A recreational area is formed by a rectangular shaped pool and a cement patio surrounding the pool. the pool has a length of 3x-3 meters and a width of 2x+7 meters. The patio extends x meters around to pool, on all sides of the pool. Write a polynomial expression that gives the total area of the recreational area.

The sum of the given two expressions -7g and 4g+2 is -3g+2.

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.

There are mainly 3 types of algebraic expressions which are:

The sum of given expressions , -7g and 4g+2 can be performed as follows:

   -7g + (4g + 2)

=  (-7+4)g + 2

= -3g + 2

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If Christopher measured a line to be 12.2 inches long. If the actual length of the line is 12.1 inches, the percent error of the measurement, to the nearest tenth of a percent is: 0.83%.

Using this formula to find the percent error

Percent error = Measurement - Actual length / Actual length

Let plug in the formula

Percent error = 12.2 - 12.1 / 12.1

Percent error = 0.1 /12.1

Percent error = 0.0083 or 0.83%

Therefore we can conclude that the percent error is 0.83%.

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The number of students at the open house is B. 468.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

We know if a and b are two quantities in a total quantity (ax + bx) the amount of a single quantity can be obtained by [a/(a+b)]× (ax + bx).

Given, The ratio of students to adults at the open house is 9 : 7 and the total number of students and adults at that place is 832.

Therefore,

The number of students is,

= (9/9+7)×832.

= (9/16)×832.

= 9×52.

= 468.

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Answer:

The ratio of the number of quarters to the number of dimes in the box is 9:10

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

A formula for connecting two statements using the equal sign (=) to denote equivalence is known as a mathematical equation. A mathematical equation in algebra is a statement that proves the equality of two mathematical expressions. For instance, the formula 3x + 5 = 14 places an equal sign between the variables 3x + 5 and 14. The mathematical relationship between the two sentences on either side of a letter is established. Most of the time, the symbol serves as both the one and only variable. for instance, 2x – 4 = 2.

Here,

the two numbers' primary factors are as follows:

-25[tex]b^{2}[/tex] + 15b

Common prime factors can be multiplied to determine the GCF:

=> -25[tex]b^{2}[/tex]  = -(5)(5) * [tex]b^{2}[/tex]

=> 15b = (5)(3)b

The expression can be factored in the following fashion because the GCF is 5b:

=> -(5)(5) * [tex]b^{2}[/tex] +  (5)(3)b

=> (5b)(-5b+3)

Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).

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Answer:

very long question

Step-by-step explanation:

The closest to the number of yards of ribbon Mario had altogether will be 11 yards

A fraction is a part of the whole number, and a way to split up a number into equal parts. Or, A number that is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Given that;

Mario had 8 1/5 yards of ribbon for a project.

And, Sue gave him 2 3/4 more yards of ribbon.

Since Mario had 8 1/5 yards of ribbon for a project. And, Sue gave him 2 3/4 more yards of ribbon.

Hence, Total ribbon for the project Mario have = 8 1/5 yards + 2 3/4 yards

= 41/5 + 11/4

= (164 + 55) / 20

= 219 / 20 yards

= 10.95 yards

≈ 11 yards

Thus, the total ribbon for the project Mario has = 11 yards

The complete question is given below;-

Mario had 8 1/5 yards of ribbon for a project. Sue gave him 2 3/4 more yards of ribbon. Which is closest to the number of yards of ribbon Mario had altogether?

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Answer:

k = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

given variation equation

y = kx

to find k substitute y = 3 and x = 4 into the equation and solve for k

3 = 4k ( isolate k by dividing both sides by 4 )

[tex]\frac{3}{4}[/tex] = k

Answer: 4

Step-by-step explanation:

Let me get to know you:)

Answer: Your answer is 60 divided by 13 = 4.165.

Step-by-step explanation: You would have to divide 12 out of 50, and that would be a decimal of 4.166666666666667 So you need an aditional 10 items but then another additional suitcase there is an answer to this but it would come out as a decimal or fraction, so you would have to specify what type of object is going into these suitcases, most people would just deal with it and carry it in the hands lol.  

