help these 3 questions (calculating positive and negative numbers)

The least common denominator is (x+5)(x-8).

identify the denominator of  [tex]\frac{8}{x^2 -3x -40}[/tex]  , [tex]\frac{-2}{x^2 -8x}[/tex]

::[tex]x^2 -3x -40[/tex] , [tex]x^2-8x[/tex]

Find the least common multiple of :[tex]x^2 -3x -40[/tex] , [tex]x^2-8x[/tex]

x(x+5)(x-8)

In arithmetic and number theory,  the smallest amount  common multiple, lowest  integer , or smallest  integer  of two integers a and b, usually denoted by least common multiple(a, b),  is that the  smallest positive integer that is divisible by both a and b.Since division of integers by zero is undefined, this definition has meaning  as long as  a and b are both different from zero. However, some authors define least common multiple(a,0) as 0 for all a, since 0  is that the  only common multiple of a and 0.

The least common multiple  is that the  "least common Denominator" (lcd) that can be used before fractions can be added, subtracted or compared.

The least common multiple of more than two integers a, b, c, . . . , usually denoted by least common multiple(a, b, c, . . .),  is additionally  well defined: It is the smallest positive integer that is divisible by each of a, b, c, . . .

A multiple of  variety  is the product of that number and an integer.  for instance , 10  may be a  multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5  and a couple of . Because 10  is that the  smallest positive integer that is divisible by both 5 and 2,  it's  the least common multipleof 5 and 2.

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If you are emphasizing on the fact that these are its only real roots, then maybe the function has any other 2 imaginary roots, so there wouldn't be any specific equation that you're looking for.

However if you mean that these real roots are the only roots of this function, meaning that they are double roots, we can argue that:

[tex]f(x) = (x + 4) {}^{2} (x + 1) {}^{2} \\ f(x) = (x {}^{2} + 8x + 16)(x {}^{2} + 2x + 1) \\ expand \: by \: multiplying \: each \: term \: by \: the \: other \: 3 \\ f(x) = x {}^{4} + 10x {}^{3} + 33x {}^{2} + 40x + 16[/tex]

The solving of equation 3²x=4 in both the given cases gives the answer x = 0.631.

So,

(1) Common logarithm:

(2) Logarithm with base 3:

Therefore, the solving of equation 3²x=4 in both the given cases gives the answer x = 0.631.

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Answer:

8.5

Step-by-step explanation:

11-3/2-1

11-1.5-1

9.5-1

8.5

Answer:

Step-by-step explanation:

A=(3,-6) B=(1,2) C=(7,-1)

The total number of boxes required to cover the kitchen floor is 14.

The dimensions of the kitchen floor are 14' × 24'

⇒Length of the kitchen floor = 14 feet

⇒Width of the kitchen floor= 24 feet

The area of the kitchen floor= Length × Width

⇒ Area = 14 × 24

⇒ Area = 336 sq. ft.

Since, 4 boxes of flooring cover 100 sq. ft.

∴1 box will cover = 100/4 sq. ft.

⇒25 sq. ft.

Now, Number of boxes required to cover the floor of the kitchen will be,

⇒ Area of the floor / Area covered by 1 box of flooring

⇒336/25

⇒ 13.44

∴ The total number of boxes required to cover the kitchen floor is 14 (rounded up from 13.44).

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After the inverse variation y = -28 when x = 2.

So,

To convert to an equation, multiply by k, the variation constant.

To find k, apply the given condition.

x = 8 when y = -7:

So, the equation is: y = -56/x

Therefore, y = -28 when x = 2.

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Answer:

(x-1)(x+1+3)=(x-1)(x+4)

Answer:

Rs 140

Step-by-step explanation:

Rs 25 is the amount of money she bought the apples

Rs 32 is the amount of money she sold the apples

32 - 25 = $7 profit per apple

7 Rs multiplied by 20 apples is equal to Rs 140 in profit.

Hope this helps!

