Using the area formula for rectangle, the largest area that can be enclosed by rope and wall = 450m².
Define a rectangle?A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are many rectangular objects all around us. The two characteristics that distinguish each rectangle are its length and its breadth. A rectangle's longer and shorter sides are its width and length, respectively.
Here in the question,
The rope used here is 60m.
Now 60m of rope is forming 3 sides of the rectangle.
The adjacent sides cannot be equal to each other as it is a rectangle.
So, the sides of the rectangle can be given as such so that area will be maximum:
length = 30m
width = 15m
So, the rope includes one length and 2 widths of the rectangle.
As such (60m = 30m + 15m + 15m).
Now, area of the rectangle =
l × w
= 30 × 5
= 450m²
Therefore, the largest area that can be enclosed by rope and wall = 450m².
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Topic: Linear Diophantine Equation
Solve: Find x,y∈Z such that 123x + 360y = 99
The solution to the equation 123x + 360y = 99 is x = 22 and y = -11.
What is Linear Diophantine Equation?
An equation with two or more integer unknowns that are all to a maximum degree of one is known as a linear diophantine equation (LDE).
To solve the equation 123x + 360y = 99, we can use the extended Euclidean algorithm, which is a method for finding the greatest common divisor (GCD) of two integers and expressing it as a linear combination of those integers. We can use the same algorithm to find a solution to the given equation.
First, we need to find the GCD of 123 and 360. We can use the Euclidean algorithm for this:
gcd(123, 360) = gcd(123, 360 - 123*2) = gcd(123, 114)
gcd(123, 114) = gcd(123 - 114, 114) = gcd(9, 114)
gcd(9, 114) = gcd(9, 114 - 9*12) = gcd(9, 6)
gcd(9, 6) = gcd(9 - 6*1, 6) = gcd(3, 6)
gcd(3, 6) = gcd(3, 6 - 3*2) = gcd(3, 0)
gcd(3, 0) = 3
Therefore, the GCD of 123 and 360 is 3.
Now we can use the extended Euclidean algorithm to find integers s and t such that 123s + 360t = 3. This is done by working backwards through the Euclidean algorithm and expressing each remainder as a linear combination of the previous two integers:
gcd(123, 360) = 3
3 = 123s + 360t
3 = 9 - 114
= 9 - (360 - 123*2)
= 123*2 - 360*1
s = 2, t = -1
Now we can multiply both sides of the equation by 33 to get a solution to the original equation:
123x + 360y = 99
123*2*33 + 360*(-1)*33 = 3*33
123*66 + 360*(-33) = 99
Finally, we can divide both sides by 3 to get a solution in integers:
123*22 + 360*(-11) = 33
Therefore, x = 22 and y = -11 is a solution to the equation 123x + 360y = 99.
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Please help me this is for a homework
Answer:
{0, 1, 2}
Step-by-step explanation:
4x<8x+2
-4x<2
x<-1/2
Only {0, 1, 2} meets all critera
Question 7 of 10
In the triangle below, b=_ If necessary, round your
answer to two decimal places.
A
33.7°
C
Answer here
8
26.4
24
SUBMIT
The length of the missing side is approximately 4.73 units.
What is a triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Here, we have
Given:
∠A = 33.7°
∠C = 26.4°
We have to find the value of b.
Let's label the missing side as b, and use sin(A) = opposite/hypotenuse to find the length of the side opposite angle A:
sin(A) = opposite/hypotenuse
sin(33.7°) = b/8
b = 8 × sin(33.7°)
b ≈ 4.726
Hence, the length of the missing side is approximately 4.73 units.
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the sum the ages Three years ago, of the father and son wal us years un After 3 years, the ratio of the agy of the father and son will be 3:1 then How much old is the father from his son?
Simplify: m² ∙ m⁶ ∙ m =
Answer:
Option A) m^9.
Step-by-step explanation:
To simplify the given expression, we can use the rules of exponents which state that when we multiply powers with the same base, we can add their exponents.
So, m² ∙ m⁶ ∙ m can be simplified as:
m² × m⁶ × m = m^(2+6+1) = m^9
Therefore, the simplified form of m² ∙ m⁶ ∙ m is m^9.
1/x+1 + 9/x+9 =1
Solve
To solve the equation:
1/(x+1) + 9/(x+9) = 1
First, we can simplify the equation by finding a common denominator:
((x+9)+9(x+1))/(x+1)(x+9) = 1
Simplifying the numerator, we get:
(10x+18)/(x+1)(x+9) = 1
Cross-multiplying gives:
10x+18 = (x+1)(x+9)
Expanding the right side of the equation, we get:
10x+18 = x^2+10x+9
Simplifying and rearranging gives:
x^2-9 = 0
Using the quadratic formula, we solve for x:
x = (±sqrt(81))/1
x = ±9
Therefore, the solutions to the equation are x = -9 and x = 9.
which two expressions are equivalent? ANSWER ASAPP!
