The area of a rectangular outdoor stage has been extended on one side. The entire new area in square meters can be written as 216+12x. Factor the expression to find the dimensions of the extended stage.

Answer:

0.333333...

Step-by-step explanation:

look this almost imposble but there is few ways that can give you an examples

divide 1 by 3 to divide fisrt put a 0 than dot becuze you can't devid it normaly naw give the 1 a 0 so it is ten so dived so 0.3 naw do it again so it endless but not infinty ok so thanks it is 0.3333333. sometimes pick ansear like this 0.3... or 0.3 white a line on top iv it

The fraction 1/3 is comparable to one third. As a result, it is a third of a sum.

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The value of [tex]\frac{\sqrt{12}}{\sqrt{10}}\cdot \frac{\sqrt{5}}{\sqrt{6}}[/tex] is closest to the whole number 1.

What is multiplication?

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

An expression,

[tex]\frac{\sqrt{12}}{\sqrt{10}}\cdot \frac{\sqrt{5}}{\sqrt{6}}[/tex].

Simplifying,

{(√2 × √6) / (√2 × √5)} × √5/ √6

= 1.

Therefore, the value is 1.

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On average, an atom's nucleus has a density of 2.31017 kg/m³.

According to nuclear density, the ratio of mass to volume inside an atom's nucleus determines its density. The nuclear density is highly high because the atomic nucleus makes up the majority of an atom's mass despite being relatively small in relation to the rest of the atom.

On average, an atom's nucleus has a density of 2.31017 kg/m³. Nuclear density is what causes this. It is the same for all nuclei since it is independent of the mass or size of the nucleus.

The nucleus is particularly dense because to its high mass and small size. A penny's worth of material would weigh more than 30 million tons if it had the same density as an atom's nucleus.

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The measure of each angle are 94.2° and 85.8°.

Let's call the measure of the first angle x.

Since the angle is supplementary to another angle, their measures add up to 180°.

So, the measure of the second angle is 180° - x.

Also, the first angle measures 8.4° more than the second angle, so:

x = (180° - x) + 8.4°

Solving for x:

2x = 188.4°

x = 94.2°

So the first angle measures 94.2° and the second angle measures 180° - 94.2° = 85.8°.

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Strategy should be, choosing purse A if number of days is less than 10,if it is more than 10 , he should choose purse B.

If there are 10 days, he can choose any of the purse.

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given,

Genie provides friend two purses,

Purse A and Purse B

Graph of Growth in amount to number of days is given.

By the graph,

Intersection point is on 10th day

Till 10th day Amount of purse A is grows more than amount of purse B.

After 10th day amount of purse B starts growing more than amount of purse A

Let no. of days be x

If x < 10, he should choose purse A.

If x > 10 he should choose purse B.

If x = 10, he can choose any purse.

Hence, Friend should choose purse A if number of days is less than 10.

Friend should choose purse B if number of days is greater than 10.

If number of days is 10, he can choose any of the purse.

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The slope of this line is m = 1.

An equation of this line is y = x.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

Substituting the parameters, we have:

y - 1 = 1(x - 1)

y = x - 1 + 1

y = x

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Answer:

5x + 8

Step-by-step explanation:

(20x + 32) / 4

5x + 8

The rate of change is 3.0, or three assignments are completed every hour when timed in hours.

m =  (6 - 3) miles / (2 - 1) hour = 3 miles / 1h

The rate of change is 3.0, or three assignments are completed every hour when timed in hours.

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The polynomial 5s2 + 5s - 30 can be factored as (s + 6)(s - 5). This is done by finding two numbers whose product is -30 and whose sum is 5. They are -6 and 5.

The factored representation of the polynomial 5s2 + 5s - 30 can be found by factoring. First, we need to find two numbers whose product is -30 and whose sum is 5. This can be done by trial and error or by using the Fundamental Theorem of Algebra. When these two numbers are found, the polynomial can be factored as (s + 6)(s - 5). To factor the polynomial, we can use the factor theorem. This states that if a and b are factors of a polynomial, then (x-a) and (x-b) are factors of the polynomial. In our case, a=6 and b=-5. So, the polynomial can be written as (s + 6)(s - 5). We can then use the distributive property to expand the polynomial and verify that it is the same as the original polynomial.

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The value of x is 3.

parallel lines are coplanar infinite straight lines that do not intersect at any point.

The lines l and m are the parallel lines.

3x-18+105=180

3x+87=180

Subtract 87 on both sides

3x=180-87

3x=93

Divide both sides by 3

x=31

Hence, the value of x is 3.

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The set S = {(6, 7, 1), (−3, 4, 7), (1, −3, 4)} spans  R³

For (x, y, z) ∈ R³, we can find scalars a, b, c for which the equation

(x, y, z) = a(6, 7, 1) + b (−3, 4, 7) + c (1, −3, 4) is true.