Answer:

[tex] \frac{3}{5} [/tex]

Step-by-step explanation:

[tex] -\frac{ 9}{10 } \times - \frac{2}{3} [/tex]

you're going to cancel the 9 using the three then, cancel the 10 using the 2 then you'll have

[tex] - \frac{3}{5} \times - \frac{1}{1} [/tex]

then you will get your answer after finding the product and remember a negative multiplied by a negative is a positive , therefore we. have a positive answer

To find the difference of two expressions, we can write them in a subtraction sentence:

[tex](5x-4) -( 2x+4)[/tex]

Solve:

[tex]= 5x-4 -2x-4\\= 3x-4 -4\\= 3x-8[/tex]

3x-8

The total amount of that Harry will need for the project is nineteen and one third feet and Hence the option B is correct.

Addition of Fraction

Wood 1:

Length of each = 2 3/4 feet

Number of pieces = 4

Total = Length of each × Number of pieces

= 2 3/4 × 4

= 11/4 × 4

= 11 meters

Wood 2:

Length of each = 1 2/3 feet

Number of pieces = 5

Total = Length of each × Number of pieces

= 5/3 ×5

= 25/3 meters

Total amount of wood needed for the project = 11meters + 25/3 meters

= 11 +25/3

= (33+25)/3

= 58/3

=19 1/3 meters

Therefore, the total amount of wood that Harry will need for the project is nineteen and one third feet

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The given equation 5n – 6 > 8n – 3n does not satisfy the inequality conditions.

The given inequality is;

5n – 6 > 8n – 3n

Ad 3n on the both side of inequality.

5n – 6 + 3n > 8n – 3n + 3n

Now, subtract the variable part,

8n - 6 > 8n

Subtract 8n both side.

8n - 6 - 8n > 8n - 8n

0 - 6 > 0

-6 > 0

But, -6 not not greater than 0.

Thus, the inequality is not valid.

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The wage of Katie before pay rise or the value of old wage is equal to $220.

What is percentage ?

Percentage is calculated by dividing the value by the total value, and then multiplying the result by 100.

It is given that the new wage is $264 as Katie gets a 20% pay rise.

Let's assume the old wage be x.

The new wage can be written as :

x + (20x / 100)

This is equal to $264.

i.e.,

(x + 20x/100) = 264

or

120x/100 = 264

Let's solve this expression to get the value of old wage.

120x = 264 × 100

or

120x = 26400

or

Old wage (x) = $220

Therefore , the wage of Katie before pay rise or the value of old wage is equal to $220.

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Answer:

9.53 x 10^5

Step-by-step explanation:

a x 10b

a = 9.53

b = 5

Answer:

9.53

Step-by-step explanation:

math math math math math math

The equivalent equation for the given equation is 5n+10d=365. Therefore, option A is the correct answer.

The given equation is 0.05n + 0.1d = 3.65.

Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.

Now, multiply by 100 on both sides of the given equation.

That is, 100(0.05n + 0.1d) = 3.65×100

⇒ 0.05n×100+0.1d×100=365

⇒5n+10d=365

The equivalent equation for the given equation is 5n+10d=365. Therefore, option A is the correct answer.

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All the expressions have a value of 3 except the expression 6 - 5.3.

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

The math operation can be addition, subtraction, multiplication, or division.

We have,

-3( 4 - 5 )

= -3 x -1

[minus x minus = positive]

= 3

|-2| + 1 ( 3 - 2)

The absolute value is always positive.

= 2 + 1 x 1

= 2 + 1

= 3

-8 ÷ -4 + 1

Minus gets canceled.

= -8/-4 + 1

= 2 + 1

= 3

6 - 5. 3

= 6 - 15

= -9

Thus all the expressions have a value of 3 except the expression

6 - 5.3.

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-7² = -49

Given options are as follows -

a. (-6)^2

b. (1/3)^2

c. 0.5^2

d. -7^2

by solving 1 option we get

(-6)×(-6)

= 36

we get a positive value

because we know that (-)×(-) = +

so this option is not less than zero

again by solving 2 option we get

1/3^2

1/3× 1/3

= 1/9

it is also a positive value

because we know that (+)×(+) = +

so this option is not less than zero

Further by solving 3 option we get

(0.5)²

(0.5)×(0.5)

= 0.25

again it is also a positive value

so this option is not less than zero

but for the option 4

-(7)²

= -49

which is a negative value .

