42 adult tickets and 421 children tickets were purchased for the field trip, based on the given information that the total cost of the tickets was $995 and the children tickets cost $11 while the adult tickets cost $13, and the number of children tickets purchased was one more than ten times the number of adults tickets purchased.
Let's use variables to represent the unknown quantities in the problem:
Let x be the number of adult tickets purchased
Then the number of children tickets purchased is 10x + 1 (since it is one more than ten times the number of adults tickets purchased)
Using these variables, we can set up an equation based on the total cost of the tickets:
13x + 11(10x + 1) = 995
Simplifying and solving for x, we get:
23x + 11 = 995
23x = 984
x = 42.7826087 (rounded to 9 decimal places)
Since we can't purchase a fraction of a ticket, we'll round x down to the nearest whole number, which means 42 adult tickets were purchased. Then the number of children tickets purchased is:
10x + 1 = 10(42) + 1 = 421
So, 42 adult tickets and 421 children tickets were purchased.
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The length of a rectangular parking lot is 4 yards more than 5 times the width. Find the area of the parking lot.
The required expression by distributing the w on the right side, we get: A = 5w^2 + 4w
Explain about Rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form.
According to question:Let's call the width of the parking lot "w". According to the problem, the length is 4 yards more than 5 times the width, so we can write the length as 5w + 4.
The formula for the area of a rectangle is A = length × width. Substituting in our values, we get:
A = (5w + 4) × w
Simplifying this expression by distributing the w on the right side, we get:
A = 5w^2 + 4w
This is the formula for the area of the rectangular parking lot in terms of its width. To find the actual area, we need to know the width. Once we have that, we can plug it into the formula and solve for A.
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in
2. The park charges $24 to enter and
$0.45 per ticket. Write an algebraic
expression to represent the total
amount spent by a guest.
Answer:
C = $24 + 0.45x
Step-by-step explanation:
If we let total amount spent by a guest to the park as $C and number of tickets bought is x then the algebraic expression to represent the total amount spent by a guest is
C = $24 + 0.45x
A, B & C form the vertices of a triangle, where ∠CAB = 90°.AB = 10.5 m and AC = 5.2 m.
Evaluate ∠CBA, giving your answer rounded to 3 SF.
Answer: In a right-angled triangle, we can use the Pythagorean Theorem to find the length of the remaining side. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of side BC can be found using the Pythagorean Theorem:
BC^2 = AB^2 + AC^2
BC^2 = 10.5^2 + 5.2^2
BC^2 = 110.25 + 27.04
BC^2 = 137.29
BC = √137.29
BC ≈ 11.68 m
Now that we have the length of side BC, we can use the inverse cosine function (cos^-1) to find the angle ∠CBA:
∠CBA = cos^-1 (BC / AB)
∠CBA = cos^-1 (11.68 / 10.5)
∠CBA ≈ 68.194°
Rounding to 3 significant figures, the answer is ∠CBA = 68.2°.
Step-by-step explanation:
Compact fluorescent light (CFL) bulbs reduce energy waste. The amount of energy
waste that is reduced each day in a certain community can be estimated by -b² + 8b
where b is the number of bulbs. Divide by b to find the average amount of energy
saved per CFL bulb.
Write an exponential function in the form y=ab x that goes through points ( 0 , 12 ) and ( 2 , 300 )
The exponential function that goes through points (0,12) and (2,300) is [tex]y = 12(5)^x[/tex].
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The coordinate points are (0,12) and (2,300).
The exponential function has form [tex]y=ab^x[/tex].
So, the x values are 0,2 and y values are 12,300.
Substitute the first x and y values in the equation -
[tex]12=ab^0[/tex]
a = 12 ...... equation (1)
Substitute the second x and y values in the equation -
300 = ab² ...... equation (2)
Substitute the value of equation (1) in equation (2) -
300 = (12)b²
b² = 300 / 12
b² = 25
b = √25
b = 5
Substitute the values of a and b in exponential function -
[tex]y = 12(5)^x[/tex]
Therefore, the exponential function is [tex]y = 12(5)^x[/tex].
