, shapes, numbers, etc. They can be finite or infinite and related to any phenomenon or thing. A group of integers that are arranged in a pattern according to a predetermined rule are called a pattern in mathematics. These guidelines specify how to compute or resolve issues. For instance, every number in the series 3,6,9,12, increases by 3. The pattern predicts that the final number will be 12 + 3 = 15.

The most frequent kind of mathematical pattern is a number pattern, in which a list of numbers is arranged in a certain order according to a rule. Algebraic or mathematical patterns, geometric patterns, and the Fibonacci pattern are the various sorts of number patterns.

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The symbols used in graphing linear inequalities are greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).

When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical, or as a combination of the two. When a polynomial of degree 1 is compared to another algebraic expression of degree less than or equal to 1, this is an example of a linear inequality, which is an inequality involving at least one linear algebraic expression. Different types of linear inequalities can be represented in a number of different ways.

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The simplified form of the expression [8q² -2 [q²-2 (3q²-3q+5)​ is 18q² −12q + 20.

Reduce a fraction to its simplest form to simplify it. A fraction is said to be in its simplest form if both its numerator and denominator only contain the number one. As we attempt to solve fractional problems, the process of simplifying difficulties is crucial. Even after we simplify them, the fraction's value will not change. This shows that the true fraction and the simplified fraction are two equivalent fractions.

Lets Simplify

= [8q² -2 [q²-2 (3q²-3q+5)​

= [8q² -2(q²−6q² +6q−10)

= 8q² + 10q² −12q + 20

= 18q² −12q + 20

Thus, The simplified form of the expression [8q² -2 [q²-2 (3q²-3q+5)​ is 18q² −12q + 20.

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Step-by-step explanation:

15 miles consume 1 gallon

450 miles consume 450÷15 = 30 gallon per a way

For round trip, it will consume 30*2=60 galloon

1 gallon costs 50 cents

30 galloon costs 30*50=1500 cents per a way

For round trip, 1500*2=3000 cents

Receives some cash from his mother for his journey. He has already put aside a total of $\$ 220$ for the trip. There is a 55-gallon gas purchase cap .

[tex]$$\begin{aligned}& 3.25 \mathrm{~g}+40 \leq 220 \\& -403.25 \mathrm{~g} \\& \frac{3.25}{3.25} \leq \frac{180}{3.25} g \leq 55.38 \approx 55\end{aligned}$$[/tex]

Chang-to has a gas purchase limit of 55 gallons.

[tex]$$\begin{aligned}& 3.25 g+40 > 92 \\& \frac{-40}{\frac{3.25 g}{3.25} > \frac{-40}{32}} \\& \mathrm{~g} > 16\end{aligned}$$[/tex]

More than 16 gallons of gas could have been purchased by him .

[tex]$$\begin{aligned}& 3.259+40 \leq 170 \\& \frac{3.2 / 59}{3.2^{\prime} 5} \leq \frac{130}{3.25} \\& g \leqslant 40\end{aligned}$$[/tex]

He only allowed to purchase 40 gallons of gas during the journey.

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Answer:

A: x < 3

Step-by-step explanation:

Answer: x < 3

Step-by-step explanation:

We start by subtracting 6 from both sides -

x + 6 - 6 < 9 - 6

Then, we get this -

x < 3

Which is the answer

The line showing this inequality is B.

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is an inequality, |x - 21| < 3

Solving, the inequality,

|x - 21| < 3

x-21 < 3 and x-21 > -3

x < 24 and x > 18

Since, we get 18 < x < 24,

Hence, the line showing this inequality is B.

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A triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 360 degrees.

No, a triangle is not always 360 degrees. In geometry, a triangle is a three-sided polygon with three angles. The sum of the angles in a triangle is always 180 degrees.

This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.

For example, if a triangle has angles of 90 degrees, 60 degrees, and 30 degrees, the sum of these angles is 180 degrees (90+60+30=180).