A negative number is any number that is less than zero

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For the relations in this problem, we have that:

1.

2.

3.

A relation represents a function if each value of the input is mapped to only one value of the output.

For a point in the format (x,y), we have that:

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.

In a graph, the domain and the range are found as follows:

For the first relation, we have that input 10 is mapped to outputs 20 and 50, hence:

For the second relation, we have a graph with no vertically aligned points, hence:

For the third relation, we have a graph with vertically aligned points, hence:

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Answer:

x = 11

Step-by-step explanation:

3x = 2 + 31​

To find the value of x, combine like terms

3x= 33

Divide each side by 3

3x/3 = 33/3

x = 11

Find the value of x.

3x = 2 + 31

x = 11

=> 3x = 2 + 31

First, add the like terms.

=> 3x = 33

Transfer 3 to RHS

=> x = 33/3

Divide 33 by 3

=> x = 11

Solution :

Properties of Functions:

Definition of a Function: A function is a rule or formula that associates each element in the set X (an input) to exactly one and only one element in the set Y (the output). Different elements in X can have the same output, and not every element in Y has to be an output.

Definition of the Domain of a Function: The set of all possible inputs of a function is defined as the domain. The domain of a real-valued function defined by a formula for y in terms of x will be the set of all x input-values that result in a real y output-value unless the domain of the function is further restricted.

Definition of the Range of a Function: The set of all possible outputs of a function is defined as the range. The range of a real-valued function defined by a formula for y in terms of x will be the set of all y output-values that result from the x input-values in the domain.

Function Notation: Given that f(x) is given by some formula containing x, f(B) will be the same formula with each x replaced by B.

Linear Function Definition: If a function may be written in the form f(x) = mx + b where x is the independent variables and m and b are constants, then f(x) represents a linear function. The variable m is defined as the slope and the point (0, b) represents the y-intercept. An equation in this form is known to be in Slope-Intercept Form.

Linear Function Slope Definition: Given that f(x) = mx + b, then m is defined as the slope where:

for any two points (x1, y1) and (x2, y2) on the line.  Graphically, the slope represents the change in y with respect to x on the graph of the line.

Linear Functions of Parallel Lines If two linear functions are given by f(x) = m1x + b and g(x) = m2x + b, and m1 = m2, then the graphs of f(x) and g(x) will consist of two lines that are parallel to each other.

Linear Functions of Perpendicular Lines If two linear functions are given by f(x) = m1x + b and g(x) = m2x + b, and m1 = -1/m2, then the graphs of f(x) and g(x) will consist of two lines that are parallel to each other.

Graphs of Even Functions Given a function f(x), if f(c) = f(-c) for all c in the domain, then f(x) is an even function and its graph will have symmetry with respect to the y-axis.

Graphs of Odd Functions Given a function f(x), if f(c) = -f(-c) for all c in the domain, then f(x) is called an odd function and its graph will have symmetry with respect to the origin.  Symmetry with respect to the origin implies that a 180-degree rotation of the graph about (0,0) results in an identical graph.

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Answer:

1.  y-intercept = 5

2.  x-intercept = -2.5

3.  slope = 2

4.  y = 2x + 5

Step-by-step explanation:

Part 1

The y-intercept is the point at which the line crosses the y-axis, so when x=0.  From inspection of the given graph, the y-intercept is 5.

Part 2

The x-intercept is the point at which the line crosses the x-axis, so when y=0.  From inspection of the given graph, the x-intercept is -2.5.

Part 3

The slope of the line is the measure of its steepness.  To find the slope of a line, substitute two points on the line into the slope formula.

Two points on the line are the y-intercept and the x-intercept:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-5}{-2.5-0}=\dfrac{-5}{-2.5}=2[/tex]

Therefore, the slope of the line is 2.

Part 4

Slope-intercept form of a linear equation:

[tex]\boxed{y=mx+b}[/tex]

Where:

Substitute the found slope and y-intercept from Part 3 and Part 1 into the formula to create an equation for the line:

[tex]y=2x+5[/tex]

The probability of taking out a pencil from the bag having 9 pens, 7 pencils and 6 crayons is 0.32.