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POINTS UP FOR GRABS!!!!
The ordinary numbers for the expressions will be
a. 3.25*10⁴ = 32500
b. 6.04*10⁻³= 0.00604
c. 2400000 = 2.4*10⁶
d. 0.00147 = 1.47*10⁻³
What are expressions exactly?
In mathematics, expressions are mathematical assertions made up of at least two sentences that contain numbers, variables, or both and are linked by an operator. Mathematical operations include addition, subtraction, multiplication, and division. For example, x + y is an equation that uses an addition operator to separate the components x and y. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is six times the size of another number, x. This sentence is mathematically stated as x/2 + 6. Mathematical expressions are used to address complex problems.
Now,
Given expressions/Numbers are a. 3.25*10⁴ then ordinary form is
3.25*10000
=32500
b. 6.04*10⁻³ then ordinary numbers is
=6.04/1000
=0.00604
c. 2400000 then standard from is
=2.4*1000000
=2.4*10⁶
d. 0.00147 then standard form is
=1.47/1000
=1.47*10⁻3
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5. Pilihan ganda5 menit1 ptQ. An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle? Leave your answer in radical form.Pilihan jawaban30√3 m10√3 m5√3 m30 m
If an equilateral triangle has an altitude of 15 meters, then the perimeter of the equilateral triangle is 30[tex]\sqrt{3}[/tex] meters
The altitude of the equilateral triangle = 15 meters
The equilateral triangle is the triangle with equal side. The interior angle of the equilateral triangle will be 60 degrees. Number of vertices and edges will be three . The line of symmetry is 3
The altitude of of the equilateral triangle h = [tex]\sqrt{3}[/tex]a /2
Where h is the altitude of the equilateral triangle
a is the side of the equilateral triangle
Then the equation will become
15 = [tex]\sqrt{3}[/tex] a /2
[tex]\sqrt{3}[/tex]a = 15 × 2
Multiply the terms
[tex]\sqrt{3}[/tex]a = 30
Move [tex]\sqrt{3}[/tex] to the right hand side of the equation
a = 30 / [tex]\sqrt{3}[/tex]
a = 10[tex]\sqrt{3}[/tex] meters
The perimeter of the equilateral triangle = 3 × 10[tex]\sqrt{3}[/tex]
= 30[tex]\sqrt{3}[/tex] meters
Therefore, perimeter of the equilateral triangle is 30[tex]\sqrt{3}[/tex]
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Help im having trouble
Answer:
3 square units
Step-by-step explanation:
You want the area of the triangle defined by the points (-1, -4), (0, -2), and (2, -4).
TriangleThe plot of the grid points and the triangle is attached. By counting grid squares, you can see that the base of the triangle is 3 units, and its heigh perpendicular to the base is 2 units.
AreaThe area formula for a triangle is ...
A = 1/2bh
For base b=3 and height h=2, the area is ...
A = 1/2(3)(2) = 3 . . . . . square units
The area of the triangle is 3 square units.
robin is twice as old as earl and adam is 8 years younger than earl. in 6 years robin will be three times as old as adam. find their present ages
The present age of Earl is 12 years, Robin is 24 years and Adam is 4 years old.
Let us consider the present age of Earl to be x years.
According to the given question, the present age of Robin is twice that of Earl = 2x
And since it is given that Adam is 8 years younger than Earl, then his age
= x - 8
After 6 years, the age of Earl will be x + 6
Robin's age will be = 2x + 6
Adam's age will be = x - 8 + 6 = x - 2
According to the given question, Robin's age will be thrice the age of Adam.
Hence, 2x + 6 = 3 (x - 2)
⇒ 2x + 6 = 3x - 6 ⇒ 6 + 6 = 3x - 2x ⇒ 12 = x
Thus, the present age of Earl is 12 years,
Robin's age = 2x = 2 x 12 = 24 years
Adam's age = x - 8 = 12 - 8 = 4 years
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if $m$ is a real number and $x^2 mx 4$ has two distinct real roots, then what are the possible values of $m$? express your answer in interval notation.