Therefore, In short, a triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 360 degrees.

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Answer:

If that means division then here

Step-by-step explanation:

4/2=2

then,

2+8=10

The solutions of the given equation are 2 or -2

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given is an equation, x²+2 = 6

x²+2 = 6

Solving we get,

x²+2 = 6

x² = 6-2

x² = 4

x = ±2

Hence, there are two solutions of the equation 2 or -2

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The number that is irrational is √19.

An irrational number is a number that cannot be expressed as a ratio of two integers (a fraction) and it cannot be represented as a repeating or terminating decimal. The square root of 19 is an irrational number because it cannot be expressed as a ratio of two integers. It is non-repeating, non-terminating decimal that goes on forever, so it cannot be represented as a decimal.

Answer:

Hi i found the answer 3/2 could you please check your options?

if you apply the slope formula here,

12-6/8-4 gives you the value 6/4 which is 3/2

good luck!

The Sin 45 value is 1/√2.For the purpose of determining the Sin 45 value, let's use the ABC right angle triangle.

The ratio of a triangle's opposing side's length to its hypotenuse is known as the Sin of an angle.

Sin ϴ = Opposite side or perpendicular / Hypotenuse

Sin ϴ = AC/AB

Sin ϴ  =  B/C

Calculation of the Value of Sin 45 Degree in Fraction

Sin 45 = √2/

= 1 / √2

Consider a right triangle with angle X= 45°,then it is obvious that third will also be 45°.hence the side length of triangle are L, L, √2L .then apply

sin 45°= L/√2L

Sin 45°= 1/√2

Sin 45°=0.7071

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The most simplified form of the given ratio  1.8: 4.2, which is a ratio of lengths in inches is 3/7.

What is meant by ratios?

In mathematics, a ratio shows how frequently one number appears in another. When expressed as a:b, a fraction has the form of a ratio. A ratio is a comparison or compressed version of two identical values. Like fractions, ratios can be entirely simplified. Divide all of the numbers in a ratio by the same number to make it simpler. Divide each integer in a ratio by their largest common factor to fully simplify the ratio. The ratio's numbers must always be whole numbers.

Given the ratio, 1.8: 4.2

The ratio can be simplified by dividing both the terms in the ratio by the highest common factor.

The highest common factor of 1.8 and 4.2 is 0.6.

So we divide both terms by 0.6.

1.8: 4.2 = 1.8/0.6 : 4.2/0.6 = 3:7

Therefore the simplified form of the given ratio, 1.8: 4.2 is 3:7.

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The length of the third side will be equal to 21.81 units.

Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given that the bigger side of the triangle is 24 and one of the legs is 10 units. The length of the third side will be calculated as,

Use the Pythagorean theorem,

B² = H² - P²  

B² = (24)² - (10)²

B² = 576  -  100

B = √476

B = 21.81 units

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Zack is expected to be at (-12,-10.5) by finding the midpoint of line segment WT and reflecting T over it.

What is coordinate ?

A coordinate is a set of numerical values that are used to identify the position of a point in a specific space, such as a two-dimensional plane or a three-dimensional space. In two-dimensional space, coordinates are commonly represented by an ordered pair (x, y) or (x, y, z) in three-dimensional space.

The problem states that the balloon lands at point W(42,-15) and Tahir ends up at point T(-18,36). We know that Tahir and Zack are flying off in opposite directions from point W at equal distances. To find the point where Zack is expected to land, we can use the midpoint formula which states that the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates.

We can find the midpoint of line segment WT by taking the average of the x-coordinates and y-coordinates:

x_midpoint = (x1 + x2) / 2 = (42 + -18) / 2 = 12

y_midpoint = (y1 + y2) / 2 = (-15 + 36) / 2 = 10.5

So the midpoint of line segment WT is (12,10.5). Since Zack is flying off in the opposite direction from Tahir at the same distance, we can expect Zack to end up at the point which is the reflection of point T over the midpoint of line segment WT.