We are given that:

We have-

Number of pens = 9

Number of pencils = 7

Number of crayons = 6

Now, the total number of objects in the bag = 9 + 7 + 6

Now, the total number of objects in the bag = 22

We have to find the probability of taking out a pencil from the bag.

P ( taking out a pencil from the bag ) = 7 / 22

P ( taking out a pencil from the bag ) = 0.32

Therefore, we get that, the probability of taking out a pencil from the bag having 9 pens, 7 pencils and 6 crayons is 0.32.

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The required set of positive two-digit even numbers less than 25 that do not contain the digit 0 is 12,14,16,18,22,24.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.

Given:

Set D is the set of positive two-digit even numbers less than 25 that do not contain the digit 0.

According to given question we have

2-digit numbers are the numbers that have two digits and they start from the number 10 and end on the number 99.

Starting at 12 going up the two digit numbers even numbers less than 25 that do not contain the digit 0.

12,14,16,18,22,24

Therefore, the required set of positive two-digit even numbers less than 25 that do not contain the digit 0 is 12,14,16,18,22,24.

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Answer:

Javier gets to 1000 first in 23 weeks

Step-by-step explanation:

Let J = Javier

Let S = Shane.

S = 640 + 15 every week.

J = 425 +25 every week. Make a time chart.

640 (week 0), 655 (week 1), 670 (week 2), 685 (week 3), 700 (week 4), 715 (week 5), 730 (week 6), 730 (week 7), 745 (week 8), 760 (week 9), 775 (week 10), 790 (week 11), 805 (week 12), 820 (week 13), 835 (week 14), 835 (week 15), 850 (week 16), 865 (week 17), 880 (week 18), 895 (week 19), 910 (week 20), 925 (week 21), 940 (week 22), 955 (week 23),

425 (week 0), 450 (week 1), 475 (week 2), 500 (week 3), 525 (week 4), 550 (week 5), 575 (week 6), 600 (week 7), 625 (week 8), 650 (week 9), 675 (week 10), 700 (week 11), 725 (week 12), 750 (week 13), 775 (week 14), 800 (week 15), 825 (week 16), 850 (week 17), 875 (week 18), 900 (week 19), 925 (week 20), 950 (week 21), 975 (week 22), 1000 (week 23)

You can replace the values in a problem with letters or words so that it's easier to use mental math to complete the computation.

This is further explained below.

Generally, A word may also refer to both a string of letters that are denoted by a certain meaning and the space that separates those characters from one another.

A graphic representation of a spoken sound is often written or printed and is the basic building block of an alphabet.

In conclusion, You may make it simpler to compute using mental math by changing the numbers in a problem to letters or words, which will make it possible for you to solve the issue more quickly.

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Answer:

d=1, 1+12=13 Variable can be a number or any number .

The inequality to represent the last statement that was made by Mai will be t <= 2.

It should be noted that an equation simply means the relationship that can be used to show the relationship among the variables.

It should be noted that the last statement made by Mai is that I think triathlon athletes generally train for no more than 2 hours a day.

Therefore, the inequality to represent this will be t <= 2.

where t = number of hours trained.

This implies that t is less than or equal to 2 hours

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Mai said, "I'm not sure the graph is right. For example, the point is in the shaded region, but it's not realistic for an athlete to swim for 10 hours and bike for 3 hours in a training session! I think triathlon athletes generally train for no more than 2 hours a day."

Write an inequality to represent Mai's last statement.

The inverse for the function f (x) = 2 / 3 x - 3 will be f ⁻¹ (x) = 3 / 2 x + 9 / 2.

We are given the function:

f (x) = 2 / 3 x - 3

we need to find the inverse of the function.

First we will write the function in the form of x.

y = 2 / 3 x - 3

y + 3 = 2 / 3 x

2 x = 3 y + 9

x = 3 / 2 y + 9 / 2

So, the inverse function will be:

f ⁻¹ (x) = 3 / 2 x + 9 / 2.

Therefore, the inverse for the function f (x) = 2 / 3 x - 3 will be f ⁻¹ (x) = 3 / 2 x + 9 / 2.

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