The m values that allow the quadratic equation [tex]x^2 + mx + 4[/tex] to have two independent real roots are m in the open range (-∞ , -4) (4 , ∞). This may be expressed in interval notation as:
m ∈ (-∞, -4) ∪ (4, ∞).
The quadratic formula tells us that the quadratic equation's roots
[tex]x^2 + mx + 4 = 0[/tex]
are provided by:
[tex]x = (-m[/tex] ± [tex]sqrt(m^2 - 16))/2[/tex]
The discriminant [tex](m^2- 16)[/tex]must be positive, i.e., [tex]m^2[/tex] > 16, for the quadratic to have two separate real roots. As a result, we have two instances to consider:
Case 1: m > 4. Because [tex](-m + sqrt(m^2 - 16)/2[/tex]and[tex](-m - sqrt(m^2 - 16)/2[/tex]are both real and unique in this case, the quadratic has two separate real roots.
Case 2: m < -4. In this situation, [tex](-m + sqrt(m^2 - 16)/2[/tex] is negative, whereas[tex](-m - sqrt(m^2 - 16)/2[/tex] is positive, indicating that the quadratic has two separate real roots.
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80% of a number is x. What is 100% of the number? Assume x>0
100% of the number is: the number x ÷ 0.8 × 1 = the number If 80% of a number is x, then the number can be found by dividing x by the percentage as a decimal.
To convert a percentage to a decimal, divide the percentage by 100.
So, if 80% of the number is x, then:
x ÷ 0.8 = the number
In other words, to find the whole number, we need to divide the part (x) by the percentage as a decimal (0.8).
Once we have the whole number, we can find 100% of it by simply multiplying the whole number by 1.
So, 100% of the number is:
the number x ÷ 0.8 × 1 = the number
In conclusion, if 80% of a number is known, the whole number can be found by dividing the part by the percentage as a decimal, and 100% of the number can be found by simply multiplying the whole number by 1. Understanding the concept of percentage and the ability to convert between percentages, decimals, and whole numbers is an important skill in various areas of life and work.
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Quadrilateral ABCD~ Quadrilateral WXYZ, AB= 15, BC= 27, WX= 10
The scale factor is 3/2. The length of XY is 18.
What are similar Quadrilaterals?
Two figures are said to be similar if they share the same shape. Congruent objects are those that are precisely the same size and shape. Real-world examples of congruent figures or objects include, for instance, both of a person's hands, both of a car's front wheels, etc.
If the corresponding angles and sides of two quadrilaterals are equal, then the two quadrilaterals are similar.
Given that Quadrilateral ABCD is similar to Quadrilateral WXYZ.
Thus
AB/WX = BC/XY = CD/YZ = AD/WZ ....(i)
The length of AB = 15, BC= 27, WX= 10
The scale factor is
AB/WX = BC/XY = CD/YZ = AD/WZ
= 15/10
= 3/2 [Divide the denominator and numerator by 5]
Take first two ratios of (i):
AB/WX = BC/XY
15/10 = 27/XY
3/2 = 27/XY
XY = 27 × (2/3)
XY = 18
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Pls answer! Lots of points! Question down below!
The dimensions of Yura's picture 10×7 square units. The length of Yura's picture 10 units and the width of 7 units.
What is a rectangle?
An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.
The number of lines along the length is 11.
The length of the frame is 10 units.
The number of lines along the width is 8.
The width of the frame is 7 units
The dimension of an object is length × width.
The dimension of the frame is 10 units × 7 units.
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In 2004, $6,000 was invested in a mutual fund that earned 9% interest per year.
a) Tell whether the model represents an exponential growth or decay and create a function that models it
b) How much was in the account in 2012?
a) The function would be A(t) = 6000(1 + 0.09)ᵗ
b) The amount in the account in 2012 was approximately $11,737.51.
