do you think that for every positive integer n there is a circle in the plane which contains exactly n lattice points in its interior?

The value of the sequence aₙ₊₁ is -5.5

The definition of the sequence is given as

8.0, 6.5, 5.0, 3.5, . . .

The above definitions imply that we simply subtract 1.5 from the previous term to get the current term

Using the above as a guide,

So, we have the following representation

aₙ₊₁ = aₙ - 1.5

From the question, we have

aₙ = -4.0

Substitute the known values in the above equation, so, we have the following representation

aₙ₊₁ = -4.0 - 1.5

Evaluate

aₙ₊₁ = -5.5

Hence, the value of aₙ₊₁ is -5.5

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Answer:

[tex]e\approx2.71828[/tex]

Step-by-step explanation:

I assume you mean [tex]\lim_{x \to 0} (1+x)^{\frac{1}{x}}[/tex], which is just the definition of the constant [tex]e[/tex], also known as Euler's Number.

Answer:

The function f(x)= 16-4x forms an arithmetic sequence when x=1,2,3,...

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive terms is always the same.

The function f(x) = 16 - 4x forms an arithmetic sequence when x = 1, 2, 3, ...

When x = 1, f(x) = 16 - 4(1) = 12

when x = 2, f(x) = 16 - 4(2) = 8

when x = 3, f(x) = 16 - 4(3) = 4

As you can see, the difference between any two consecutive terms is 4, which is the same for all terms, therefore the function f(x) = 16 - 4x forms an arithmetic sequence when x = 1, 2, 3, ...

On the other hand, the function f(x) = 8 (2)^x increases exponentially, so the values obtained would be not part of an arithmetic sequence. The function f(x) = x^2/5 has no common difference between the consecutive terms, so it is not an arithmetic sequence. The function f(x) = 4/x -2 is not an arithmetic sequence either, due to the division of 4 by x and the subtraction of 2.

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Answer:

0 slice of pizza

Step-by-step explanation:

Total no of slice is 12

Dwayne ate half (6 slice) and

Mark ate half (6 slice)

12 -6 -6 = 0

Given that there were 12 slices of pizza, if Dwayne ate half (6 slices) and Mark ate a quarter (3 slices) for example, there would be 3 slices left. However, the question doesn't specify how much pizza Mark ate.

This question involves a concept in Mathematics known as fractions. Dwayne and Mark ordered a pepperoni pizza that was cut into 12 slices. If Dwayne ate half of the pizza, he ate 12/2 slices, which equals 6 slices. Since the question does not specify how much pizza Mark ate, we cannot provide the exact number of slices left. However, if for example, Mark ate 1/4 of the pizza, he would have eaten 12/4 slices, which equals 3 slices. Therefore, the number of slices that were left after both of them finished eating, in this example, would be 12 - (6+3) = 3 slices remaining.

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No, only 21% of the seats were occupied if 117 children had seats in the stall. Yes, more than 60% of the seats were occupied if if 117 children had seats in the circles. 63% of seats were occupied.

Ratio: The numerical relationship between two numbers indicating how frequently one value contains or is included within the other.

Percentage: Whenever a quantity or ratio can be stated as a fraction of 100, it is said to be a percentage. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "%" is used to denote it.

According to question:-

3/4 of children had seats in the stalls.

if  117 children has seats in the stalls.

Let the number of children be x, since 3/4 had seats in the stall, we have:

3/4*x = 3/4x.

The 3/4 fraction of children was 117.

= 3/4 of x = 117

= 3x/4 = 117

3x =117 x 4

3x = 468

x = 156 children in total.

117 children has seats in the stalls and 39 had seats in the circle

The ratio of the number of adults to the number of children was 5:2= 5+2=7

To find the total number of people: represent as y and use the ratio of children. Thus, we have

2/7 of y = 156

2y/7 = 156

2y = 156x7

2y= 1092

y = 546

Thus, the total number of people there are 546 and they occupy 546 seats out of 2600 seats. Thus we have:

546 / 2600 = 0.21 = 21%.

If 117 children had seats in the circle, then we have, 117 x 4 = 468 (total number of children)

Then using the ratio: 2/7 of y = 468 =     2y = 468x7

2y = 3276

y= 1,638

Thus, the total number of people there are 1,638 and they occupy 1,638 seats out of 2600 seats. Thus we have:

1638 / 2600 = 0.63 = 63%.

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The total amount paid for the car is $13,200.00.

The simple interest formula is expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Convert the interest rate to decimal

Rate r = 3.5%

Rate r = 3.5/100

Rate r = 0.035

Plug the given values into the above formula and solve for accrued amount A.

