How do you factor to find all real solutions?.

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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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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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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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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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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Answer:

If that means division then here

Step-by-step explanation:

4/2=2

then,

2+8=10

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:

(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]

Answer:120

Step-by-step explanation:

given x= 3 and y= 8,

we have to find the value of 5xy

so let us put the values of x and y in the given expression i.e 5xy.2

= 5×3×8

= 120

 Hence the value of 5 xy is 120.

Answer:

Step-by-step explanation:

If x = 3 and y = 8, then the value of 5xy is simply 5 times the product of x and y.

To find the product of x and y, we simply multiply x and y together:

xy = 3 * 8 = 24

To find the value of 5xy, we simply multiply 5 by the value of xy:

5xy = 5 * 24 = 120

So the value of 5xy when x = 3 and y = 8 is 120

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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Answer:

-30 < s

Step-by-step explanation:

16 > -14 - s

30 > -s

Divided by negative. Because divided by negative, the > will switch to be <

So, the answer is

-30 < s

or

s > -30

The inverse of a function "swaps" the x and y values of the original function. To find the inverse of f(x) = 9x², we need to switch the x and y values and solve for x in terms of y:

y = 9x²

To find the inverse function we must isolate x.

x = √(y/9)

So the inverse of the function f(x) = 9x², x ≤ 0 is f^-1(x) = √(x/9), x ≤ 0.

Answer:

[tex]f^{-1}(x)=\dfrac{\sqrt{x}}{3}, \quad x \leq0[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=9x^2[/tex]

The domain of the given function is restricted:  {x : x ≤ 0}

The range of the given function is restricted:  {f(x) : f(x) ≤ 0}

To find the inverse of a function, swap x and y:

[tex]\implies x=9y^2[/tex]

Rearrange the equation to make y the subject:

[tex]\implies x=3^2y^2[/tex]

[tex]\implies x=(3y)^2[/tex]

[tex]\implies \pm\sqrt{x}=3y[/tex]

[tex]\implies y=\dfrac{\pm\sqrt{x}}{3}[/tex]

As x ≤ 0 then:

[tex]\implies y=\dfrac{\sqrt{x}}{3}[/tex]

Replace y with f⁻¹(x):

[tex]\implies f^{-1}(x)=\dfrac{\sqrt{x}}{3}[/tex]

The domain of the inverse of a function is the same as the range of the original function.  Therefore, the domain of the inverse function is restricted to {x : x ≤ 0}.

Answer:Hi there the answer is in quizlet is another page :)

Step-by-step explanation:

1/3 of the bag would be eaten by both cats in 2 minutes while 5/6 of the bag would be eaten by both cats in 5 minutes.

An equation is an expression showing the relationship between numbers and variables.

One little cat can eat a bag of treats in 15 minutes while another cat can eat the same bag of treats in 10 minutes.

a) In 2 minutes:

Part of bag eaten = (1/15 minutes) * 2 minutes + (1/10 minutes) * 2 minutes = 1/3

1/3 of the bag would be eaten by both cats in 2 minutes.

b) In 5 minutes:

Part of bag eaten = (1/15 minutes) * 5 minutes + (1/10 minutes) * 5 minutes = 5/6

5/6 of the bag would be eaten by both cats in 5 minutes.

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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 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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To determine a parabola's equation, we can utilize the vertex form. The aim is to formulate a graph's equation in the form y=a(xh)^2+k using the coordinates of its vertex, or maximum or minimum point.

Assuming we can get the coordinates (h,k) from the graph), and then to determine the value of the coefficient a. It is done by writing a quadratic equation in vertex form, which is y=a(x-h)^2+k, where (h,k) is the vertex of the parabola.

The top or bottom point of a parabola is known as its vertex.

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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

Answer: C. 3/11

Step-by-step explanation:

first add up all the flowers so 3 roses, 4 daisies, and 4 lilies, 3 +4 + 4 = 11. if only one flower is pink, and there are 3 roses, then there's a 3/11 chance its a rose.

Answer:

Yes

Step-by-step explanation:

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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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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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Answer:

31kg will cost $ 182.9

Step-by-step explanation:

If 18kg = $106.20

than 31kg = ?

= 31kg/18kg × $106.20

= 3,292.2 /18

=$182.9

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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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 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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These the five sentence about the most important thing to learn about the software engineer career:

Software engineer is a branch of computer engineer science that mainly work to create, secure and manipulating a software. The career on this field mostly start from :

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Answer:

Hexagon

Step-by-step explanation

A hexagon can be defined as a closed two-dimensional polygon with six sides. Hexagon has 6 vertices and 6 angles also. Hexa means six and gonia means angles

Answer:

22

Step-by-step explanation:

n + (n+1 )+( n+2) = 69

3n+3 =69

3n=66

n=66/3

n=22

Answer:

first number is 21

second number 23

third number 25.

Step-by-step explanation:

The sum of three consecutive numbers is 69

Let the first number be n

the second number be 2 + n

the third number be 4 + n

n + (2 + n) + (4 + n) = 69

=n + n + n + 2 +4 = 69

=3n + 6 = 69

=3n = 69 - 6

=3n = 63

=3n/3 = 63/3

n = 21

therefore the first number n = 21

the second number 2 + n = 2 + 21 = 23.

the third number 4 + n = 4 + 21 = 25.