What is the function model?
In mathematics, a function model is a mathematical equation or expression that represents a relationship between two or more variables. It is a way of describing the behavior or pattern of a particular phenomenon or system.
a) The model represents exponential growth since the amount in the account is increasing with time. The function that models the growth of the investment over time is given by:
A(t) = 6000(1 + 0.09)ᵗ
where A(t) is the amount in the account after t years.
b) To find the amount in the account in 2012, we need to find the value of A(2012 - 2004) = A(8). Substituting t = 8 into the function above, we get:
A(8) = 6000(1 + 0.09)⁸
= 6000(1.09)⁸
≈ $11,737.51
Therefore, the amount in the account in 2012 was approximately $11,737.51.
Hence,
a) The function would be A(t) = 6000(1 + 0.09)ᵗ
b) The amount in the account in 2012 was approximately $11,737.51.
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How does the distance change during the last section of tom’s journey? What does this mean? Explain your reasoning
The distance is decreasing with time meaning that the object is going back to the starting point.
What does it mean when distance decreases with time?When distance decreases with time, it means that the object is moving towards its starting point or moving in the opposite direction from its initial position. In other words, the object is moving backwards or reversing its direction of motion.
Distance is a measure of the total amount of ground covered by an object in motion, while time is a measure of how long it takes the object to cover that distance. If the object is moving towards its starting point, it means that it is covering less and less distance over time, or the distance it covers is decreasing.
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Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6} if you roll the die once, calculte the following probabilities. Write you answers in fraction form and in lowest terms (e. G. 1/4) a) the probability of getting a 6 is. B) the probability of getting an even number is. C) the probability of getting a number greater than 2 is
The probability for the sample space of a fair die rolled out {1, 2, 3, 4, 5, 6} with different conditions are :
a. Probability of getting 6 = 1/6
b. Probability of an even number on a die = 1/2
c. Probability of number more than 2 = 2/3.
Sample space is equal to {1, 2, 3, 4, 5, 6}
Number of times die rolled out = only once.
Total number of outcomes = 6
Probability = ( Number of favourable outcomes ) / ( Total outcomes )
Required probability in fraction form with lowest terms:
a. Probability of getting 6
Favourable outcomes ={ 6 }
Number of favourable outcomes = 1
Probability of getting 6 = 1 / 6
b. Probability of getting an even number
Favourable outcomes = { 2, 4, 6 }
Number of favourable outcomes = 3
Probability = 3 / 6
= 1 / 2
c. Probability of getting number greater than 2
Favourable outcomes = { 3, 4, 5, 6 }
Number of favourable outcomes = 4
Probability = 4 / 6
= 2 / 3
Therefore, the required probability as per the mentioned conditions are:
a. Probability of getting 6 = 1/6
b. Probability of even number = 1/2
c. Probability of number greater than 2 = 2/3.
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the price of gasoline is $2.27 per gallon and decreases at the rate of $0.03 every two months. oil costs $0.45 per gallon and increases at a rate of $0.05 every six months. how many years will it take for them to be equal in price?
The price of gasoline and oil will be equal in price after 4 years when the price of gasoline is $2.27 per gallon and decreases at the rate of $0.03 every two months.
To find out when the price of gasoline and oil will be equal, we have to set the two prices equal to each other and solve for time. The price of gasoline decreases at the rate of $0.03 every two months and the price of oil increases at a rate of $0.05 every six months.
We can start with the initial prices and solve for the time when they are equal:
$2.27 - 0.03t = 0.45 + 0.05t
where t represents the time in years.
Solving for t, we get:
$2.27 - 0.03t = 0.45 + 0.05t
$1.82 = 0.08t
t = 22.5
Since t is in months, we have to divide by 12 to convert it to years:
t = 22.5 / 12 = 1.875
So the price of gasoline and oil will be equal in price after approximately 4 years.
