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Answer:

i. (10-y)(100x^2 +10xy + y^2)

ii. See the explanation

Step-by-step explanation:

i. 1000x³-y³ =

10³x³ - y³ =

(10x)³ - y³ =  ==> use formula: x³ - y³ = (x-y)(x^2+yx+y^2)

(10-y)((10x)^2 +10xy + y^2) =

(10-y)(10^2 * x^2 +10xy + y^2) =  ==> simplify

(10-y)(100x^2 +10xy + y^2)

ii. 992/124=

(992-192)/(124-24)=

800/100 = 8

As a result, 8*124=992.

Hence, 124 (and 8) is a factor of 992

The fraction 2.666666666667 equals   [tex]\frac{8}{3}[/tex] .

A fraction is used to represent a portion/part of something larger. It symbolises the equal parts of the whole. A fraction is comprised of two components the numerator and the denominator. The top number is referred to as that of the numerator, and the bottom number is known as the denominator. The denominator specifies the total number of equal parts in a whole, whereas the numerator describes the number of equal parts taken.

1. Assume that x = 2.666667 (1)

2. Six is the repeating digit.

To the left of the decimal point, put the repeating digit.

In this instance, multiply the decimal point by 10 to move it one place to the right.

Thus,

(x = 2.666667) * 10

Equation 10x = 26.66667 (2)

4. Take Eq. (1) away from Eq (2)

10x - x = 26.66667 - 2.666667

9x = 24

9 divided by both sides

x = [tex]\frac{24}{9}[/tex] or [tex]\frac{8}{3}[/tex]

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A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.

Example of Function is f(x) = 2x + 5.

A formula, rule, or legislation that specifies how one variable (the independent variable) and another variable are related (the dependent variable).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.

Based on Elements

Based on Equation

Based on the Range

Based on the Domain

Example of Function is f(x) = 2x + 5.

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Answer:

we know that

The rule of the translation is

That means

The translation is  units to the right and   units down

therefore

the answer in the attached figure

Step-by-step explanation:

In this given equation, any value of x and y will work, which will cause it to have infinite number solutions

What is an equation?

An equation is a mathematical statement showing that two or more values or mathematical expressions are equal or equivalent.

We represent an equation with the equation symbol (=).

Given the equation:

3x + 2y = 5

The lineear equation has infinitely many solutions

We know the standard form of a linear equation is:

ax + by = C

In this given equation, any value of x and y will work, which will cause it to have infinite number solutions

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It is a AAA similarity theorem If and only if the corresponding sides of two triangles are in proportion, they will have identical corresponding angles.

According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.

Theorem: Two triangles have identical corresponding angles if and only if their corresponding sides are proportionate.

It can also be rephrased as the AAA (angle-angle-angle) similarity theorem.

A triangle is said to be comparable to another triangle if any two of its three angles are equal to any two of its three angles.

Therefore, it is a AAA similarity theorem If and only if the corresponding sides of two triangles are in proportion, they will have identical corresponding angles.

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The standard From of the quadratic Function is (−2,3).

y=-3x²-12x-9

Find the given parabola's characteristics.

To continue, tap...

Opens down in the direction of ( 2, 3), with

( -2, 35 /12) as the focus.

x = 2 is the symmetry axis.

The directrix is y = 37 /12

By entering a few x values into the equation, you may get the associated y values. You should choose the x values close to the vertex.

To continue, tap...

x y − 4 − 9 − 3 0 − 2 3 − 1 0 0 − 9

Using the chosen points and the parabola's attributes, draw the curve.

Opens downward in direction

Focus: ( 2, 35 12) Vertex: ( 2, 3)

x = 2 is the symmetry axis.

The following directrix: y = 37 12 x y 4 9 3 0 2 3 1 0 0 9.

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The number of zeros for each function is given as follows:

1. Three zeros.

2. One zero.

3. Two zeros.

The number of zeros for each function is obtained looking at the graph of the function, counting the number of times that the function either touches or crosses the x-axis, which is the horizontal axis.