We can write above equation (x, y, z) = a(6, 7, 1) + b (−3, 4, 7) + c (1, −3, 4)  as system of equations,

6a - 3b + c = x

7a + 4b - 3c = y

a + 7b + 4c = z

Above system of equations in matrix form as,

[tex]\begin{bmatrix}6 & -3 & 1 \\7 & 4 & -3 \\1 & 7 & 4\end{bmatrix}\begin{bmatrix}a\\b \\c\end{bmatrix}=\begin{bmatrix}x \\y \\z\end{bmatrix}[/tex]

The determinant of coefficient matrix is,

[tex]\left|\begin{matrix}6 & -3 & 1 \\7 & 4 & -3 \\1 & 7 & 4\end{matrix}\right|=360[/tex]

Since the determinant of the coefficient matrix is not zero (it equals 360), the coefficient matrix is invertible.

This means, the system of equations must have solution.

Therefore, S = {(6, 7, 1), (−3, 4, 7), (1, −3, 4)} spans  R³

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The piece of cardboard needed will be 44 by 44 inches.

The volume of a square box can be defined as the space occupied by the square box or the cube, It is equal to the cube of the length of the side of the square box.

The formula for the volume is V = s³

The volume will be L*W*H

We are cutting 3 inches from each corner, so the length and width will each be x-6.

The height will be 4.

4332 = 4* (x - 6)* (x - 6)

1444= (x - 6)²

38 = x-6

x=44 inches.

The piece of cardboard needed will be 44 by 44 inches.

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The total surface area painted black is 12.6 sq. feet.

The surface area of a cone with height h and circumference of the base c can be calculated using the formula:

A = πr^2 + πrs,

where,

r = the radius of the base

s = the slant height.

We can find the radius of the base by dividing the circumference by 2π:

r = c / (2π)

  = 8π / (2π)

r = 4.

The slant height can be found using the Pythagorean theorem:

s = √(r² + h²)

  = √(4² + 12²)

  = √(16 + 144)

  = √(160)

s = 12.7279

So the surface area of each cone is:

A = πr² + πrs

= π * 4² + π * 4 * 12.7279

= 3.14 * 4² + 3.14 * 12.7279

= 50.265...

The base and 50% of the lateral surface are painted red, which is a total of 50% + 100% / 2 = 75% of the surface area.

So the total surface area painted black is:

(100% - 75%) * A

= 25% * A

= 25% * 50.265

= 12.566

Rounding to the nearest tenth, the total surface area painted black is 12.6 sq. feet.

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x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

This is the symmetric equation of the line that passes through the point P and is parallel to the vector .

What is symmetric equation?

A line that passes through the point P and is parallel to the vector v can be represented by the parametric equation:

x = -2 + 0t

y = 1 + 2t

z = 0 - 3t

where t is a scalar parameter. To find the symmetric equation of this line, we need to convert the parametric equation to a normal form. We'll start by finding a point on the line other than P, then use those two points to find the direction vector of the line. Let's use t = 1, then the line passes through the point Q(-2 + 01, 1 + 21, 0 - 3*1) = (-2, 3, -3). The direction vector of the line is found by subtracting the position vectors of P and Q:

d = Q - P = (-2 - (-2), 3 - 1, -3 - 0) = (0, 2, -3) = v

So, the direction vector and the vector v are equal, which means the line is parallel to v. Now we have two points on the line, P and Q, which we can use to find the symmetric equation of the line:

(x + 2)/0 = (y - 1)/2 = (z + 3)/(-3) = t

x + 2 = -2t

y - 1 = 2t

z + 3 = 3t

Rearranging the above equations, we get:

x = -2 - 2t

y = 2t + 1

z = 3t - 3

Since t is a scalar parameter, it can be eliminated from the equations to obtain the symmetric equation of the line:

x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

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x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

This is the symmetric equation of the line that passes through point P and is parallel to the vector.

What is the symmetric equation?

