The expected enrolment in 7 years is 1845.
What is the expected enrolment?The formula for calculating future value of the number of students is an exponential equation with this form:
FV = P (1 + r) ^n
FV = Future populationP = Present populationR = rate of growth of the populationN = number of years1500 x (1.03)^7 = 1845
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Quadrilateral ABCD was rotated 360° clockwise with the origin as the center of rotation to create a new figure. Which rule describes this transformation?
A (x, y)-(x,y)
B(x, y)(x, y)
c(x, y)-(x, y)
D (x, y)-(x, y)
The rules describes the transformation is (x, y)(x, y).
The correct option is (B)
what is Transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
If the figure is rotated 360 degrees then the coordinates remains unchanged.
This is because when from where it started it stops there again.
As the 360 degree rotation is complete circle rotation.
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The volume of a box is 5x^3 + 20x^2 + 15x cm^3. If the height of the box is 5x cm, find the width and length of the box.
Answer:
The product of the Width and Length is x^2 + 4x + 3 cm^2.
Step-by-step explanation:
The volume of a box = 5x^3 + 20x^2 + 15x cm^3.
Volume of a Box = W*L*H [Width(W), Length(L), and Height(H)]
W*L*(5x) = 5x^3 + 20x^2 + 15x cm^3
W*L = (5x^3 + 20x^2 + 15x cm^3)/5x cm
W*L = x^2 + 4x + 3 cm^2
We know the area of the base of the box (W*L). It is x^2 + 4x + 3 cm^2.
To find the actual width and length, we need to know one of the variables, L or W. Without that, all we can say is that their product (W*L) is x^2 + 4x + 3 cm^2.
all natural numbers (N) are integers (Z), but not all integers are natural numbers true or false
True. All natural numbers N are integers Z, but not all integers are natural numbers.
Natural numbers:
Natural numbers starts from zero to infinity are all positive.All the natural numbers are whole numbers.It is denoted by NThe set of natural numbers are N = 1,2,3, ...Integers:
Integers are the whole numbers that contain positive numbers, zero and negative numbersIt is denoted by ZThe set of integers are Z = ... ,-3,-2,-1,0,1,2,3, ...Since natural numbers are all positive, N is positive integers but not all integers are natural numbers.
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Which of the numbers below is greater than −7/3? Select all that apply. A) −3 B) −5.5 C) −2 D) −3/2 E) 1.25
Answer:
C, D and E
Step-by-step explanation:
The numbers which are greater than given number are : -2, -1.5, and 1.25.
What is Fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts.
Here, given number: -7/3
or we can write this as -2.33
Now, Converting option fraction value into decimal
A). -3
B) -5.5
C). -2
D). -1.5
E). 1.25
On comparing options from the given value we get
the number which are greater than -2.33; -2, -1.5, and 1.25
Thus, the numbers which are greater than given number are : -2, -1.5, and 1.25.
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What are the first 10 digits after the decimal point (technically the hexadecimal point...) when the fraction frac17 is written in base 16?
We happen to have
[tex]\dfrac17 = \dfrac18 + \dfrac1{8^2} + \dfrac1{8^3} + \cdots[/tex]
which is to say, the base-8 representation of 1/7 is
[tex]\dfrac17 \equiv 0.111\ldots_8[/tex]
This follows from the well-known result on geometric series,
[tex]\displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac a{1-r}[/tex]
if [tex]|r|<1[/tex]. With [tex]a=1[/tex] and [tex]r=\frac18[/tex], we have
[tex]\displaystyle \sum_{n=1}^\infty \frac1{8^{n-1}} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac1{1-\frac18} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac87 = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac17 = \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots[/tex]
Uniformly multiplying each term on the right by an appropriate power of 2, we have
[tex]\dfrac17 = \dfrac2{16} + \dfrac{2^2}{16^2} + \dfrac{2^3}{16^3} + \dfrac{2^4}{16^4} + \dfrac{2^5}{16^5} + \dfrac{2^6}{16^6} + \cdots[/tex]
Now observe that for [tex]n\ge4[/tex], each numerator on the right side side will contain a factor of 16 that can be eliminated.