This point would be (-12,-10.5)

Therefore , Zack is expected to be at (-12,-10.5) by finding the midpoint of line segment WT and reflecting T over it.

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Hey there!

There are various concepts that are used in the world of Geometry, however there are some simple concepts that may be easier to work with.

_____________________________________________________

So, in summary to all of this, it really depends on what concepts in geometry you are currently learning and which concept(s) you personally find the most useful and helpful.

Nate have enough money to buy everything in his cart because his total expenses is lees than 50 dollars.

Nate has $50 to go spend at the grocery store. He fills his shopping cart with items total and $46.  He will have to pay a sales tax of 6% on al items on the cart.

Therefore, let's check if Nate have enough money to buy the groceries.

Hence,

sales tax amount = 6% of 46

sales tax amount = 6 / 100 × 46

sales tax amount = 276 / 100

sales tax amount = 2.76 dollars

Therefore,

the amount in total of the grocery = 46 + 2.76 = 48.76 dollars

Therefore, he has enough money to pay for his groceries.

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Answer:

(x-3)^3

Step-by-step explanation:

[tex]= x^3-9x^2+27x-27 \\ =(x − 3) (x² + 3x + 9) − 9x (x - 3) \\ =(x − 3) · (x² + 3x + 9 − 9x) \\ =(x-3)·(x²-6x+9) \\ =(x − 3) · (x − 3)^2 \\ = {(x - 3)}^{3} [/tex]

Or Apply cube of difference rule

[tex]{x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} [/tex]

Answer:

[tex](x-3)^3[/tex]

Step-by-step explanation:

Given polynomial:

[tex]x^3-9x^2+27x-27[/tex]

Given (x - 3) is a factor of the polynomial, divide the polynomial by the factor using long division to find the other factor:

[tex]\large \begin{array}{r}x^2-6x+9\phantom{)}\\x-3{\overline{\smash{\big)}\,x^3-9x^2+27x-27\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-3x^2)\phantom{-b0000000)}}\\-6x^2+27x-27\phantom{)}\\-~\phantom{()}\underline{(-6x^2+18x)\phantom{0000.}}\\9x-27\phantom{)}\\-~\phantom{()}\underline{(9x-27)\phantom{}}\\0\phantom{)}\end{array}[/tex]

Therefore:

[tex]x^3-9x^2+27x-27=(x-3)(x^2-6x+9)[/tex]

Factor (x² - 6x + 9):

[tex]\implies x^2-6x+9[/tex]

[tex]\implies x^2-3x-3x+9[/tex]

[tex]\implies x(x-3)-3(x-3)[/tex]

[tex]\implies (x-3)(x-3)[/tex]

Therefore, the fully factored polynomial is:

[tex]\implies x^3-9x^2+27x-27=(x-3)(x-3)(x-3)[/tex]

[tex]\implies x^3-9x^2+27x-27=(x-3)^3[/tex]

The answer is, the no: of students who took the bus is =352 .The given question is a percentage calculating problem.

There were a total of 640 students at a school on Friday.

Every student either walked or took the bus

45% of the total number of students walked to school

Since, 45% of them walked to the school,

Therefore, percentage of the students took the bus =

100%-45% = 55%

Now, finding the number of students took the bus,

55% of 640 = 640×55/100 = 352

Hence, There were 352 students who took the bus

A ratio or value that can be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The Symbol "%" stands for it.

There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Percentage formula = (Value/Total value) × 100

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In algebra, the notation "FG" refers to the composition of two functions, "F" and "G", where the output of "G" is used as the input for "F" and the notation is represented as "F(G(x))".

The composition of functions is a way to combine two functions to create a new function. The output of the first function "G" is used as the input for the second function "F". This process is represented by the notation "F(G(x))", where "x" is the input for both functions. The function "F" is applied to the output of the function "G". This composition of functions is useful for modeling complex systems and can simplify mathematical expressions.

