A square swimming pool is surrounded by a cement sidewalk that is 3 feet wide. Enter two different functions representations for the total area that the swimming pool and sidewalk enclosed, A(x), if the length of the pool is x feet long



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After 23.1 years the population of Texas will reach 32 million.

In this question, we have been given the population P (in millions) of Texas from 2001 through 2014 can be approximated by the exponential function P = 20.913 e^(0.0184t),

where t represents the year, with t = 1 corresponding to 2001.

We need to find the time period t when the population reach 32 million.

For P = 32, we need to find t.

Substitute P = 32 in given exponential function.

32 = 20.913 e^(0.0184t)

32/20.913 = e^(0.0184t)

1.53 = e^(0.0184t)

ln(1.53) = 0.0184 * t

t = 0.4253/0.0184

t = 23.11 years

Therefore, after 23.1 years the population will reach 32 million.

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The complete question is:

The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P = 20.913e0.0184 t, where t represents the year, with t = 1 corresponding to 2001. According to this model, when will the population reach 32 million? (Source: U.S. Census Bureau)

Answer:

(1,2)

(3, -1)

Step-by-step explanation:

2x + 5y = 12

4x -y = 2  Multiply this through by 5 and then add to the equation above

2ox - 5y = 10  

2x + 5y = 12        

22x = 22  Divide both sides by 22

x = 1

Substiture in 1 for x in either of the two original equations

2x +5y = 12

2(1) + 5y = 12  

2 + 5y = 12  Subtract 2 from both sides

5y = 10  Divide both sides by 5

y = 2

(1,2)

2nd Problem

2x - 5y = 11 Multiply through by 2      4x - 10 y = 22

3x  + 2y = 7    Multiply through by 5    15x + 10 y = 35

Add the two bold equation together

4x - 10y = 22

15x +10y = 35              

19x = 57  Divide both sides by 19

x = 3            

Substitute in 3 for x in one of the original equations to solve for y.          

2x - 5y = 11

2(3) - 5y = 11

6 - 5y = 11  Subtract 6 from both sides

-5y = 5  Divide both sides by -5

y = -1

(3,-1)

The value of x= 35.5, y= 43.75 and z= 62.75

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the three angles are x, y and z.

x+ y + z = 180............(E3)

The sum of the measures of the second and third angles is three times the measure of the first angle.

So, y+ z = 3x

3x- y- z= 0.............(E1)

and, third angle is 19 more than the second

z= y+ 19

y- z= -19..........(E2)

So, E1+E2, and E3-E2,

3x- 2z= -19

x+ 2z= 161

Now, adding above

4x = 142

x= 35.5

and, y + z = 106.5, y- z = -19

Again, adding

2y= 87.5

y= 43.75

and, z= 62.75

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The bacteria after 24 hours will be equal to 450000.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria.

The number of bacteria will be calculated as,

N = 125×(60×60)

N = 125×3600

N = 450000

Therefore, the bacteria after 24 hours will be equal to 450000.

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To prove the given statement we can take into account the matrix produced by the tuples (1,2,0), (1,0,1) and (1,0,1). The three vectors are linearly independent if the matrix's where determinant is nonzero.

det ( -1 2 0

        -1 0 1

         1  0 1 )   = 4

Now that P2 has a dimension of 3, those three vectors serve as the foundation for P2 by definition.

Therefore, the polynomial forms the basis of P.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x2+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x2, x, and -12.

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The line segment's unit of measure is 75.6 inches.

What is the conversion factor?

A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value.

Here, we have

Given

12in/1ft

We have to convert this into inches.

So, we apply here conversion factor and we get

= 6.3ft × 12in ÷1ft

= 75.6 inches

Hence, the line segment's unit of measure is 75.6 inches.

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The domain of the function are all real numbers between -1 and 0. {x∈R|-1≤x≤0}

What is a function ?

A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.

See if any vertical lines that were drawn touch the curve more than once by carefully examining the graph. The graph does not represent a function if there is any such line. The graph does reflect a function if no vertical line can cross the curve more than once.

The domain of function are set of values of x for which the function covers.

For the given function, from the graph the function starts from x =-1 and ends at x = 0.

So, the domain of the function are all real numbers between -1 and 0.

{x∈R|-1≤x≤0}

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Answer: 62 rows

992 divided by 16 is 62, so there are 62 rows.