Thus the graph for each function is plotted, using a graphing calculator, as shown by the image at the end of the answer, and the number of zeros for each of the functions is given by the number of times that the function touches or crosses the x-axis.

The colors of each function are given as follows:

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Answer:

All the sides of the square are equalso the squares are congruent.. Are congruent shapes? Two shapes that are the same size and the same shape are congruent.

hope this helps

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Step-by-step explanation:

In grade 11 math, the slope is a concept that is typically introduced in the study of linear equations and graphing.

The slope of a line serves as a gauge for its steepness. It is defined as the change in y (the vertical distance) divided by the change in x (the horizontal distance) between two points on the line.

A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope rises as it goes from left to right, while a line with a negative slope falls as it goes from left to right. A line with a slope of zero is horizontal, while a line with an undefined slope is vertical.

The slope is often represented by the letter m in the equation of a line, which is written in the form y = mx + b. The slope of the line is the coefficient of the x term (the m in the equation).

For example, the slope of the line represented by the equation y = 3x + 4 is 3, while the slope of the line represented by the equation y = -2x + 1 is -2.

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The Excel formula to enter in cell H4 is = (G4 + 14)

Excel formulas are expressions used to perform computation.

To determine the formula:

From the question,

The date the client was last contacted is in cell G4

14 days is to be added to the content of cell G4

So, the formula is:

G4 + 14

Add bracket

(G4 + 14)

Excel formulas begin with the equality (=) sign

So, we have:

= (G4 + 14)

Hence, the formula to enter the cell H4 is = (G4 + 14)

Complete question:

In the cell, H4 creates a formula without a function that adds 14 days to the date the client was last contacted cell G4

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Excel formulas are expressions used to perform computation.

The date the client was last contacted is in cell G4

14 days is to be added to the content of cell G4

So, the formula is:

G4 + 14

Add bracket

(G4 + 14)

Hence, the formula to enter the cell H4 is = (G4 + 14)

In the cell, H4 creates a formula without a function that adds 14 days to the date the client was last contacted cell G4

Answer:

infinite, no solutions, and uniquely solution

Step-by-step explanation:

Answer:

Binomial,Trinomial,Monomal,Linear equation

Step-by-step explanation:

The statement is "a car wash operator wants to see if offering a discount to local residents would create a greater income." This is an observational study.

A method of study in which participants are observed or certain outcomes are measured. There is no attempt made to change the outcome (for example, no treatment is given).

Experimental investigations include introducing an intervention and observing its results. Experimental investigations are frequently randomized, which means that the individuals are assigned to groups at random. People who qualify are randomly allocated to one of two or more groups in a randomized controlled experiment (RCT).

Cohort studies, case-control studies, and cross-sectional studies are the three different kinds of observational research.

In an observational study, the researchers just observe the participants without interfering with them or attempting to sway the results. In other words, neither the researchers nor the individuals are placed in experimental groups or in charge of the therapies.

Thus, the above mentioned statement is an observational study.

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Part A

Adding the costs, [tex]2s+5t=49.50[/tex].

Since a pair of shorts costs twice as much as a T-shirt, [tex]s=2t[/tex].

The correct answer is option 3.

Part B

[tex]2(2t)+5t=49.50 \\ \\ 9t=49.50 \\ \\ \boxed{t=5.50} \imploes \boxed{s=11}[/tex]

If a local park is open for biking every 12 day open for paddling every 8 day and if today the park is open for both options, then the next date when the park will be open will be on the 24th day. So Hana should pick 24th day from today next.

Every 12 day the local park is open its path for biking and every 8 day they open their lake or paddling. That is in every multiple of 12 days the biking option is available and every multiple of 8 days the paddling option is available.

If today both the biking and paddling option are open, then the next day where both options will be open can be determined by calculating the least common multiple of 12 and 8.