It also allows for the creation of more complex functions by combining simpler functions. However, not all functions can be composed and the order of the functions also matters. It's important to note that the order of the functions in composition matters and can change the result of composition.

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The minimum number of hikers who could have walked between 6 miles and 17 miles is 9 and the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.

The minimum number refers to the smallest value that is possible, allowed, or required based on the given interval. The maximum number refers to the largest value that is possible, allowed, or required based on given interval. The provided table provides intervals for the number of miles x the number of hikers can walk and the corresponding number of hikers.

In order to determine the minimum and maximum number of hikers that could walk between 6 miles and 17 miles, we look at the intervals which include the range between 6 miles and 17 miles.

a) The minimum value is determined by considering the common interval 10 ≤ x < 15 (5 ≤ x < 10 and 15 ≤ x < 20 are not considered as it includes values outside the range). Hence the corresponding number of hikers is 9.

b) The maximum value is determined by considering all the intervals which include the range between 6 miles and 17 miles, i.e. 5 ≤ x < 10, 10 ≤ x < 15, 15 ≤ x < 20. Hence, the maximum number of hikers is 2 + 9 + 8 = 19.

Note: The question is incomplete. The complete question probably is: The table below shows information about the distance walked by some hikers. a) Work out the minimum number of hikers who could have walked between 6 miles and 17 miles. b) Work out the maximum number of hikers who could have walked between 6 miles and 17 miles.

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a. Let t represent the time in hours when it started raining. We can use function notation to represent the amount of rain r at any time t with r(t) = 37 millimeters. This is because after 6 hours, the amount of rain was 37 millimeters. Therefore, we can use the equation r(t) = 37 millimeters to represent this statement.

b. We can use function notation to represent the amount of rain at any time t with r(t) = r(t-1.5). This is because the amount of rain 90 minutes after it started raining was the same as the amount 120 minutes after it started raining. Therefore, we can use the equation r(t) = r(t-1.5) to represent this statement.

This type of function notation is useful for representing relationships between different values related to the same property or phenomenon. It allows us to quickly and easily analyse and compare data, as well as make predictions about future values. It is also useful for describing how certain parameters are changing over time.

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Correct option is C, the correct equation is Y - 2 = -1/3 (x + 6).

Y=mx+b, where m is the slope and b is the y-intercept, is the slope intercept form. The graph of the linear equation can be drawn on the x-y coordinate plane using this form of the equation. Y = m x + b y=mx+b y=mx+by, equals, m, x, plus, b, where m is the slope and b is the y-intercept, is the slope intercept form.

Given points are (-6,2)

The required line should be perpendicular to y=3x-8.

When two lines are perpendicular,

their slopes are such that,

m1 = - 1/m2                    [1]

⇒ slope of line 2 =

⇒ -1/3    [using (1) relationship ]

Now substituting the points are slope in the equation of line -

y - y₀ = m (x - x₀)

⇒ y - 2 = -1/3 (x + 6)

⇒ 3y - 6 = -x - 6

⇒ 3y + x = 0

⇒ x = -3y

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Each monthly payment will be $1,294 and the total cost of the car's hire purchase will be $4,158.

given simple interest is 30%

Installments every month

a. Recurring payment  

30 months in 2 1/2 years

First move

Payment due: [49,500 * (1-.30)] / 30 months

Amount due = (49,500 *.70) / 30 months

$34,650 payments over 30 months

Amount due: $1,155

Second action

Monthly payment equals [$1,155* (1+0.12)]

Monthly payment equals $1,155 * 1.12

The monthly payment is $1,293.6

The monthly payment equals $1,294 (Approximately)

Hire-purchase (b)

Hire purchase equals $1,155 * .12 over 30 months

=> 1155 * 0.12* 30

$4,158 for a hire buy

As a result, each monthly payment will be $1,294 and the total cost of the car's hire purchase will be $4,158.

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