[tex]\dfrac{2^n}{16^n} = \dfrac{2^4\times2^{n-4}}{16^n} = \dfrac{2^{n-4}}{16^{n-1}}[/tex]
That is,
[tex]\dfrac{2^4}{16^4} = \dfrac1{16^3}[/tex]
[tex]\dfrac{2^5}{16^5} = \dfrac2{16^4}[/tex]
[tex]\dfrac{2^6}{16^6} = \dfrac4{16^5}[/tex]
etc. so that
[tex]\dfrac17 = \dfrac2{16} + \dfrac4{16^2} + \dfrac9{16^3} + \dfrac2{16^4} + \dfrac4{16^5} + \dfrac9{16^6} + \cdots[/tex]
and thus the base-16 representation of 1/7 is
[tex]\dfrac17 \equiv 0.249249249\ldots_{16}[/tex]
and the first 10 digits after the (hexa)decimal point are {2, 4, 9, 2, 4, 9, 2, 4, 9, 2}.
(a − b)(2x − 3) + (6x + 7)(a − b)
factorise and ignore the first question it was wrong
Answer:
8ax - 8bx + 4a - 4b
Step-by-step explanation:
(a - b)(2x - 3) + (6x + 7)(a - b)
2ax -3a -2bx +3b + 6ax - 6bx + 7a -7b
8ax + 4a - 8bx - 4b
1. Identify your variables using let statements.
2. Determine the equations for the linear system.
3. Determine the solution to the linear system (point of intersection)
4. Explain the meaning of the solution using a therefore statement.
Chris is mixing 2 different types of fruit juice together for a summer drink. The two types of juices he is using is one that is 30% strawberry concentrate and the other is 55% lemon concentrate. If he wants 2 L that is 40% concentrate of the fruit juices, how much of each should be used to create the drink?
The meaning of the solution is; Therefore, 1.2 liters of the strawberry concentrate and 0.8 liters of the lemon concentrate.
What is the solution to the system of equations?It follows from the task content that the variables are;
let x be the amount of 30% strawberry concentrate.
let y be the amount of 55% lemon concentrate.
The equations of the linear system according to the task content are as follows;
x + y = 20.30x + 0.55y = (2 ×0.4)From the first equation; x = 2-y;
Hence, upon substitution; we have;
0.30(2-y) + 0.55y = 0.8
0.25y = 0.2.
y = 0.2/0.25 = 0.8L.
Hence, x = 2- 0.8 = 1.2L.
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Change the decimal to a fraction. (Use the “/“ in your fraction.) 0.45454545….
The decimal: 0.4545...
Can be written in fraction form as 45/99.
How to write the number as a fraction?
Here we have the number:
N = 0.4545...
Notice that the repeating digits are two, 4 and 5.
Then we can multiply our number by 100 (same number of zeros as repeating digits) so we get:
100*0.4545... = 45.4545...
Now if we subtract the original number, we get:
45.4545... - 0.4545... = 45
This means that:
(100 - 1)*0.4545... = 99*0.4545... = 45
Then we can multiply and divide our number by 99, so we get:
[tex]0.4545... = 0.4545...\frac{99}{99} = \frac{45}{99}[/tex]
So the fraction is 45/99
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3. Jeff Ruiz wants to purchase chocolates. The price of a 2-ounce box is $1.10, a 16-ounce box is $8.98, and a
32-ounce box is $17.98.
Jeff should purchase 25 , 2 ounce box and it will cost him $27.5 .
What is an ounce ?Ounce is defined as 1/16 part of a pound.
It is given that
price of a 2-ounce box is $1.10,
a 16-ounce box is $8.98
a 32-ounce box is $17.98.
As Jeff wants to purchase total 48 ounce chocolates , the box which is more cheaper has to be determined
The price of 1 ounce in a 2 ounce box is $1.1 /2 = $ 0.55
The price of 1 ounce in a 16 ounce box is $8.98 /16 = $ 0.56
The price of 1 ounce in a 32 ounce box is $17.98 /32 = $ 0.56
Therefore Jeff should purchase 25 , 2 ounce box and it will cost him $27.5 .
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can someone please help mee (20 points and i will give brainliest!!!)