12 = 2×2×3

8 = 2×2×2

LCM (12, 8) = 2×2×2×3

LCM(12, 8) = 24

LCM of 12 and 8 is 24. So 24 days from today, the park will be open for both options.

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Answer:

23

Step-by-step explanation:

Given in the picture below (BODMAS rule is applied)

I hope my answer helps you

Answer:

Step-by-step explanation:

5 + 2 x 3² =                         (remember PEMDAS)

5 + 2 x 9 =

5 + 18 =

23

To compare two numbers, a, and b, we can write two inequalities:

a < b when a is less than b

a > b when a is greater than b.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We may write two inequalities to compare two numbers, a and b:

a < b

a > b

If a is less than b, then the first inequality is true and the second is false. If a is greater than b, then the first inequality is false and the second is true. Otherwise, if a and b are equal, then both inequalities are false.

We can determine which inequality is true by comparing the values of a and b and using the rules of inequality.

For example, if a=3 and b=5, then we can determine that a < b is true and a > b is false because 3 is less than 5.

On the other hand, if a=8 and b=2, then we can determine that a < b is false and a > b is true because 8 is greater than 2.

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The table that shows the correct t and d values is

Distance Covered (m)           Time Taken (hr)

8                                               6

32                                              15

How to determine the correct values for t and d

The table of values is given as:

Distance Covered (m)           Time Taken (hr)

8                                               6

16                                              12

32                                              15

48                                              18

The distance covered in 15 hours is 32 m and the time taken to cover 8 m is 6 hours

When these values are extracted, we have:

Distance Covered (m)           Time Taken (hr)

8                                               6

32                                              15

The above represents the table that shows the correct t and d values

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The (a) Hole in the expression is x, (b) The vertical assumption is -10 and (c) the horizontal assumption is that the denominator is greater than the numerator.

You should know that a hole occurs if there is a common term between the the numeration and the denominator when factorized, For vertical assumption, the denominator must be equal to zero and horizontal assumption, numerator will be equal to denominator

The given expression is:

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

The Hole is

Factorize the numerator= x²-2x

x is common in the expression

x(x-2)

Factorize the denominator= x³-9x²-10x

x(x²-9x-10)

= [x²-10x+x-10]

x[(x²-10x)+(x-10)]

Simplify further to get

x[x(x-10)+1(x-10)]

=x[(x+1)(x-10)]

Combine numerator and denominator to see the hole

[tex]\frac{x(x-2)}{x(x+1)(x-10)}[/tex]

From the expression the hole is x

b. vertical assumption

The denominator =0

x³+9x²-10x=0

Differentiate to have

dy/dx= 3x²-18x-10

2nd order derivative is

d2y/d2x=6x-18

Applying limit as x approaches 0

6x-10

Therefore x=-10

c. horizontal assumption the numerator is less than the denominator

x²-2x<x³-9x²-10x

In conclusion, the Hole in the expression is x, The vertical assumption is -10 and the horizontal assumption is that the denominator is greater than the numerator.

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at least 67 inches, but at most 73 inches if  Jed can be 67 inches or

shorter

The  inequality in which involves one or more rational expressions is Rational inequality.

What is inequality?

Using the terms greater than, larger than or equal to, less than, or less than or equal to as a declaration of the order connection between two integers or algebraic expressions is known as inequality. Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income (the amount of money people are paid) (the amount of wealth people own). There are significant forms of economic inequality amongst various groups of people in addition to economic disparity between nations or states.

An inequality with a rational expression is said to be rational. Inequalities with rational expressions, such as 32x>1, 2xx34, 2x3x6x, and 142x23x, are referred to as rational inequalities.

67 ≤ x ≤ 73 are the solutions to the absolute value inequality |x − 70| ≤ 3

the complete question is

What are the solutions to the absolute value inequality |x − 70| ≤ 3? Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3 or as x − 70 ≤ 3 and x − 70 ≥ −3.

Answer: 67 ≤ x ≤ 73

Remember, Jed's height is within 3 inches of Pablo's height.

Describe the solutions in words.