A line that passes through the point P and is parallel to the vector v can be represented by the parametric equation:

x = -2 + 0t

y = 1 + 2t

z = 0 - 3t

where t is a scalar parameter. To find the symmetric equation of this line, we need to convert the parametric equation to a normal form. We'll start by finding a point on the line other than P, then use those two points to find the direction vector of the line. Let's use t = 1, then the line passes through the point Q(-2 + 01, 1 + 21, 0 - 3*1) = (-2, 3, -3). The direction vector of the line is found by subtracting the position vectors of P and Q:

d = Q - P = (-2 - (-2), 3 - 1, -3 - 0) = (0, 2, -3) = v

So, the direction vector and the vector v are equal, which means the line is parallel to v. Now we have two points on the line, P and Q, which we can use to find the symmetric equation of the line:

(x + 2)/0 = (y - 1)/2 = (z + 3)/(-3) = t

x + 2 = -2t

y - 1 = 2t

z + 3 = 3t

Rearranging the above equations, we get:

x = -2 - 2t

y = 2t + 1

z = 3t - 3

Since t is a scalar parameter, it can be eliminated from the equations to obtain the symmetric equation of the line:

x + 2 = -2y + 2

y - 1 = 2z + 2

z - 3 = 3x + 6

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Answer:

The transformation to make the graph of y=1/x^2 into y=1/(x-2)^2 +3 involves shifting the graph horizontally by 2 units to the right, and vertically by 3 units up.

The transformation can be achieved by applying the following changes to the original equation:

Substitute x with (x-2) in the denominator of the fraction: 1/(x-2)^2

Add 3 to the fraction: 1/(x-2)^2 +3

This will give us the new equation y=1/(x-2)^2 +3, and the graph of this equation will be a parabola shifted 2 units to the right and 3 units up from the original graph of y=1/x^2.

Answer:

x = 5, -5

Step-by-step explanation:

3x² + 14 = 89

​3[tex]x^{2}[/tex] = 75

[tex]x^{2}[/tex] = 25

x = 5 or -5

By completing squares, we will see that the solutions of the given quadratic equation are:

x = -3 ± √(21/2)

Here we know that Inga is solving the quadratic equation below:

2x² + 12x - 3 = 0

The steps that she can do is try to complete squares, first we can take the 2 as a common factor to get:

2(x² + 6x) - 3 = 0

Now we can add 18 in both sides, then we will get:

2(x² + 6x) - 3 + 18 = 18

We can put that 18 inside the first term:

2(x² + 6x + 9) - 3  = 18

And now we can complete squares, because:

x² + 6x + 9 = x² + 2*3*x + 3² = (x + 3)²

Replacing that we will get:

2(x + 3)² - 3 = 18

2(x + 3)²= 18 + 3 = 21

2(x + 3)² = 21

(x + 3)² = 21/2

x = -3 ± √(21/2)

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As per the FIFO algorithm, there have been a total of 13 page faults.

The FIFO algorithm is a page replacement strategy used in operating systems to manage the allocation of memory frames to pages.

For the given reference string of

=> 1, 2, 3, 4, 5, 3, 4, 1, 6, 7, 8, 7, 8, 9, 7, 8, 9, 5, 4, 5, 4, 2

with four-page frames, we can see that there will be multiple page faults. Initially, all four frames are empty, so there will be four page faults as the first four pages are brought into memory.

Then, when page 5 is needed, the oldest page in memory, page 1, is replaced leading to another page fault.

As the reference string continues, there are several page faults that occur as pages are replaced

By the end of the reference string, there have been a total of 13 page faults.

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For performing this analysis Brewer can use a method such as a survey for gathering the data.

Brewer would like to determine how often college students are going to local restaurants to eat lunch instead of eating on campus. He will require a large amount of data to determine this.

This data that he requires can be gathered using the method of survey, and a conclusion can be drawn from the data with the help of statistical analysis and probability analysis.

Surveys can be conducted by email or in an online survey form and can include both open-ended and closed-ended questions to gather both quantitative and qualitative data on the subject.

In this case, the survey can also be conducted by using orthodox methods of gathering data, such as observing people who are going to eat at local restaurants and on campus, although this is not the most ideal method.

Surveys allow the researcher to reach a large number of participants and gather data efficiently and effectively.

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The best way for her to find this data reliably is by using survey's

She can go around campus and survey the other students, and eventually get enough data to find an answer to her question (I also took the test and this answer was right)

have a good day :)

The population of the city in 2023 is 1.6 * 10^6.

The exponential function is a mathematical function that describes the growth of a quantity as a power of another quantity.

In mathematics, the exponential function is used to model a wide range of phenomena including exponential decay, compounding interest, and population growth.

Using the exponential growth model;

P = Poe^rt

P = population at time t

Po = Initial population

r = Population growth rate

t = time

4Po = Poe^rt

If t = 1

4Po/Po = e^r

4 =  e^r

r = ln4

r = 1.4

The population in 2023 is;

P = 88e^1.4 * 7

P = 1.6 * 10^6

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If WEATHER A same-day forecast of the temperature tends to be within 2.25°F of the actual temperature. The range of possible temperatures for the day when the forecast is 16°F is: 13.75°F  to 18.25°F.

Let x be the actual temperature.

Find the range of possible temperatures for the day when the forecast is 16°F.