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Answer:

992÷16=62

Step-by-step explanation:

I hope I helped you

All of the statements that correctly describe line ST include the following;

A. Perpendicular bisector of PQ.

C. Median of ΔPQR.

D. Altitude of ΔPQR.

In Mathematics, an isosceles triangle can be defined as a type of triangle that has two (2) of its sides equal in length and two (2) equal angles. This ultimately implies that, an isosceles triangle comprises two (2) angles and two (2) side lengths that have the same measure or are equal in magnitude.

In every isosceles triangle such as triangle PQR (ΔPQR), both the median and altitude are the same and they will lie on the same line segment when drawn from the top to the base in accordance with the Isosceles Triangle Theorem.

In conclusion, we can logically deduce that the vertex that runs from point T to point S is a perpendicular bisector that bisects line PQ into two (2) equal halves.

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Answer:

Hi, the answer to your question is ×=20

X = 20

when we solve the given equation,

9/12 = 15/x

hence,

X = 15*12/9

X = 20

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There is a Rotation of 180 degrees

What is Co-ordinate Geometry?

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

We are given that point A is (4, 5) this means that the point lies in the First Quarter of the Co-ordinate System

and the transformed point lies in the Third Quarter of the Co-ordinate System

So, it can be very well said that there is a Rotation of 180 degrees

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Answer:

(3+2)

Step-by-step explanation:

Perimeter of a square = 4L

L is the length of one side of the square

Given the expression 12 + 8 that represents the perimeter of a square, factoring out 4 from both terms;

12 + 8

= (4*3)+(4*2)

= 4(3+2)

Comparing with 4L

4L = 4(3+2)

Divide both sides by 4

4L/4 = 4(3+2)/4

L = (3+2)

Hence the expression that represents one side of the square is (3+2).

Hope this helps!!! :)

Answer:

The answer is 9

Step-by-step explanation:

The given triangle is equivalent triangle

We know that in equivalent triangle all angles are equal to 60°

So,

(7x - 3)° = 60°

7x - 3° = 60°

7x - 3° + 3° = 60° + 3°

7x = 63°

x = 63°/7°

x = 9°

Thus, The value of x is 9°

For Verification Only;

(7x - 3)° = 60°

[7(9) - 3]° = 60°

(63 - 3) = 60°

60° = 60°

Hence,

L.H.S = R.H.S

The pilot is 231 mi from his destination at the time he notices the error.

What is the law of cosines?

The square of a side of a plane triangle is equal to the sum of the squares of the other sides minus twice the product of those sides and the cosine of the angle between them, according to a trigonometry rule.

Here, we have

This line is 300 mi long and makes an angle of 40° from the horizontal (based on N50°E bearing).

From point A draw a horizontal line to point C. This line=(35/60)*250=145.8 mi.

Draw a line connecting point C to point B. You now have a triangle with sides AB = 300 mi and AC = 145.8 mi and their included angle of 40.

Using the Law of cosines to find CB:

(CB)² = (AB)²+(AC)² -2*AB*AC*cos 40°

(CB)² = (300)²+(145.8)²-2*300*145.8*cos 40°

(CB)²  = 90000+21257 - 46928 = 64329

CB =√64329 = 253 mi

Hence, the pilot is 231 mi from his destination at the time he notices the error.

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The sampling distribution refers to the distribution of the sample mean (X-bar) computed from a set of n independent, normal random variables (X1,...,Xn).

The sampling distribution is a theoretical distribution that describes how the sample mean would vary if you were to take multiple samples from the population and compute the sample mean for each sample. It is based on the assumption that the X1,...,Xn are independently and normally distributed with a common mean and variance.

The sampling distribution is important because it allows us to make inferences about the population mean based on the sample mean. By understanding the properties of the sampling distribution, we can calculate confidence intervals and perform hypothesis tests to determine whether the sample mean is significantly different from the population mean.

In contrast, the distribution on the individual random variables (X1,...,Xn) is the distribution of the individual observations in the sample. The distribution on the means of the individual random variables (Xi) is the distribution of the mean of each individual random variable.

The frequency distribution obtained from a set of n experimental data values is the distribution of the observed data values in the sample.

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The completed sentences that describe the height reached by the ball specified by the function, f(x), that indicates the balls height, based on the number of bounces, x, f(x) = 64·(0.75)ˣ, which is similar to a geometric progression, is presented as follows;

The variable, x, represents the number of times the ball bounces.

The variable f(x) represents the height of the ball after x bounces.