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those provided

[tex]R(\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\qquad S(\stackrel{x_2}{15}~,~\stackrel{y_2}{31}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{31}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{15}-\underset{x_1}{5}}} \implies \cfrac{ 24 }{ 10 } \implies \cfrac{12 }{ 5 }[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{12}{5}} ~\hfill \stackrel{reciprocal}{\cfrac{5}{12}} ~\hfill \stackrel{negative~reciprocal}{ {\Large \begin{array}{llll} -\cfrac{5}{12} \end{array}} }}[/tex]

Step-by-step explanation:

the slope of a line is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

the perpendicular slope is simply turning that ratio fraction upside down and flips the sign.

(5, 7) to (15, 31)

x changes by +10 (from 5 to 15).

y changes by +24 (from 7 to 31).

the slope (or gradient) is therefore

+24/+10 = 12/5

the perpendicular slope or gradient is then

-5/12

Answer:

3.5 hours to read

Step-by-step explanation:

Before the trip, Tyler read 24 pages of his Philadelphia guidebook in an hour. The guidebook is 84 pages long. If he continued to read it at the same rate, how long did it take Tyler to finish reading the guidebook before his family's trip?

total pages / reading rate per hour

Equation: 84/24

Solution:  = 3.5 hours

Answer:2024

Step-by-step explanation: 44x46

Answer: 1.15384615385

Step-by-step explanation:

divide

The current value of property is 4000

The capitalization rate (also known as cap rate) is used in the world of commercial real estate to indicate the rate of return that is expected to be generated on a real estate investment property. Formula: Capitalization Rate = Net Operating Income / Current Market Value

Given here cap rate as 10% and income as 40000, Thus Current market value of property is = 40000/10

                                 =4000

Hence, The current value of property is 4000

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The graph representing the solution will be of the form a line tending towards left from the point -7/22.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Here the given inequality is less than inequality.

1/7 m < -1/22

Dividing both sides by 1/7, we get,

m < -1/22 ÷ 1/7

m < -1/22 × 7/1

m < -7/22

Hence the graph of the solution will be of the form a straight line tending leftwards from -7/22.

Hence the graph of the given inequality is a straight line tending leftwards from -7/22.

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-2

Step-by-step explanation:

12x＝x+26

-13x＝26

x＝-2

Answer:

The answer is 0.26.

I wish you luck on your assignments.

Answer: 0.26

Step-by-step explanation:

1. The hundredths place is two digits from the decimal point

2. Look at the thousandths place and if it is larger or equal to 5 then we round up, otherwise we round down and the hundredths digit remains the same

3. 7 is larger than 5 therefore the hundredths place digit of 5 rounds to a 6

4. Our final answer is 0.26

Answer:

Perimeter = 9x + 6

Step-by-step explanation:

Perimeter = x+14 + x-1 + x+5 + 3x + 2x-10 + x-2

Perimeter = 9x + 14 + 5 - 1 - 10 - 2

Perimeter = 9x + 19 - 13

Perimeter = 9x + 6

a. The model represents exponential growth.

b. The annual percentage increase is 3%.

c. After 2390 decades the population was about 590000.

The formula for exponential growth is [tex]y = y_₀.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_₀.e^{(-kt)}.[/tex]

Given, The population P(in thousands) of Austin Texas during a recent decade is approximated by [tex]y = 492(1.03)^t[/tex].

The model represents exponential growth as time can not be negative.

The annual percentage increase in the model [tex]y = 492(1.03)^t[/tex] is 3%

as 1.03×100% = 103%.

The time when the population was about 590000 since the beginning of a decade is,

[tex]590000 = 492(1.03)^t[/tex].

[tex](1.03)^t = 590000/492[/tex].

[tex](1.03)^t = 1199.1869[/tex].

[tex]log_{1.03}1.03^t = log_{1.03}1199.1869[/tex].

t = 2389.84 Or 2390 decades.

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The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

The table below shows the ratios of boxed donuts to the cost.