Jed can be

67 inches or shorter.

at least 67 inches, but at most 73 inches.

73 inches or taller.

67 inches or shorter, or 73 inches or taller.

Just found out it's the 2nd choice.

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Answer:

B: at least 67 inches, but at most 73 inches.

Step-by-step explanation:

The number of CDs that can be bought are { 5, 4, 3, 2, 1 }.

What is an inequality ?

A relationship between two expressions or values that is not equal to each other is referred to as "inequality" in mathematics. So inequality emerges from an imbalance.

Given, No. of CDs = x

A CD costs $11 and He has total $60.

So, According to the question,

No. of CDs × Cost of each CD ≤ 60

                                         x × 11 ≤ 60

                                         11x ≤ 60

                                          x ≤ 60/11

Since the number of CDs can't be in fraction and The maximum CDs can be bought is 5.

So, The possible No. of CDs that can be purchased are { 5, 4, 3, 2, 1 }

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The value of a is ( x - 5 ) factor of f (x) = x ³ - 3x²  + ax -10 is found to be 8 .

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used.

Let f (x) = x ³ - 3x²  + ax -10 be the given polynomial.

By factor theorem,  ( x - 5 ) is the factor of f (x) , if f ( 5 ) = 0

Therefore,

f ( 5 ) = 3 ( 5 )²  + a ( 5 ) - 10 = 0

           125 - 75 + 5a - 10 = 0

            5a = -40

            a = -8

Hence, a = -8

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The linear inequality represented by the graph is given as follows:

y < 1/4x + 2.

The dashed line is a linear function, hence the slope-intercept format of the inequality is given as follows:

y < mx + b.

(the sign is < because the line is dashed and not solid).

In which the coefficients are given as follows:

The line crosses the y-axis at y = 2, hence the intercept b is given as follows:

b = 2.

When x = -8, y = 0, thus when x increases by 8, y increases by 2, meaning that the slope is given as follows:

m = 2/8

m = 1/4.

Thus the inequality is given as follows:

y < 1/4x + 2.

The graph of the linear inequality is given by the image shown at the end of the answer.

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The product rule must be used to find the number of strings of four decimal digits, that have exactly three digits that are 9s.

What is product rule ?

The Product Rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

To obtain the number of strings of 4 decimal digits that have exactly 3 digits that are 9s ; we use the product rule,

In first digit 1 possible way between 0 to 9

In second digit 1 possible way between 0 to 9

In third digit 1 possible way between 0 to 9

In fourth digit 9 possible ways between 0 to 9

That's mean 1 * 1* 1* 9* 4 = 36

Thus 36 possible ways.

The product rule must be used to find the number of strings of four decimal digits.

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Step-by-step explanation:

that means that we need to transform the equation so that we get a form

h = ...

A = ½h(b1 + b2) | multiply both sides by 2

2A = h(b1 + b2) | divide both sides by (b1 + b2)

2A/(b1 + b2) = h

that's it.

Shawna finds The correct answer as "explanatory variable: weight response variable: calories burned per minute."

In this scatterplot, the explanatory variable is the weight of the individuals and the response variable is the number of calories burned per minute. The explanatory variable is the variable that is being manipulated or tested in the study, while the response variable is the variable that is being measured or observed.

In this case, the study is examining the relationship between weight and calories burned per minute, with weight being the explanatory variable and calories burned per minute being the response variable. The other answer choices do not correctly identify the explanatory and response variables in the scatterplot.

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Answer:

4 is correct

Step-by-step explanation:

The Pythagorean Theorem states that because a pyramid's height, slant height, and apothem form a right triangle with slant height as its longest side:  (apothem)² + (height)² = (slant height)².

A pyramid is a three shape having a base that is a polygon and triangular sides that come together at the apex, which is located directly just above center of the base.

Let's start by taking a look at a pyramid with both the height, slant height, the apothem shown in order to demonstrate how to use the Pythagorean Theorem to get a pyramid's height.

a² + b² = c².

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