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How do you score 102 students play at least once by there is 40% of the students at the school how many students are at the school
If 102 students at least plays one sport and this is 40% of the students at the school, then there 255 students at the school
Let's assume that the total number of students in the school is "x".
40 percentage of the students at the school play at least one sport. So, the number of students who play at least one sport is 0.4x.
We also know that the number of students who play at least one sport is 102. Therefore, we can write:
0.4x = 102
Move 0.4 to the right hand side of the equation
x = 102 / 0.4
Divide the numbers
x = 255
Therefore, there are 255 students at the school.
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6. A triangle has two side lengths
3 feet. Select all the measures that could be the
length of the third side.
3 ft
9.2 ft
4.6 ft
8 ft
7.4 ft
2 ft
The length of the third side of the triangle will be 2 feet. Then the correct option is F.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Any two parts of a triangle can be added together to have a length larger than the third side.
A triangle has two side lengths of 3 feet. Let 'x' be the third side.
By the theorem, the inequality is given as,
x < 3
The length of the third side of the triangle will be 2 feet. Then the correct option is F.
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What is the perimeter of the parallelogram?
A 12
B 15
C 30
D 44
Answer:
C. P = 30
Step-by-step explanation:
Parallelogram opposite (or parallel) sides are equal,
so:
2x = x + 2
5y - 9 = 2y + 3
For x:
2x = x + 2
2x - x = 2
x = 2
For y:
5y - 9 = 2y + 3
5y - 2y = 3 + 9
3y = 12
y = 4
the smallest sides are equal 2x and x + 2 => 2 * 2 = 4
the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11
P = 2 * (a + b)
P = 2 * (4 + 11)
P = 2 * 15
P = 30
Write a linear equation in slope intercept form y=mx+b that passes through (-6,-1) and is parallel to y=-2/3x+1
On solving the provided question we can say that the slope intercept of line is y = (3/2)x + 8
What is slope intercept?In mathematics, the intersectiοn point is the place on the y-axis where the slοpe of the line crosses. a place where the y-axis crosses οn a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equatiοn for the straight line to shοw this. The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept form.
When an equation has the intercept fοrm (y=mx+b), the slope is m and the y-intercept is b. Sοme equations can alsο be rewritten such that they seem to be slοpe intercepts. If y = x is rewritten as y=1x+0, for instance, the slοpe and y-intercept are bοth changed to 1.
the line is y = -2/3x+1
so the slope, m = -2/3
since it parallel , new slope = 3/2
the slope intercept of line is
y +1 = 3/2(x+6)
y + 1= (3/2)x + 9
y = (3/2)x + 9 - 1
y = (3/2)x + 8
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selecting christmas presents if a person can select presents from presents under a christmas tree, how many different combinations are there?
Sselecting A, B, and C is the same as selecting B, C, and A, so = 720/(3*2*1) = 120 combinations
When the decision's order is unimportant, a combination is a choice made in mathematics from among a group of distinct elements. A pear and an orange, an apple and an orange, or a trio of fruits—an apple, an orange, and a pear—can be paired into one of three pairs. An official definition of a k-combination of a set S is a subset of S's k unique items. Consequently, two combinations are considered to be same if and only if they both contain the same elements. If a collection contains n elements, a combination is any set of n objects taken k at a time without repetition.
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i need the answers to the marked answers! please help me!! :)
The results are given below.
What is congruency of triangles?Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'
Consider the first triangles,
Given, L is the midpoint of KN and MP.
To find ΔMKL ≅ΔPNL
Using side-angle-side congruency ,
Here, the corresponding sides , KM and MP, KL and LP are equivalent.
But the angle ∠L is not an included angle.
So this triangles are non congruent.
Consider the next triangles.
BD bisects ∠ABC ∠BAD≅∠BCD
To find ΔABC≅BCD
By side- side-side congruency,
The corresponding sides AB and BD, AD and DC, BD are equivalent.
Therefore this ΔABC≅BCD proved.
Hence the proof.