Answer:
a. y-intercept:(0, -6), x-intercepts: (3, 0) and (-2, 0). vertex: (0.5, -6.25)
b. y-intercept: (0, 6), x-intercepts(3, 0) and (-2, 0). vertex: (0.5, 6.25)
Step-by-step explanation:
a:
So finding the y-intercept is really easy and is simply when x=0. If you plug in 0 as x it makes [tex]y=(0)^2-0-6[/tex] which simplifies to -6, which is the y-intercept. As for the x-intercepts you can calculate that by using the quadratic equation [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]. In this case a=1, b=-1, c=-6. So plugging those values in you get [tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(-6)}}{2(1)}[/tex], which simplifies to [tex]x=\frac{1\pm5}{2}[/tex]. This gives you the x-intercepts 6/2 and -4/2 which are 3 and -2. The vertex can be calculated by manipulating the equation so it's in the form of [tex]y=(x-h)^2+k[/tex] where (h, k) is the vertex of the parabola. This is done by moving c to the other side and then completing the square and the isolating y. So the first step will be
Move c to the other side
[tex]y+6=x^2-x[/tex]
Complete the square by adding (b/2)^2
[tex]y+6+0.25 = x^2-x+0.25[/tex]
Rewrite as square binomial
[tex]y+6.25 = (x-0.5)^2[/tex]
Isolate y
[tex]y=(x-0.50)^2-6.25[/tex]
(h, k) = 0.50, -6.25 which is the vertex
b: To identify the y-intercept you plug in 0 as x which will only leave c which in this case is 6 which is the y-intercept. (0, 6). To identify the x-intercepts you can simplify plug in the values a, b, c into the quadratic equation which was stated in the previous answer. In this case a, b, c = -1, 1, 6. Plugging these values in gives the equation [tex]y=\frac{-(1)\pm\sqrt{1^2-4(-1)(6)}}{2(-1)}[/tex]. which simplifies to [tex]x=\frac{-1\pm5}{-2}[/tex] which gives the values -2 and 3. To find the vertex it's the same process as before
Factor out -1
[tex]y=-(x^2-x-6)[/tex]
Add 6 to both sides (on the left side add -6 since -1 was factored out).
[tex]y-6=-(x^2-x)[/tex]
Complete the square by adding (b/2)^2 to both sides (add -(b/2)^2 to left side since -1 was factored out)
[tex]y-6-0.25 = -(x^2-x+0.25)[/tex]
Rewrite as square binomial
[tex]y-6.25=-(x-0.5)^2[/tex]
Add 6.25 to both sides
[tex]y=(x-0.50)^2+6.25[/tex]
(h, k) = (0.50, 6.25)
When you graph the parabolas you'll notice there just flipped relative to the x-axis. This can be deduced by simply looking at the two equations, since the two equations have the same absolute value coefficients, the signs are just different, and more specifically they're all opposite. If you took the first equation and multiplied the entire right side by -1 you would get the same equation. And since that equation really represents the value of y (since it's equal to y) you're reflecting it across the x-axis.
Answer:
a) y-intercept (0, -6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, -6.25)
b) y-intercept (0, 6); x-intercepts (3, 0) and (-2, 0); vertex (0.5, 6.25)
Step-by-step explanation:
(75 POINTS PLEASE RESPOND ASAP)
Explain how to solve 4x + ^3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.
Answer:
1.596
Step-by-step explanation:
So you can rewrite log as: [tex]log_{b}a=x = > b^x=a[/tex] So in this case it's already in exponential form which we'll use to rewrite into logarithm form.
[tex]4^{x+3} = 7\\log_47=x+3\\\\\frac{log7}{log4}=x+3\\1.404\approx x+3\\x\approx1.596[/tex]
Answer:
x = -1.596
Explanation:
[tex]\rightarrow \sf 4^{x + 3} = 7[/tex]
take log on both sides
[tex]\rightarrow \sf log(4^{x + 3}) = log(7)[/tex]
[tex]\rightarrow \sf (x + 3)log(4) = log(7)[/tex]
[tex]\rightarrow \sf x + 3= \dfrac{log(7)}{log(4)}[/tex]
[tex]\rightarrow \sf x= \dfrac{log(7)}{log(4)} -3[/tex]
calculate
[tex]\rightarrow \sf x= -1.596322539[/tex]
[tex]\rightarrow \sf x= -1.596 \quad (rounded \ to \ nearest \ thousand)[/tex]
The population of a small town was 3,150 last year. After a new factory opened close by, the population increased by 8%. What
is the new population of the town?
Add/Subtract the linear expression. -4(3x - 2) - 2(7x + 1)
Answer:
10
Step-by-step explanation:
multiply -4 and 3 to get -12
multiply -12 and -2 to get 24
multiply 2 and 7 to get 14
multiply 14 and 1 to get 14
subtract 14 from 24 to get 10
Which ordered pair is included in the solution set to the following system?
y > x2 + 1
y < x2 – x + 1
(–3, 4)
(–2, 6)
(0, 2)
(2, 4)
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The ordered pair which will satisfy both the inequalities will be the solution to the system of inequalities. Therefore, let's substitute each solution in the given inequalities,
A.) (–3, 4)
y > x² + 14 > (-3)² + 1
Since the first inequality is not satisfied this is not a part of the solution.
B.) (–2, 6)
y > x² + 16 > (-2)² + 1
6 > 5
y < x² – x + 16 < (-2)² - (-2) + 1
6 < 7
Since both the inequalities are satisfied this is the solution to the given system of inequalities.
