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A cup is 6.4 cm tall, not including a 0.6 cm lip. Cups are stacked inside one another. You may want to draw a diagram t
you see how the height of the stack of cups increases. Select the function that represents the height of a stack of cups
terms of the number of cups in the stack.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.

The most common symbols used in inequalities are:

">" (greater than): indicates that the value on the left side is larger than the value on the right side.

"<" (less than): indicates that the value on the left side is smaller than the value on the right side.

"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.

"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.

"≠" (not equal to): indicates that the values on both sides are not equal.

Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

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Answer:

20 students are randomly selected from the school.

One factor of 30 is 1. One multiple of 30 is 60. Multiples of a number are obtained by multiplying that number by any whole number. Therefore, when we multiply 30 by 2, we get 60, which is a multiple of 30.

One component of 30 is a number that partitions uniformly into 30 without leaving a remaining portion. For this situation, 1 is a variable of 30 since it separates 30 precisely.

One numerous of 30 is a number that can be gotten by duplicating 30 by another entire number. Products of a number are boundless, yet for giving a model, we should consider 60 as a numerous of 30. At the point when we duplicate 30 by 2, we get 60, and that implies 60 is a numerous of 30.

Along these lines, one component of 30 is 1, and one numerous of 30 is 60.

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The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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Answer:

Step-by-step explanation:

y = -3x + 3

-2x + 2y = 6

-2x + 2(-3x + 3) = 6

-2x - 6x + 6 = 6

-8x + 6 = 6

-8x = 0

x = 0

y = -3(0) + 3

y = 0+ 3

y = 3

(0, 3)

The linear and exponential equations for the amount of money in the banks indicates;

TCF Bank Equation

y = 100·x + 1000

Well Fargo Bank Equation

y = (1.06)ˣ

The number of years it will take for both accounts to have the same amount of money is about 17 years

An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.

The equation for calculating the amount in each bank, based on the details are;

TCF Bank;

Amount invested = $1,000

Amount added each year = 100·x

Well Fargo Bank Equation

The percentage of the amount earned as interest each year = 6% = 0.06

The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ

Therefore; y = 1000·(1.06)ˣ

When the amount in the two accounts have the same amount of money, we get;

1000·(1.06)ˣ = 100·x + 1000

Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1

(1.06)ˣ = 0.1·x + 1

Solving the above equation using the substitution method and graphing indicates that we get;

x = 0, and x ≈ 17.125732

Therefore, it takes about 17 years for the two accounts to have the same amount of money

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The median of the distances is M = 6.5 kilometers

Given data ,

To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arranging the given set of numbers in ascending order: {4, 5, 8, 11}

Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:

(5 + 8) / 2 = 13 / 2 = 6.5

Hence , the median of the given set {4, 5, 8, 11} is 6.5

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Answer:

4x² + 24x + 36

Step-by-step explanation:

(2x + 6)² = (2x + 6)(2x + 6) = 4x² + 12x + 12x + 36 = 4x² + 24x + 36

Answer:

perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4

On solving the provided question, by the help of BODMAS we can say that - Subtract 22 from both sides is the answer to the given question.

BODMAS and PEDMAS are both names for it in various places. This stands for exponents, parenthesis, division, multiplication, addition, and subtraction. The BODMAS rule states that parentheses must be answered before powers or roots (that is, of), divisions, multiplications, additions, and lastly subtractions. The BODMAS rule states that the degree (52 = 25), parenthesis (2 + 4 = 6), any division or multiplication (3 x 6 (bracket response) = 18), and any addition or subtraction (18 + 25 = 43) come before any other operations.

\(f/3 +22 = 17\)

\(f/3 +22 -22 = 17 -22\) Subtracting the same value from both sides keeps the equation equal.  

Then simplify. The \(+22 and -22= 0\) They "cancel"   \(17-22 = -5\)

\(f/3 = -17 f/3\) is now isolated-- by itself-- in the equation.

If we have to solve  f, the next step we to take is to multiply on the both sides by  3.

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(f ◦ g)(x) is the composition of f(x) with g(x), equivalently

(f ◦ g)(x) = f(g(x))

To get f(g(x)), replace every instance of x in the definition of f(x) with g(x):

f(x) = -x + 7   ⇒   f(g(x)) = f(√(x - 3)) = -√(x - 3) + 7

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

A

Step-by-step explanation:

To solve the equation 7x-3(x-6)=30, we need to use the distributive property to simplify the left-hand side of the equation:

7x - 3(x-6) = 30

7x - 3x + 18 = 30

4x + 18 = 30

Next, we need to isolate the variable term on one side of the equation. To do this, we can subtract 18 from both sides:

4x + 18 - 18 = 30 - 18

4x = 12

Finally, we can solve for x by dividing both sides by 4:

4x/4 = 12/4

x = 3

Therefore, the solution to the equation 7x-3(x-6)=30 is x = 3. Answer A is correct.

The value of \(f\) is \(0\), by using the concept of slope of a line.

The equation to find the slope of a line is given by:

\(\(\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}\)\)

Given that the slope is -8 and the points (-7, f) and (-6, -8) lie on the line, we can substitute the coordinates into the equation:

\(\(-8 = \frac{{-8 - f}}{{-6 - (-7)}}\)\)

Simplifying the equation:

\(\(-8 = \frac{{-8 - f}}{{1}}\)\)

Multiply both sides by 1:

\(\(-8 = -8 - f\)\)

Rearranging the equation:

\(\(-8 + 8 = -f\)\(0 = -f\)\)

The concept used in this problem is finding the slope of a line using two given points. The slope represents the rate of change of the line, indicating how much the line rises or falls for each unit of horizontal distance.