A = P( 1 + rt )

A = $12,000( 1 + (0.035 × 3) )

A = $12,000( 1 + 0.105 )

A = $12,000( 1.105 )

A = $13,200.00

Therefore, the accrued amount is $13,200.00.

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This is the simplified form of the expression.

2x^2 + 4x - 9y^2 - 4y

Simplifying:

3x^2 + 2y^2 - x^2 + 4x - 5y^2 - 4y

The process of simplifying an expression involves combining like terms and eliminating any unnecessary terms. In the given expression, we have multiple terms that have the same variable and exponent, these are called like terms. Like terms can be combined by adding or subtracting their coefficients.

In this case, we have 3x^2 and -x^2, the x^2 terms have the same exponent and variable so they can be added together by combining their coefficients (3-1) = 2x^2.

3x^2 - x^2 + 4x - 5y^2 - 4y + 2y^2

Similarly, we have -5y^2 and 2y^2, the y^2 terms have the same exponent and variable so they can be added together by combining their coefficients (-5+2) = -3y^2.

The x terms and y terms are separated and not interacting with each other, so we can't combine them. Finally, we have -4y and 4x, they are not like terms and can't be combined.

So, we have 2x^2 + 4x - 3y^2 - 4y as the simplified form of the expression.

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Answer:

  180.1 g

Step-by-step explanation:

You want to know the mass of a radioactive isotope on the 19th day if it was 1200 g on the first day and decreased 10% per day.

The form of the equation for exponential decay is ...

  m(t) = a·b^(t-n)

where m is the remaining mass, 'a' is the amount on day n, and 'b' is the growth factor, equal to 1 plus the growth rate.

Here, we have a=1200 g on day n=1, and the growth rate is -10%, so ...

  b = 1 -0.10 = 0.90

That means ...

  m(t) = 1200·(0.90^(t -1))

On day 19, the beginning amount is ...

  m(19) = 1200·0.90^18 ≈ 180.1 . . . . grams

The mass of the sample at the beginning of day 19 is 180.1 grams.

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The other point on the graft points of coordinates is  (3,0)

(-3,-5) and (-3,0) satisfy the condition given.

The coordinates of a point is the values of the the two straight lines that intersected at that point.

A point on a vertical line has coordinates (3,12).

Since, the other points lie on that line, those must have same x component with pre-defined point (3,12)

This implies that  (3,12) and (3,0) satisfy the coordinates of the points

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Correct question:

A point on a vertical line has coordinates (3.12). Which points would be on the same line?

The graph of the inequality y ≥ -√6x  is attached below.

A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Given:

y ≥ -√6x

Find the coordinates by putting the value of x in the above inequality as shown below,

For x = 0, y ≥ 0

For x = 1, y ≥ -√6

For x = 2, y ≥ -2√6

For x = 3, y ≥ -3√6

For x = 4, y ≥ -4√6

For x = 5, y ≥ -5√6

For x = -1, y ≥ √6

Mark the above value on the graph, and find the solution.

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The best approximation of the area of a circle with a radius of 5 ft is 75.4 ft².

Area is a quantity that expresses the size of a two-dimensional figure or shape, or planar lamina, in the plane. It can be thought of as the amount of surface that the shape covers. Calculating the area of a shape or surface can be an important step in many mathematical problems. There are several methods for calculating area, including the use of geometric formulas and equations, as well as using tools such as a ruler or calculator.

This is calculated using the formula A=πr², where π is 3.14 and the radius is 5 ft. Thus, A=3.14 x 5² = 75.4 ft².

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To determine the value of an expression, substitution entails substituting numbers for letters.

In an algebraic statement, substitution refers to substituting the variables' (variables') letters with their numerical values. After that, we may calculate the expression's overall value.

To determine the value of an expression, substitution entails substituting numbers for letters.

Steps for the Replacement Method

x plus 3x equal to 32

4x equal to 32

xequal to 8

Therefore, the answer is -8.

The complete question is:

System of equations using substitution.

y=3x

x+y=-32

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The required solution of the given equation is x = y = -8.

The replacement strategy is the arithmetical technique to tackle synchronous straight conditions. As the word says, in this strategy, the worth of one variable from one condition is subbed in the other condition.

We have,

x = y

And 3x + y = -32

Then

3x + x = -32

4x = -32x

x = -8 = y

Thus, solution of equation x = y = -8.