The parameter, 64, represents the initial height of the ball.

The parameter, 0.75, represent the percentage of height left from each previous bounce.

A geometric progression is a number sequence, arranged such that the ratio between a term and the previous term is a constant, known as the common ratio of the geometric progression.

The exponential function that models the specified situation of finding the height of the ball is presented as follows;

f(x) = 64·(0.75)ˣ

The initial height from which the student drops the ball = 64 feet

The height the ball reaches after one bounce = 48 feet

Height of the ball after 2 bounces = 36 feet

The exponential function, f(x) = 64·(0.75)ˣ, is similar to the equation for a geometric progression, aₙ = a₁·r⁽ⁿ⁻¹⁾

Where;

a₁ = The first term = The initial height

r = The common ratio = 48/64 = 36/48 = 0.75

n = The number of times the ball bounces, in addition to the time the ball is dropped from the initial height, therefore;

x = n - 1, therefore;

x = The number of times the ball bounces

n = x + 1

The terms that complete the sentences are therefore:

The variable that represents the number of time the ball bounces = x

The variable that indicates the height of the ball after x bounces = f(x)

The initial height of the ball = The parameter 64

The percentage of the height the ball bounces to after the previous bounce = 0.75

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Answer:Above $297 we need to add 34%. Thus the result :

297 X 34/100 =100,98

Result = 297 + 100,98 = 397,98

Step-by-step explanation:Good luck

With the given coordinates (-3, 1) and (0, 4), the slope is 1.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)

Here,

1) (-3, 1) and (0, 4)

Δy=(4-1)=3 and Δx=(0(-3))=3

So, m= Δy/Δx =3/3 =1

2) (-6, 27) and (2, 3)

Δy=(3-27)=24 and Δx=(2-(-6))=8

So, m= Δy/Δx =24/8 =3

3) (5, 27) and (0, -8)

Δy=(-8-27)=-35 and Δx=(0-5)=-5

So, m= Δy/Δx =(-35)/(-5) =7

4) (1, 0) and (-7, -24)

Δy=(-24-0)=-24 and Δx=(-7-1)=-8

So, m= Δy/Δx =(-24)/(-8) =3

5) (-3, 20) and (-5, 32)

Δy=(32-20)=12 and Δx=(-5-(-3))=-2

So, m= Δy/Δx =12/(-2) =-6

6) (5, -4) and (0, -9)

Δy=(-9-(-4))=-5 and Δx=(0-5)=-5

So, m= Δy/Δx =(-5)/(-5) =1

7) (-8, -2) and (-1, -4.5)

Δy=(-4.5-(-2))=-2.5 and Δx=(-1-(-8))=7

So, m= Δy/Δx = -2.5/7

8) (-7, -2) and (6, 11)

Δy=(11-(-2))=13 and Δx=(6-(-7))=13

So, m= Δy/Δx =13/13 =1

9) (-2, -6.5) and (4, -8)

Δy=(-8-(-6.5))= -1.5 and Δx=(4-(-2))=6

So, m= Δy/Δx = -1.5/6 = -1/4

Therefore, slope of a line with the coordinates (-7, -2) and (6, 11) is 1.

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Answer:

12

Step-by-step explanation:

pythagoras thereom

a^2 +b^2=c^2

13^2-5^2=144

144 square root = 12

Answer:

12

Step-by-step explanation:

13^2 - 5^2 = 144

square root of 144 = 12

The function that is parallel to the graph of y = -4x + 4 is y = -4x - 9

From the question, we have the following parameters that can be used in our computation:

y=-4x+4

To start with, we need to express the equation properly

So, we have the following representation

y = -4x + 4

Also, from the question;

We have the following points

The point is given as

Point = (-1, -5) i.e.  (x, y) = (-1, -5)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = -4

This means that the slope is -4

The slopes of parallel lines have the same values

This means that the slope of the other line is -4

The equation of the line is then calculated as

y = m(x - x₁) + y₁

Where

m = -4

(x₁, y₁) = (-1, -5)

So, we have

y = -4(x + 1) - 5

Open the brackets

y = -4x - 4 - 5

Evaluate the like terms

y = -4x - 9

Hence, the line has an equation of y = -4x - 9

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Step-by-step explanation:

function of the organelle in question 4.

Using the diagram and your knowledge of biology, identify the following:

a. Organelle A_____

b. Substance A_____

c. Substance B_____

RT 2: Regents Review!

ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.

scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose

function of the organelle in question 4.

Using the diagram and your knowledge of biology, identify the following:

a. Organelle A_____

b. Substance A_____

c. Substance B_____

RT 2: Regents Review!

ections: Recall what you learned in unit 1 about designing an experiment to answer the ientist is interested in the effect that the amount of glucose given to a mitochondria n unt of carbon dioxide that is produced.

scientist sets up three containers: Container 1 holds 20 mitochondria and a 0.5 %cor ainer 2 holds 20 mitochondria and a 1.0 % concentration of glucose; and Container 3 hondria and a 5.0 % concentration of glucose. 0.5 % concentration of glucose

Step-by-step explanation:

[tex]( {x}^{2} - x)(x + 5)[/tex]

[tex]x(x - 1)(x + 5)[/tex]

[tex]x = 0[/tex]

[tex]x - 1 = 0[/tex]

[tex]x = 1[/tex]

[tex]x + 5 = 0[/tex]

[tex]x = - 5[/tex]

So our zeroes are 0,1, and -5

2.

[tex] {x}^{3} + 4 {x}^{2} - 5x[/tex]

If a sample consists of 600 test scores, 516 of them would be at or below the 86th percentile. If a sample consists of 600 test scores, 228 of them would be at or above the 62th percentile.

A percentile is a score that compares a specific score to the scores of the other members of a group. It displays the proportion of other scores that a given score outperformed. For instance, if you have a test score of 75 and are placed in the 85th percentile, it signifies that your score is greater than those of 85% of other test takers.

Given that,

In general, 70 % of the values in a data set lie at or below the 70th percentile.

20 % of the values in a data set lie at or above the 20th percentile.

Generally percentile defines the percentage of a data set that is below or at a value that is being considered.

Hence the percentage of the values of a data set that lies below or at the 16th percentile is  16%

Also  the values of a data set that lies below or at the 24th percentile is  24%

Given a sample of 600 test scores , the number of test scores that will be at or below the 86th percentile is 86% of  600 which is mathematically represented as:

K = [tex]\frac{86}{100}[/tex] × 600

K = 516 test scores

Given a sample of 600 test scores , the number number of test scores that will be above  the 62 th percentile is (100 - 62 = 38 )% of  600 which is mathematically represented as:

a = [tex]\frac{38}{100}[/tex] × 600

a = 228 test scores.

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The total years taken to double the money according to Compounding will be  12.5 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $2500

Total amount = $5000

Compounded semi -anually,

so formula becomes,

Total amount = amount (1+r/200)^2t

T = [tex]A (1+\frac{r/2}{100})^{2t}[/tex])

5000 = 2500 (1+3/100)^2t

2 = [tex](1+0.03)^{2t}[/tex]

2 = [tex]1.03^{2t}[/tex]

taking log on both sides

log 2 = 2t *log 1.03

0.3/0.012 = 2t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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X = 1

X + 6 = 7

     -6   -6

X = 1

Self check : 1 + 6 = 7

The value of the x in the given equation is 1.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, If X + 6 = 7, then X is equal to

Solving the equation, we get,

x + 6 = 7

Subtracting 6 from both side, we get,

x + 6 - 6 = 7 - 6

x = 1

Hence, The value of the x in the given equation is 1.

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A linear function would best fit the data because as x increases, the y values change by an approximate constant. The rate of change of this function is approximately 8950 people a year.

To classify a function as linear or exponential, we have to check whether the differences or the quotients between consecutive terms are constant, as follows:

The differences for the consecutive terms in the table are given as follows:

The ratios for the table are given as follows:

The differences have less variation then the ratios, then a linear function best models this data, with an slope of approximately (8995 + 8905 + 8941)/3 = 8947, which is the mean of these differences.

(rounded to 8950).

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number line with open circle on point negative 5 and arrow shaded to the right is the right description for the graph of the inequality.

inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

let the number be x

so that 2.5 > -0.5x

dividing through by -0.5 we revert the inequality sign

2.5/-0.5 < x

-5 < x

Taking x to the other side we revert the inequality sign back to greater than

x > -5

In conclusion, number line with open circle on point negative 5 and arrow shaded to the right is the description of the graph

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Answer: D

Step-by-step explanation: I have proof! i got it right on test and i have a picture.

Answer:The answer is B

Step-by-step explanation:

The reason that the answer is b is because he wants to keep the prices low from them getting charged by the bank