C.) (0, 2)
y > x² + 12 > 0 + 1
2 > 1
y < x² – x + 12 < (0)² - (0) + 1
2 < 1
Since the second inequality is not satisfied this is not a part of the solution.
B.) (2,4)
y > x² + 14 > (2)² + 1
4 > 5
Since the first inequality is not satisfied this is not a part of the solution.
Hence, the correct option is B.
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evaluate: (36/49)^1/2
Answer:
6/7, -6/7
Step-by-step explanation:
Which one is it? I need help
The statement that must be true about square WXYZ are as follows;
WX ≅ XYWX ≅ YZ∠W is a right angle.Properties of a Square.All sides are equal to each other.Opposite sides are parallel to each other.All the angles are right angle.The diagonals bisect each other and are perpendicular.Therefore, the statement that must be true about square WXYZ are as follows;
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1.1 divided by 1.54 simplified
Answer:
1•4
Step-by-step explanation:
1•54÷1•1
1•54
1•1
divide by 10 both side with can move decimal
15•4
11
=my answer is 1•4.
Answer:
The correct answer for algebraic expression 1.54÷1.1 is = 1.4.
Step-by-step explanation:
this is question based on simple algebra -
Simple Algebraic equations - An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. we can apply many operations on algebraic equations like addition, subtraction, multiplication, division and raising to a power, and extraction of a root.
these equations are two algebraic expressions that are joined together using an equal to ( = ) sign. An algebraic equation is also known as a polynomial equation because both sides of the equal sign contain polynomials
so in the question algebraic operation used to solve is simple division.
therefore here in question we have to divide 1.54 with 1.1,
using the concept written above,
let the value of division be 'x'
we can write 1.54/1.1 = x
by dividing and multiplying the equation by 100 to remove the decimals.
(1•54/ 1•1)×100/100 = x
154/110 = x
now by simple division,
1.4 = x answer
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A square its diagonal length = 12cm then its area =
Answer:
72 sq cm
Step-by-step explanation:
For any rectangle, the diagonal is the hypotenuse of the right triangle formed by the base of the rectangle(b) and the height (h) of the rectangle
By the Pythogorean formula
[tex]d^{2} = b^{2} + h^{2}[/tex]
where d is the diagonal
For a square, all sides are equal so b = h = a and we get the formula
[tex]d^{2} = a^{2} + a^{2} = 2a^{2}[/tex]
[tex]a^{2} = d^{2} /2[/tex]
In this case we have d =12 so
[tex]a^{2} = 12^{2} /2 = 144/2 = 72[/tex]
But for a square of side a, the area is [tex]a^{2}[/tex] so 72 is the area
Answer:
72 square cm
Step-by-step explanation:
Area of square:[tex]\sf \boxed{\bf Area = \dfrac{d^{2}}{2}}[/tex] , here d is the length of the diagonal
[tex]\sf =\dfrac{12* 12 }{2}\\\\ = 6*2\\\\= 72 \ cm^2[/tex]
Two candles are light at the same time one burns for 6 hours and the other one lasts 2 hours. The first candles flame is 3 times longer than the other ones. How long do the both candles burn for? (please write with the way you found the answer I will give brainliest.)
At 150 minutes the length of the first candle is 3 times that of the other.
The complete question is
There are two candles of same length and same size. Both of them burn at uniform rate. The first one burns in 5 hours and the second one burns in 2 hours. Both the candles are lit together. After how many minutes the length of the first candle is 3 times that of the other?
What is an Equation ?When two algebraic expression are equated using an equal sign an equation is formed.
First candle burns for 5 hours
Second candle burns for 2 hours
Let the length of candle be l.
After t time (in minutes), length of first candle =l−(lt/300)
Length of second candle =l− (lt/120)
From the data given
l - (lt/120) = 3 * (l−(lt/300))
On simplifying
4t = 600
t = 150 minutes
Therefore after 150 minutes the length of the first candle is 3 times that of the other.