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The perimeter of an equilateral triangle with sides (11x - 2) will be;

⇒ (33x - 6)

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The side of equilateral triangle = (11x - 2)

Now,

Since, The side of equilateral triangle = (11x - 2)

We know that,

⇒ The perimeter of equilateral triangle = 3 × Side

Thus, We get;

⇒ The perimeter of equilateral triangle = 3 × Side

                                                             = 3 × (11x - 2)

                                                             = (33x - 6)

Thus, The perimeter of equilateral triangle = (33x - 6)

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Using the concept of rounding off and with the numerical values provided, The answer is 1350 and 300 rounding to nearest tens.

Rounding off refers to the process of approximating a number to a nearby value that has a certain number of significant digits or decimal places. For example, rounding the number 3.14159 to two decimal places would give 3.14, and rounding the number 12345 to the nearest thousand would give 12000. Rounding is often used in situations where precise measurements are not necessary or when the precision of a calculation is limited by the available resources.

A real number is a value that can represent a quantity along a continuous number line, such as integers and fractions. Real numbers include both rational numbers, which can be expressed as the ratio of two integers (such as 3/4), and irrational numbers, which cannot be expressed as the ratio of two integers (such as the square root of 2). Real numbers can be positive or negative, and they can be expressed in decimal form or in fractional form.

426+926 = 1352

round to nearest tens, 1350

739-437 = 302

round to nearest tens, 300

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Inverse variation is the relationships between variables that are represented in the form of [tex]y=\frac{k}{x}[/tex], where [tex]x[/tex] and [tex]y[/tex] are two variables and [tex]k[/tex] is the constant value. It states that if one quantity's value rises, the other quantity's value falls.

We notice that the variation in values of one quantity depends on the variation in values of another quantity in our day-to-day lives. A variable's inverse variation in relation to another variable is known as inverse variation. It exemplifies the opposite relationship that exists between two quantities. As a result, a variable and another variable are inversely proportional.

In everyday life, there are numerous real-world examples of inverse variation. For instance:  If a train travels at a constant speed for a greater distance, it takes longer to complete the journey, and vice versa. On the other hand, if more people are assigned to a job, it takes less time to complete it.

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Answer:

Step-by-step explanation:

the answer is C

The slope of the line y = 1/2 x - 3 is equal to 1/2.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would use an online graphing calculator to plot the given equation in slope-intercept form. By critically observing the graph (see attachment), we can logically deduce that the y-intercept is equal to -3 while the slope's line is equal to 1/2.

In conclusion, the linear function does not represent a proportional relationship because the line didn't pass through the origin (0, 0).

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14. The value of 15 - 3.2 + 2(0.5) is 12.8

15. The value of -3/4 + (3/4 - 4/5) is - 4/5.

16. The value of -2(2 3/4) + (-2)(-1/4) is -5.

17. The value of -2(4.6 - 3.5) is -2.2

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator

The value of 15 - 3.2 + 2(0.5) is:

= 15 - 3.2 + 1

= 12.8

The value of -3/4 + (3/4 - 4/5) is:

= -3/4 + 4 - 4/5

= - 4/5.

1The value of -2(2 3/4) + (-2)(-1/4) is:

= -5 1/2 + 1/2

= -5.

The value of -2(4.6 - 3.5) is:

= -2(1.1)

= -2.2

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Therefore , the solution of quadratic equation comes out to be the provided expression's factor is x-8.

Regression modeling for one-variable equations uses the polynomial result x = ax2 + b + c=0. Given that this polynomial has a second order, the First Thesis of Algebra states that there is only one solution. It is possible to find both simple and sophisticated solutions. Four variables make up a "quadratic formula," as the name suggests. This implies that there may only be one squared word. In the equation "ax2 + bx + c = 0," which is widely employed to solve arithmetic problems, the three mathematical variables a, b, and c are frequently used to depict the unknown variable "X."

Here,

x²+6x+16 is the algebraic expression provided.

The following identity can be used to factorize this:

(x+a)(x+b)=x²+(a+b)x+ab

We must therefore first identify the elements of 16.

8×2=4×4=16

That is obvious as 8-2=6.

So, as indicated, we divided the statement.

=>x²+2x−8x−16

=>x(x+2)−8(x+2)

=>(x+2)(x−8)

In light of this, the provided expression's factor is x-8.

Therefore , the solution of quadratic equation comes out to be the provided expression's factor is x-8.

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Three out of the six points shown that is a solution to the equation 2x+y=6 is (1,-6), (-1,8), and (5, -4).

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The graph's points often show the relationship between two or more things.

By employing X and Y coordinates, a point is plotted on a coordinate plane.