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Evaluate x² + 2y + 3x for x = 5, y = 8
Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≥8) , n=9 , p=0. 8
The probability of getting 8 or more successes in 9 trials, with given success rate in each trial is 0.8, is 0.9520.
To find the probability , we can use the cumulative distribution function (CDF) of the binomial distribution:
P(X ≥ 8) = 1 - P(X < 8) = 1 - P(X ≤ 7)
Using a binomial calculator or a binomial probability distribution table, we can find:
P(X ≤ 7) = 0.0480 (rounded to four decimal places)
Therefore,
P(X ≥ 8) = 1 - 0.0480 = 0.9520
So the probability of getting 8 or more successes in 9 trials, given the probability of success in each trial is 0.8, is 0.9520 (rounded to four decimal places).
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what is 13 over 16 as a decimal rounded to the nearest tenth
13/16 as a decimal rounded to the nearest tenth is 0.8.
A decimal is a way to represent the same thing but in a different form. In this case, we will convert the fraction 13/16 into a decimal and round it to the nearest tenth.
To convert a fraction to a decimal, we divide the numerator (top number) by the denominator (bottom number). In this case, 13 divided by 16 is equal to 0.8125. This means that 13/16 as a decimal is 0.8125.
To round a decimal to the nearest tenth, we look at the digit in the hundredths place (the second digit after the decimal point).
If this digit is 5 or greater, we round up the tenths place (the first digit after the decimal point). If it is less than 5, we leave the tenths place as is. In this case, the digit in the hundredths place is 2, which is less than 5.
Therefore, we leave the tenths place as is, and the final answer is 0.8.
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You type 170 words per minute. How many minutes does it take you to type 3400 words?
Answer:
Step-by-step explanation:
3400/170 = 20 minutes.
Answer:
20 minutes
Step-by-step explanation:
3400 words / 170 wpm
20 minutes
Please help, I’ll give brainliest!!!!!!!!!!!!
Answer: (2, -1)
Step-by-step explanation:
Linda wants new carpeting for her bedroom her bedroom is a 75m by 50m rectangle if carpeting cost AED 12 per square meters how much will it cost to lay carpet for her entire bedroom?
(please answer as soon as possible i need this answer) thank you
If carpeting cost AED 12 per square meters for the bedroom of 75m by 50m, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.
To calculate the cost of laying carpet for Linda's bedroom, we need to know the area of the bedroom and the cost per square meter of the carpeting.
Linda's bedroom is a rectangle with a length of 75 meters and a width of 50 meters. To calculate the area of the bedroom, we multiply the length by the width:
Area = length x width = 75 meters x 50 meters = 3750 square meters
Now that we know the area of the bedroom is 3750 square meters, we can find the total cost of the carpeting by multiplying the area by the cost per square meter. The cost per square meter is given as AED 12, so:
Total cost = area x cost per square meter = 3750 square meters x AED 12/square meter
Multiplying the area by the cost per square meter gives us:
Total cost = AED 45,000
Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.
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Julieta has 58 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 204 square meters. Solve for the dimensions (length and width) of the field
The dimension of rectangular piece of land is 17 x 12 square units in size.
The space surrounding a shape is known as its perimeter. It is the length of the shape's sides taken together.
The space occupied by a flat shape or an object's surface can be referred to as the area.
What is the rectangular area formula?
Rectangle area equals length x width
Let the rectangle plot's length and breadth be x and y, respectively.
Juliet has a 58-meter fence.
The rectangular piece of land's perimeter is 58 meters.
2(length + width) = 58
x + y = 58\2
⇒ x + y = 29
Moreover, the plot's total area is 204 square units.
x × y = 204
⇒ x × (29 - x) = 204
[tex]29x-x^{2} =204\\x^{2} -29x+204=0\\x^{2} -12x-17x+204=0[/tex]
(x-12) (x-17) = 0
x = 12, x = 17
When, x= 17
y = 29 - 17 = 12m
when x = 12
y = 29 - 12 = 17m
As a result, the rectangular land parcel has dimensions of 17 x 12 square units.
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