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The sum of three times a first number and twice a second number is 14. If the second number is subtracted from twice the first number, the result is 7. Find the numbers. The sum of three times a first number and twice a second number is 14. If the second number is subtracted from twice the first number , the result is 7 . Find the numbers . Or as points
Sara can travel 23 feet in 11 hours. Please calculate Sara's rate of speed. (round to 2 decimal places)
Answer:
12 is the answer
Step-by-step explanation:
FIRST do 23 - 11 and you will find your answer
The two-way table shows the estimated number of students who will enroll in three area high schools next year. a 5-column table has 4 rows. the first column has entries mount woodson high school, valley high school, riverside high school, total. the second column is labeled tenth grade with entries 110, 180, 160, 450. the third column is labeled eleventh grade with entries 120, 150, 140, 410. the fourth column is labeled twelfth grade with entries 80, 120, 200, 400. the fifth column is labeled total with entries 310, 450, 500, 1,260. in decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twelfth grade? 0.2 0.3 0.4 0.5
Answer:
A. 0.2
Step-by-step explanation:
First make the table.
10-grade 11-grade 12-grade Total
Woodson high school | 110 | 120 | 80 | 310 |
Valley high school | 180 | 150 | 120 | 450 |
Riverside high school | 160 | 140 | 200 | 500 |
Total | 450 | 410 | 400 | 1260 |
Question: In decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twelfth grade?
First, find 12-grade and riverside high school number. 200. Take the total lined up with total number, which is 1260, and divide 200 divided by 1260.
200/1260=0.2
The answer is 0.2.
Hope this helps!
If not, I am sorry.
Answer:
its .4
Step-by-step explanation:
i got it wrong when i tried it says it is .4 or the third option c
Which number line represents the solution set for the inequality 3(8-4x) < 6(x - 5)?
[tex]3(8 - 4x) < 6(x - 5) \\ 24 - 12x < 6x - 30 \\ 24 + 30 < 6x + 12x \\ 54 < 18x \\ \frac{54}{18} < \frac{18x}{18} \\ x > 3[/tex]
Solution : ] 3 , + ♾️ [
PLEASE GIVE BRAINLIEST
30 point!!!! Help me fast!!!PLS!!Question is attached!!!
Answer:
This is an extremely easy question bro!
1. 3²
2. 3 (Base) ² (Exponent)
3. Expanded form: (9 * 1)
Standard form: 9
Step-by-step explanation:
Well, there's none.
Please mark me as Brainliest! Thanks! :)Given the equation y = x – 2, you substitute 5 for x. Check all true statements below.
The correct value of the given function at x = 5 is y =3.
What is Equation?An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.
Here, the given equation :
y = x - 2
put x = 5 in the given equation, we get
y = 5 - 2
y = 3
Thus, the correct value of the given function at x = 5 is y =3.
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HELP ITS ABOUT ANGLES :((((
Answer:
its D. 2 and 3
Step-by-step explanation: supplementary angles are angles that add up to 180 (or that make a straight line) the angle pairs that make a straight line are 1 and 2, 2 and 3, 3 and 4, and 4 and 1.
So D would be correct
please help!! The dot plots below show the ages of students belonging to two groups of salsa classes:
Based on visual inspection, which group most likely has a lower mean age of salsa students? Explain your answer using two or three sentences. Make sure to use facts to support your answer.
Im thinking group A but at this point im just plain out confused
Question 2 multiple choice worth 1 points)
(01.02 lc)
solve for x: 6x + 3 = 5x - 8
0-11
11
0-5
5
[tex]6x+3=5x-8[/tex] (given)
[tex]x+3=-8[/tex] (subtract 5x from both sides)
[tex]x=\boxed{-11}[/tex] (subtract 3 from both sides)
Chris lost $8.59 playing poker in one week. If this continued, what would be his net
winnings or losses after five weeks?
Answer:
$42.95
Step-by-step explanation:
If Chris lost $8.59 playing poker in one week, in five weeks he would lose $42.95.
$8.59 lost per week.
5 weeks.
$8.59 x 5 = $42.95.
Hope this helps!
If not, I am sorry.
The width of a rectangle measures (10u + 3) centimeters, and its length measures (7u - 8) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle? The width of a rectangle measures ( 10u + 3 ) centimeters , and its length measures ( 7u - 8 ) centimeters . Which expression represents the perimeter , in centimeters , of the rectangle ?
Answer:
Perimeter of a rectangle: 2L + 2W
2(7u - 8) + 2(10u + 3)
= 14u - 16 + 20u + 6
= 34u - 10
A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
The perimeter of a rectangle.
P = 2 ( length + width)
The perimeter of the rectangle is represented by the expression
(34u - 10) centimeters.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The width of a rectangle = (10u + 3) centimeters.
The length of the rectangle = (7u - 8) centimeters.
The perimeter of a rectangle is given as,
P = 2 ( length + width)
P = 2 ( 7u - 8 + 10u + 3)
P = 2 (17u - 5)
P = (34u - 10) centimeters.
Thus,
The perimeter of the rectangle is represented by the expression
(34u - 10) centimeters.
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