If the equation 2x+y=6 is plotted on a graph along with the points (1,-6), (7,-3), (3,-5), (-1,8), (3,0), and (5,-4), the equation will be solved. Afterward, it can be seen that the line's connecting points are (1,-6), (-1,8), and (5, -4).

As a result, the graph's points are (1,-6), (-1,8), and (5, -4).

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The measures of the missing angles for m<1, m<2, m<3, m<4, and m<5 are 35°, 145°, 55°, 125°, and 55°, respectively.

[tex]$m \angle 1=$[/tex] 35°

[tex]$m \angle 2=$[/tex] 180° - 35° = 145°

[tex]$m \angle 3=$[/tex] 90° - 35° = 55°

[tex]$m \angle 4=$[/tex]180° - ∠5 = 180° - ∠3 = 180° - 55° = 125°

[tex]$m \angle 5=$[/tex]∠3 = 55°

When we have two sides and the angle between them, we have "SAS." Calculate the unknown side using the Law of Cosines, then find the lesser of the other two angles using the Law of Sines, and finally find the final angle by adding the three angles together to make 180 degrees.

The law of sines states that the ratio of a triangle's side length to the sine of its opposing angle is constant. Given enough data, it is possible to use the law of sines to determine the unknown angles and sides of a triangle. The law of sines states that the ratio of a triangle's side length to the sine of its opposing angle is constant.

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By solving a linear equation, we will see that lines are parallel only if x = 15.

Ok, so we know that:

Notice that angle 2 is on the third quadrant of the intersection at the top, and angle 4 is on the second quadrant of the intersection below.

The two lines will be parallel only if these two angles are supplementary, this means that the measures add up to 180°.

Then we need to solve this linear equation:

2x + 10 + 4x + 80 = 180

Now we can solve that for x.

2x + 4x + 10 + 80 = 180

6x + 90 = 180

6x = 180 - 90

6x = 90

x = 90/6 = 15

So the lines A and B are parallel if and only if x = 15.

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Answer: D. x+2/x^3+2

Step-by-step explanation:

x2+x−2/x3−x2+2x−2

x2+x−2/x3−x2+2x−2

(x−1)(x+2)/(x−1)(x2+2)

x+2/x2+2

Answer:

D. x > -2 and x ≤ 1

Step-by-step explanation:

-5 < 4x + 3 ≤ 7

-8 < 4x ≤ 4

-2 < x ≤ 1

x > -2 and x ≤ 1

The unknown value of the given expression is 750.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

Let x represents the square.

And y and z represent the triangle and star, respectively.

So, from the diagram we have,

x + 3y + z = 51   ....(1)

12x + 5z = 234   .....(2)

8x -6x + 3x = 60

That means,

x = 12

So, from the equation (2),

144 + 5z = 234

z = 18

Then y = 7.

Now, the required diagram in the equation form,

z(y+z-x) + x(y + z + z) = n

Substituting, the value of x, y and z,

n = 234 + 516

n = 750

Therefore, the unknown value is 750.

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Answer:2. and 4 it looks like

Step-by-step explanation:

Answer:

The ratio of paper bags to hard bags is 6:2, which can also be written as 6/2 = 3/1. This means that for every 3 units of paper bags, there is 1 unit of hand bags.

If there are 192 bags in total, and the ratio of paper bags to hard bags is 3:1, then there must be 3 + 1 = 4 parts in total. We can find the number of bags in each part by dividing the total number of bags by the number of parts: 192 bags / 4 parts = 48 bags/part.

Since there are 3 parts of paper bags for every 1 part of hard bags, there must be 3 * 48 bags/part = 144 paper bags. Answer: {144}.

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

The chance to get a blue marble at the start is 7/14 which is 50%

If you take out a blue marble, it becomes 6/14, then 5/14

5x6x7÷14=15 15%

The values of x and y are x= 24 and y=25

What are transversal lines ?

In geometry, a transversal is any line that intersects two straight lines at distinct points

3y and 75 are alternate interior angles that are equal

3y=75

=> y=75/3 = 25 degrees

4x+9 and 3y add up to 180 degrees

4x+9 + 3y = 180

=>  4x+9 + 3(25) = 180

=>  4x+9 +75 = 180

=>  4x+ 84 = 180

=> 4x = 180 -84 = 96

=> x= 96/4 = 24

The values of x and y are x= 24 and y=25

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Answer:

speed=distance/time

v= m/s

we will convert the hours to seconds

1 hour= 3600 secs

5hours =x secs

we cross multiply ❌

5 × 3600 = 18,000

converting minutes to seconds

60 minutes make one hour

so 60 × 15 = 900

18000+900= 18,900

380/18900= 0.02 ans