By substituting the coordinates of the two given points (-7, f) and (-6, -8) into the formula, we can calculate the slope.

Thus, the value of \(f\) is \(0\).

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15 is the value of x that will make the linear equation true .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

x + 5= 20

X = 20 - 5

x = 15

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There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Step 1 : Given the function below

Step 2: Write the function for h(3), this is done by substituting 3 for x in the function h(x) above

Step 3: Write the corresponding value for the function g(9) and an inverse function of R⁻¹ (3) on the table.

Step 4: Substitute the g(9) and R⁻¹ (3) values in the h(3) equation and simplify

Hence, the value of h(3) is -11

The second option is the correct answer.

Answer:

5670 usd

Step-by-step explanation:

27000×0.21=5670

1. The decrease in dollars in Tammy's investment account, based on a 7.5 percent decrease, is $615.

2. The balance in Tammy's investment account at the end of last year was $7,585.

The percentage is the proportion of a value in relation to another.

Percentages show how much a variable is contained in another.

The percentage gives the fractional value of the decrease in the investment account.

Initial investment = $8,200

Decrease in investment = 7.5%

Decrease in dollars = $615 ($8,200 x 7.5%)

Balance = $7,585 ($8,200 - $615)

Thus, we can conclude that Tammy's investment account decreased by $615, representing a 7.5% decrease.

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If the sum of the first 10 terms and the sum of the first 100 terms of a given arithmetic progression are 100 and 10, respectively, then the sum of the first 110 terms is -110.

Let 'a' be the first term of the sequence and let 'd' be the common difference of the sequence.

Let us use the formula for the sum of the terms in the arithmetic progression  - \(S_n = \frac{n}{2} (2a + (n-1)d)\)

The sum of the first 10 terms.

\($\frac{10}{2}(2a+9d)=100\)

that implies, 2a + 9d = 20      .............1

The sum of the first 100 terms.

\($\frac{100}{2}(2a+99d)=10\)

that implies, 2a+99d = 1/5      ........2

Solving equation 1 and equation 2, we get,

d = -11/50, a = 1099/100.

The sum of the first 110 terms is -

Sum = \($\frac{110}{2}(2a+109d)\)

       = 55(-2)

       = - 110

Therefore, The sum of the 110 terms is -110.

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We may conclude after answering the presented question that As a expression result, the total new land following the transaction is 92 acres.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

a. The sale reduced the overall land by 8%, therefore the new acreage is 92% of the original. As a result, two equivalent formulations for the additional acreage, let's call it "n," are as follows:

n = 0.92v

n = v - 0.08v

b. We may use any of the formulas from part 1 to calculate the new acreage (a). Here are two approaches:

In the equation n = 0.92v, substitute the initial acreage, "v."

To determine the new acreage, "n," simplify the equation.

For instance, if the initial acreage, v, is 100 acres, n = 0.92v = 0.92(100) = 92 acres.

As a result, the total new land following the transaction is 92 acres.

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Answer:

1200

1. X represents the number of buttons Markie has: 200 times 5 = x

2. 200 X 5 = 1000, so Markie has 1000 buttons

3. Add Markies Buttons and Johns buttons: 200 + 1000 = 1200

4. Sentence: John and Markie have 1200 buttons all together.

The constant that will be used in Digby's linear inequality will be 8.

What are linear inequalities, exactly?

Inequality is a mathematical statement that states that neither side is equal. When a link causes a non-equal comparison between two expressions, an inequality develops. The inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), replace the equal sign "=" in the sentence. In mathematics, inequalities are classified into three types: polynomial inequalities, rational inequalities, and absolute value inequalities.

The characters '<' and '>' denote severe inequalities, whereas " ≤ and ≥ " denote slack inequalities.

Now,

Given that The temperature during a winter day was less than 8 degrees Fahrenheit.

let x be the temperature in degree Fahrenheit

then the linear inequality to show the statement will be

x<8 where 8 is a constant

Hence,

          The constant that will be used in Digby's linear inequality will be 8.

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Answer:

The awnser is 8.

Step-by-step explanation:

i just know<33

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer:

2

Step-by-step explanation:

29 % 3 = 9

3x9 = 27

29 - 27 = 2

Answer:

4

Step-by-step explanation:

The statement means that there are 4 "groups"(stars) of 5 "items"(points), so there are 4 groups.

There were 4 stars and 5 points on each star we gets, The groups were there 4.

We have given that,

There were 4 stars and 5 points.

Any combination of a finite number of the operations of addition, multiplication, subtraction, and division

We have to determine How many groups were there

The statement means that there are 4 groups(stars) of 5 items(points), so there are 4 groups.

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Answer:

The equation is W = 1600 + .03S

Answer:

Y=6.3 and X=-3.15

Step-by-step explanation:

Plug in 0 for x and y in separate equations

-6(0)+3y=18.9

3y=18.9

3/3y=18.9/3

y+6.3

-6x+3(0)=18.9

-6x+18.9

-6/-6x+18.9/-6

x=-3.15

Answer:

13m²

Step-by-step explanation:

Area=6.5*4÷2=13

Answer:

13m

Step-by-step explanation:

1/2 × bas × perpendicular height