Hence, the expressions 8 x + 1 and 5/x are equal. F) 8x+(66) and J) 5x + (101) are the two equivalent expressions.
what is expression ?A mathematical sentence without an equal sign that comprises numbers, quantities, and operations is known as an expression. By changing variables with constants and using the order of actions, it can be evaluated or made simpler. For instance, the phrases "3x + 7" and "4y - 2" are equations, whereas "3x + 7 = 16" is an expression.
given
F and J are the two expressions that are equivalent.
F: 8 ÷ x + (6/6)
6/6 reduced to 1: 8 x + 1
J: 5 x x 1 Converting 5 x to 5x-1, 5x-1 x 1 equals 5/x
Hence, the expressions 8 x + 1 and 5/x are equal. F) 8x+(66) and J) 5x + (101) are the two equivalent expressions.
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The complete question is:-
Which two expressions are equivalent?
(6.7D | Lesson 6)
F 8÷x+(6'6) and 8÷x. 1
G 6-2 (x - x) and 6 ÷ 2
H 14 ÷ 7. (xx) and 14 ÷ 7
J 5÷x(101)10+and 5 x 1•
Statistics. I would like to understand this question. We are using minitab. I don't understand what exactly I should input to get this information.
The maximum head breadth that the helmets will fit is apprοximately 7.96 inches, which rοunds tο 8.0 inches (οptiοn A).
Hοw tο find Z-scοre cοrrespοnding tο the cutοff pοint?We can use the Z-scοre fοrmula tο find the Z-scοre cοrrespοnding tο the cutοff pοint:
Z = (X - μ) / σ
where X is the head breadth we want tο find, μ is the mean head breadth, σ is the standard deviatiοn, and Z is the Z-scοre cοrrespοnding tο the cutοff pοint.
We want tο find the Z-scοre such that the area tο the right οf it under the standard nοrmal distributiοn curve is 0.025. We can use a standard nοrmal distributiοn table οr calculatοr tο find this Z-scοre, which turns οut tο be apprοximately 1.96.
Tο find the maximum head breadth that the helmets will fit, we need tο find the cutοff pοint beyοnd which the head breadths are in the largest 2.5%.
Nοw we can sοlve fοr X:
1.96 = (X - 6.0) / 1.0
X - 6.0 = 1.96
X = 7.96
Therefοre, the maximum head breadth that the helmets will fit is apprοximately 7.96 inches, which rοunds tο 8.0 inches (οptiοn A).
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An arc of a circle radius 7cm is 14cm long. What angle does the arc subtend at the centre? (π =22/7).
The central angle of the given arc, subtending a circle with a radius of 7 cm and a length of 14 cm, is approximately 103.13 degrees.
What is arc of a circle?An arc is a section of a circle's or curve's border in mathematics. It is additionally known as an open shape. The circumference, also referred to as the perimeter, is the measurement around a circular that defines its edge. Consequently, the arc is defined as the separation between any two locations along its circumference.
The angle that an arc of a circle subtends at the center is called the central angle. The central angle is measured in degrees and is formed by the radii that make up the arc.
Given:
Radius of the circle (r) = 7 cm
Length of the arc (s) = 14 cm
To find the central angle (θ) of the arc, we can use the formula:
θ = (s / r) * (180 / π)
where:
s = length of the arc
r = radius of the circle
π = pi (approximately 3.14159...)
Plugging in the given values:
θ = (14 / 7) * (180 / π)
θ = 2 * (180 / π)
θ ≈ 103.13 degrees (rounded to two decimal places)
So, the central angle of the given arc, subtending a circle with a radius of 7 cm and a length of 14 cm, is approximately 103.13 degrees.
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If I watch tv 4 days out of 7 each and I watch 28 days how many days will I watch tv i NEED THIS ASAP
you will watch TV for approximately 16 days out of the 28 days.
If you watch TV for 4 days out of 7 each week, then the fraction of the week that you spend watching TV is:
4/7
To find the total number of days you will watch TV over 28 days, you can use the proportion:
4/7 = x/28
where x is the number of days you will watch TV.
To solve for x, you can cross-multiply:
4 * 28 = 7 * x
112 = 7x
x = 112/7
x ≈ 16
Therefore, you will watch TV for approximately 16 days out of the 28 days.
What is proportion?
Proportion is a mathematical concept that expresses the relationship between two quantities or values. It is often represented as a fraction, with the numerator and denominator representing the values being compared.
In a proportion, the two ratios are equal. For example, if you have a bag of marbles containing 6 red marbles and 4 blue marbles, the proportion of red to blue marbles is 6:4, or 3:2. This can also be written as a fraction: 3/2.