Donuts    A       4        5     C

Cost    13.80  27.60   B   55.20

Now, By definition of ratio, we get;

⇒ A / 13.80 = 4 / 27.60

⇒ A = 13.80 × 4 / 27.60

⇒ A = 2.00

And,

⇒ 4 / 27.60 = 5 / B

⇒ B = 5 × 27.60 / 4

⇒ B = 34.5

⇒ 4 / 27.60 = C / 55.20

⇒ C = 55.20 × 4 / 27.60

⇒ C = 8

Thus, The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

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Answer:

a

Step-by-step explanation:

i took the test :)

Answer:

6,9 and 3 times respectively

The line segment AB is d = [tex]\sqrt{106}[/tex] in  length if (-5, 4) and (B), and A = (-5 , 0) .  A line segment is hence a section or component of a line with two endpoints.

A line segment in geometry is bordered by two separate points on a line. A line segment has two fixed or distinct endpoints, whereas a line has no endpoints and can stretch in both directions indefinitely. A line segment is hence a section or component of a line with two endpoints. A line segment, unlike a line, has a set length. Measuring the length of a line segment can be done using either metric measurements, such as millimeters or centimeters, or conventional measurements, such as feet or inches.

given

d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]

(5 )2 + ( 9 ) 2 = d

d = 25 + 81

d = [tex]\sqrt{106}[/tex]

The line segment AB is d = [tex]\sqrt{106}[/tex] in  length if (-5, 4) and (B), and A = (-5 , 0)

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Answer:

The mechanic spent 12 hours on the repair.

Step-by-step explanation:

The mechanic spent 12 hours on the repair.

Therefore , the solution of the given problem of perimeter comes out to be  PQRS  = 29 units.

The perimeter, or total length, of a shape is referred to as its perimeter in geometry. A shape's perimeter is calculated by summing the lengths of all of its sides and edges. By adding together the lengths of all a shape's sides, one may determine its perimeter.  The circumference of a field, for instance, will be 78 yards for a rectangle with dimensions of 24 yards long by 15 yards wide.

Here,

Given : PQRS has the length 12

and TUVW has length 15.

thus ,

To find the perimeter of PQRS:

we find,

TUVW = 35 units

and

PQRS = 35 - 6

=> PQRS  = 29

Therefore , the solution of the given problem of perimeter comes out to be  PQRS  = 29 units.

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The first equation will be multiplied by 3 and that of the second by 4.

An elimination method is a process of solving a system of linear equation, in this we make coefficients of the one variable equal and subtract the equations.

Given that are two equations to be solved by using elimination method,

-4x+4y = 32.....(i)

3x-y = 12......(ii)

To eliminate x, we will multiply eq(i) by 3 and eq(ii) by 4

-12x+12y = 96.....(iii)

12x-4y = 48....(iv)

Solving the equations, we get,

8y = 144

y = 18

Put y = 18 in eq (ii)

3x-18 = 12

3x = 30

x = 10

Hence, the first equation will be multiplied by 3 and that of the second by 4.

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Answer:

Slope: -1/2

Step-by-step explanation:

You can find the slope from this equation by adding 1/2 to each side of the equation since the way you find the slope of a line is by using: y = mx + b. The "m" must ALWAYS be on the right for it to be a valid slope equation, therefore, we have to use inverse operations for -1/2x to bring it to the right side.

Now, after we added 1/2x to each side, we get this equation:

-y = 1/2x + 3/4

We are not yet done since the y is accompanied by a negative 1, so, to isolate the variable, you use inverse operations once again and you get this equation:

y = -1/2x - 3/4

Therefore, the slope for this equation is -1/2.

Hope this helped! :D

The image point of (0, 4) is (0, -4).

The intersection of the x- and y-axes creates the two-dimensional coordinate plane known as the cartesian plane. The origin is the point at where the x- and y-axes cross perpendicularly.

The Cartesian coordinate point (x, y) indicates that the distance from the origin is x in the horizontal direction and y in the vertical direction. The point is to the right of the origin if the sign of x is positive; otherwise, it is to the left.

Given points (0, 4)

to find image of the point (0,4) after a rotation of 180 degrees,

The initial coordinates (x, y) of a point become when we rotate it by 180 degrees around the origin (-x, -y).

So,

-0 is just 0 (since 0 is both negative and positive)

-(4) is -4

This makes our new point (0, -5).

Hence the image of point is (0, -4).

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Answer: y=(x+3)2−17

Step-by-step explanation: