The total area of the recreational area can be represented by the polynomial expression 26x² + 57x + 35.
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
The area of the rectangular pool is given by its length times its width, so the area of the pool is (3x - 3) meters × (2x + 7) meters = (6x² + x - 21) square meters.
The area of the patio is given by the length of the pool plus twice the extension (x) on each side, times the width of the pool plus twice the extension on each side, so the area of the patio is (3x - 3 + 2x) meters × (2x + 7 + 2x) meters = (5x + 4) × (4x + 14) = 20x² + 56x + 56 square meters.
The total area of the recreational area is the sum of the areas of the pool and the patio, so it can be represented by the polynomial expression:
20x² + 56x + 56 + 6x² + x - 21 = 26x² + 57x + 35
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sum of -7g and 4g+2
The sum of the given two expressions -7g and 4g+2 is -3g+2.
What are algrbraic expressions?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.
What are the types of algebraic expressions?There are mainly 3 types of algebraic expressions which are:
Monomial ExpressionBinomial ExpressionPolynomial ExpressionThe 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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Christopher measured a line to be 12.2 inches long. If the actual length of the line is 12.1 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
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%.
How to find the percent error?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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What is the image of the point (0,4) after a rotation of 180 degrees counterclockwise about the origin?
The image point of (0, 4) is (0, -4).
What is Cartesian plane?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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Which is the constant of variation, k, if y=kx, and y=3 when x=4?
3/4
4/3
3
4
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
find quotient 5/4 divided by 13/12
Answer: 1.15384615385
Step-by-step explanation:
divide
Please someone help me
Answer:
6,9 and 3 times respectively
Which graph represents the solution to 1/7 m < - 1/22
The graph representing the solution will be of the form a line tending towards left from the point -7/22.
What is Linear Inequalities?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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Mario had yards of ribbon for a project. Sue gave him more yards of ribbon. Which is closest to the number of yards of ribbon Mario had altogether?
The closest to the number of yards of ribbon Mario had altogether will be 11 yards
What is meant by Fraction?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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Quad. PQRS ~ Quad. TUVW, Owe side of PORS has the length 12. The corresponding side of TUVW has length 15. The perimeter of TUVW is 35 and the perimeter of PQRS is?
Pls help me solve this!!
Therefore , the solution of the given problem of perimeter comes out to be PQRS = 29 units.
Establish a perimeter.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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19.
A box contains only quarters and dimes. If there were 10% more quarters, the total
value of the money in the box would increase by 7.5%. What is the ratio of the number of quarters to the
number of dimes in the box? Express your answer as a common fraction.
Answer:
The ratio of the number of quarters to the number of dimes in the box is 9:10
Step-by-step explanation:
44x46 ayuda plssss speak spanish plssssss
Answer:2024
Step-by-step explanation: 44x46
hey could anyone solve this for me and make sure its correct
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
A prescription indicates that 1.25 grams of a given drug should be taken
Twice a day. If the drug is available in 500 milligram tablets, how many tablets does it Will the patient take every 12 hours?
how many full cases and additional items are needed to fulfill the order 50 items ordered 12 items per case
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.
Net income in a property is 40000 and cap rate is 10% value of property using the income capitalization method
The current value of property is 4000
What is the capitalization rate?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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Round 0.25773438 to the nearest hundredth
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
A mechanic charges $45 per hour for labor plus $55 for a computer diagnostic test. The mechanic charges a customer $595 to repair a vehicle. How many hours did the mechanic spend on the repair?
Answer:
The mechanic spent 12 hours on the repair.
Step-by-step explanation:
$595-$55=£540. £540 is the total of the amount the mechanic charges for an hour, MINUS the computer diagnostic testTo find out how many hours the mechanic spent on the repair, we have to do $540 divided by $45, which is 12.The mechanic spent 12 hours on the repair.
Please help me solve this
a. The model represents exponential growth.
b. The annual percentage increase is 3%.
c. After 2390 decades the population was about 590000.
What is the formula for exponential growth and exponential decaying function?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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Find the length of the line segment shown below.
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.
what is line segment ?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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what is the slope for the equation?
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
F(x)=2 sin (1/2x)+1
What is the midline of the functionless
Answer: 4
Step-by-step explanation:
Let me get to know you:)
PLS HELP!! Thank you so much
Perimeter stuff
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
The product of -12 and a number is the same as the sum of the number and 26
-2
Step-by-step explanation:
12x＝x+26
-13x＝26
x＝-2
Logic, Reasoning and Puzzles Assignment
Solving a Payment Puzzle
A wealthy and generous owner of an Internet company offers two
options of payment to her new vice president.
Option 1: a monthly salary
of $50000 per month paid
at the beginning of each
month
Name: Yaseen
Option 2: a monthly salary
based on 1¢ the first day,
2¢ the second day, 4c the
third day, 8¢ the fourth day,
and so on. The monthly salary
will be the amount calculated
for the last day of the month.
Assume there are 30 days in the month.
A. How can you calculate the vice president's earnings under
Option 2?
B. Compare the monthly earnings for the two options.
1.9
C. Which payment option would you take if you were the vice
president? Why?
Answer:
very long question
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRIANLI EST
The number of students at the open house is B. 468.
What is a fraction?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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What is the vertext of the following parabola: x^2 - y + 6x + 8 = 0
Answer: y=(x+3)2−17
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?
Equation:
Solution X:
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
I need help with this?
The first equation will be multiplied by 3 and that of the second by 4.
What is an elimination method?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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The Chess Club president brought donuts to the club meeting each week. As the club grew, more donuts were needed so that each member could have a donut. 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
Determine which table has the correct values for A, B, and C.
Donuts 3 4 5 7
Cost 13.80 27.60 34.95 55.20
Donuts 2 4 5 8
Cost 13.80 27.60 34.95 55.20
Donuts 3 4 5 6
Cost 13.80 27.60 34.50 55.20
Donuts 2 4 5 8
Cost 13.80 27.60 34.50 55.20
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
What is mean by Ratio?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 :)
Help!! Factor the common factor out of each expression
Therefore , the solution of the given problem of equation comes out to be factor is (5b)(-5b+3).
What is the equation?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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