The range of possible temperatures for the day is:

Range =  16°F - 2.25°F

Range = 13.75°F

Range = 16°F + 2.25°F

Range = 18.25°F

The range is from  13.75°F  to 18.25°F.

Therefore  the actual temperature can be anywhere from 13.75°F to 18.25°F.

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The inverse function of the function g(x) will be y = √(x) - 10.

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by swapping x with y and y with x.

The function is given below.

g(x) = (x + 10)²

Replace x with y and g(x) with x, then we have

x = (y + 10)²

(y + 10)² = x

y + 10 = √x

y = √(x) - 10

The inverse function of the function g(x) will be y = √(x) - 10.

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The equation does not hold true, indicating that point C does not lie on line AB.

The equation of line AB can be written in slope intercept form as y = mx + b. The slope of line AB can be found using the equation m = (y2-y1)/(x2-x1). Substituting the coordinates of points A and B into the equation, we get m = (2-4)/(-5-2) = -2/7. The slope-intercept form of this equation is y = -2/7x + b. We can find the value of b by substituting the coordinates of point A into the equation. We get b = 4 + 2/7 = 19/7.

Therefore, the equation of AB in slope-intercept form is y = -2/7x + 19/7. To check whether point C lies on line AB, we must substitute the coordinates of point C into the equation. We get y = -2/7(-1)+19/7 = -2/7 + 19/7 = 17/7. Since the y-coordinate of point C is 8, the equation does not hold true, indicating that point C does not lie on line AB.

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The correct solution are,

(C) a=1, b=2, c=3.

The code segment does not work in the case where a > b, c > b, but a < c.

In this case, the value of 'low' is set to 'b' instead of 'a', which causes the code segment to print the incorrect value.

The values of a, b, and c that fall into this case are a=1, b=2, and c=3.

Let's trace through the code segment using a=1, b=2, and c=3:

Since a=1 and b=2, the first conditional statement (a > b && b > c) evaluates to false, so we skip the first 'if' block.

Since a=1 and c=3, the second conditional statement (a > b && c > b) evaluates to true, so we set 'low' to 'b'.

However, since we have an 'else' block following the second conditional statement, it will always be executed. So, 'low' is set to 'a' instead.

Finally, the code segment prints the sum of a + b + c - low, which is 1+2+3-1 = 5, which is incorrect.

The correct answer should be 1 + 3 = 4.

Therefore, the answer is (C) a=1, b=2, c=3.

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The function sin(x-y)/cosec(x+y)=sin²x-sin²y

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to prove that sin(x-y)/cosec(x+y)=sin²x-sin²y

Using the identity cosecx=1/sinx

We get sin(x-y)/cosec(x+y)=sin(x-y)sin(x+y)

We know sin(x+y)=sinxcosy+cosxsiny

sin(x-y)=sinxcosy-cosxsiny

Now sin(x-y)sin(x+y)=(sinxcosy-cosxsiny)(sinxcosy+cosxsiny)

=sin²xcos²y-cos²xsin²y

=sin²x(1-sin²y)-(1-sin²x)sin²y

=sin²x-sin²xsin²y-sin²y+sin²xsin²y

=sin²x-sin²y

Hence, we proved that sin(x-y)/cosec(x+y)=sin²x-sin²y

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As per the concept of hypothesis the collection of all cans the process has or could have generated is defined as the population

In statistics, a hypothesis is an assumption made about a population of data, usually with the goal of testing it.

The term "population" refers to the collection of all possible items of data or objects, while a "sample" is a smaller subset of the population that is used to draw conclusions about the population.

In the case of the manufacturing process for cans of frozen concentrated orange juice, the "population" would be the collection of all cans that the process has or could have generated.

This is because the goal is to make conclusions about the entire population, rather than just a portion of it.

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m = 4

13=2m+5

-5 -5 subtract 5 from both side

8=2m

8/2=2m/2 divide both side by 2

4=m

Answer:

0.0000000045, 0.0000097 and 0.000167 isthe acending order

Writing the function P = 35(1.3)^t in the form P(0)e^{kt}, the value of k = log(1.3) and P(0) = 35.

The function is P = 35(1.3)^t

At t = 0, P = 35, so P(0) = 35

P = 35e^{kt} .................Equation 1

P = 35(1.3)^t .................Equation 2

Now dividing the equation, we get

P/P = 35e^{kt}/35(1.3)^t

1 = e^{kt}/(1.3)^t

Multiply by (1.3)^t on both side, we get

1.3^t = e^{kt}

Now taking log of both side, we get

log [1.3^t] = log[e^{kt}]

Using the formula log[m^n] = n logm

t log(1.3)= kt loge

t log(1.3)= kt

Divide by t on both side, we get

k = log(1.3)

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