Proportions are useful in many areas of mathematics and everyday life, including geometry, statistics, and finance. They are also used in problem-solving to find missing values or to determine if two values are proportional to each other.
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1 The points (-8, 5) and (-4, r) lie on a line with slope 1/4. Find the missing coordinate r.
Answer:
Step-by-step explanation:
We can use the slope formula to find the slope of the line passing through the two given points:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-8, 5) and (x2, y2) = (-4, r).
Substituting these values, we have:
1/4 = (r - 5) / (-4 - (-8))
1/4 = (r - 5) / 4
r - 5 = 1
r = 6
Therefore, the missing coordinate is r = 6.
Darrius is single and lives in Pennsylvania, which has a state income tax rate of 3.07%. He earns an annual salary of $42,350. Calculate his monthly take-home pay.
Answer:
To calculate Darrius' monthly take-home pay, we first need to calculate his annual state income tax. We do this by multiplying his yearly salary by the state income tax rate:
$42,350 x 3.07% = $1,292.94
Next, we subtract the state income tax from his annual salary to get his annual net income:
$42,350 - $1,292.94 = $41,057.06
Finally, we divide his annual net income by 12 to get his monthly take-home pay:
$41,057.06 / 12 = $3,421.42
Therefore, Darrius' monthly take-home pay is $3,421.42.
Step-by-step explanation:
What is 3÷2/5? the quotient is seven?
Answer:
3 ÷ 2/5 = 3 × 5/2 = 15/2 = 7 1/2
60% of the students in a class are boys. If there are 16 girls in the class, how many boys are there?
Answer:
24 boys
Step-by-step explanation:
If 60% of the students in a class are boys, 40% of the students are girls.
Then 16/0.4 = 40 students total
40 - 16 = 24 boys
or you can use 40 x 0.6 = 24 boys
(Easy question) Please give answer and will get 10 pts
Answer:
The volume is 60cm³
Step-by-step explanation:
(bxhxl)/2 = answer
(5x4x6)/2
5x4 = 20
20x6=120
120/2 = 60
The combined city/highway fuel economy of a 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas is a normally distributed random variable with a range of 17mpg to 22mpg answer A and B URGENT
We need a sample size of 98 to estimate the mean with 90% confidence and an error of ±0.25 mpg, using the given range of fuel economy for the 2016 Toyota 4Runner.
What is standard deviation?Standard deviation is a measure of the amount of variation or dispersion in a set of data. It is a statistical measure that is used to quantify the amount of variation or spread of a set of data values relative to the mean or average value of the data.
(a) Using Method 3, the Empirical Rule for a normal distribution, we know that for a normal distribution, approximately 68% of the values fall within 1 standard deviation from the mean, 95% fall within 2 standard deviations from the mean, and 99.7% fall within 3 standard deviations from the mean.
Therefore, to find the standard deviation for the given range of 17 to 22 mpg, we can use the Empirical Rule as follows:
The range between the mean and the upper limit (22 mpg) is 3 standard deviations, so the standard deviation can be estimated as (22-17)/3 = 1.6667 mpg.
Thus, the estimated standard deviation using Method 3 is 1.6667 mpg, rounded to 4 decimal places.
(b) To find the sample size required to estimate the mean with 90% confidence and an error of ±0.25 mpg, we can use the following formula:
[tex]n = (z*(E))^2[/tex]
where n is the sample size, z is the z-score corresponding to the desired confidence level (90% = 1.645), σ is the estimated standard deviation from part (a), and E is the desired margin of error (±0.25 mpg).
Substituting the values, we get:
[tex]n = (1.645*(1.6667/0.25))^2[/tex]
n ≈ 97.15
Rounding up to the nearest whole number, we get the sample size of 98.
Therefore, we need a sample size of 98 to estimate the mean with 90% confidence and an error of ±0.25 mpg, using the given range of fuel economy for the 2016 Toyota 4Runner.
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The circle graph shows the results of a survey about
favorite kinds of books. If 600 people were surveyed, how
many more people prefer mystery books than historical
fiction books?
Thus, number of more people who prefer mystery books over historical
fiction books are 48.
Explain about the pie chart:A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarise a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments. A certain category is represented by each segment.
Given data:
mystery books = 18%historical fiction books = 10%Total books = 600Number of mystery books = 18% of 600
= 18*600 / 100
= 108
Number of historical fiction books = 10% of 600
= 10*600 / 100
= 60
Difference = Number of mystery books - Number of historical fiction books
Difference = 108 - 60
Difference = 48
Thus, number of more people who prefer mystery books over historical
fiction books are 48.
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Complete question:
The circle graph shows the results of a survey about favorite kinds of books. If 600 people were surveyed, how many more people prefer mystery books than historical fiction books?
The picture is attached.
Pete wants to put a fence around a rectangular section of his backyard.
The space he wants to enclosc measures 30 feet in length, and it is as
wide. How many feet of fencing does he need?
(1) 10
(2) 30
(3) 40
(4) 80
(5) 120
What is the difference of the rational expessions below? 6/x - 5x/x+2
Answer:
B
Step-by-step explanation:
You want the difference of the rational expressions (6/x) and (5x/(x+2)).
DifferenceThe difference of rational expressions is found the same way any difference of fractions is found. The fractions are written using a common denominator, and the difference is taken of the numerators.
[tex]\dfrac{6}{x}-\dfrac{5x}{x+2}=\dfrac{6(x+2)}{x(x+2)}-\dfrac{x(5x)}{x(x+2)}\\\\\\=\dfrac{6x+12-5x^2}{x(x+2)}=\boxed{\dfrac{-5x^2+6x+12}{x^2+2x}}[/tex]
__
Additional comment
Once you realize the common denominator is x(x+2) = x²+2x, you have eliminated all but the correct answer choice.
is 4.702 greater than 47.02
Determine if the point is a solution of the linear inequality. Point: ( 3 , 2 ) Linear inequality: 3 x + 2 y < 6
The statement is not true, since 13 is not less than 6. Therefore, the point (3, 2) is not a solution of the linear inequality 3x + 2y < 6.
To determine if the point (3, 2) is a solution of the linear inequality 3x + 2y < 6, we substitute the values of x and y in the inequality and check if it is a true statement or not.
A linear inequality is an inequality in which the variables have a degree of one, and the inequality can be expressed as a linear equation with an inequality symbol. A linear inequality can be represented graphically as a line with a shaded region that either includes or excludes certain points in the coordinate plane.
For example, the inequality 2x + 3y > 6 is a linear inequality. To graph this inequality, we can first plot the line 2x + 3y = 6 by finding its x and y intercepts, which are (3, 0) and (0, 2), respectively. Then, we can choose a test point not on the line, such as (0, 0), and substitute its coordinates into the inequality to see if it is a solution.
3(3) + 2(2) < 6
9 + 4 < 6
13 < 6
The statement is not true, since 13 is not less than 6. Therefore, the point (3, 2) is not a solution of the linear inequality 3x + 2y < 6.
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Select the correct answer.
f(x) =2x + 4,
4 + 1⁄2x,
-x + 5,
x < -2
-2 < x < 2
2 ≤ x
Which of the following is the graph of the function shown above?
The identified graph of the function is graph Y (bottom left)
How to determine the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2x + 4, x ≤ -2
4 + 1⁄2x, -2 < x < 2
-x + 5, 2 ≤ x
The above function is a piecewise function
By the domain of the functions, we have the following endpoints
f(x) = 2x + 4, x < -2 = closed endpoint
4 + 1⁄2x, -2 < x < 2 = open endpoint
-x + 5, 2 ≤ x = closed endpoint
When the above endpoints and functions are compared to the graph, we have the graph to be graph Y (bottom left)
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The period p of a pendulum, or the time it takes for the pendulum to make one complete swing, varies directly as the square root of the length L of the pendulum. If the period of a pendulum is 1.8 s when the length is 2 ft, find the period when the length is 3 ft.
The period of the pendulum when the length is 3 ft is approximately 2.08 seconds.
What is the period?
We are given that the period P varies directly as the square root of the length L of the pendulum. We can write this as:
P ∝ √L
Using a proportionality constant k, we can write this as an equation:
P = k√L
To find the value of k, we can use the information given in the problem: when L = 2 ft, P = 1.8 s. Substituting these values into the equation, we get:
1.8 = k√2
To solve for k, we can isolate it by dividing both sides by √2:
k = 1.8 / √2
Now we can use this value of k to find the period when the length is 3 ft. Substituting L = 3 ft and the value of k we just found into the equation, we get:
P = k√L
P = (1.8 / √2) √3
P ≈ 2.08 seconds
Therefore, the period of the pendulum when the length is 3 ft is approximately 2.08 seconds.
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x value of {3x+4y=36y=−12x+8
Answer: x= -20
Step-by-step explanation:
A flower bed is in the shape of a rectangle. It measures
21 ft long and 12 ft wide. Charlie wants to use mulch to
cover the flower bed. The mulch is sold by the square
yard. Use the facts to find the area of the flower bed in
square yards.
Answer
2268 ft²
Step-by-step explanation
1 yard is equivalent to 3 feet. Using this conversion factor, the equivalence of 21 yd is:
[tex]21 \ \text{yd}=21 \ \text{yd}\times\dfrac{3 \ \text{ft}}{1 \ \text{yd}}[/tex]
[tex]\text{Simplifying the units:}[/tex]
[tex]21 \ \text{yd}=\dfrac{21\times3}{1 \ \text{}} \ \text{ft}[/tex]
[tex]21 \ \text{yd}=63 \ \text{ft}[/tex]
Similarly, the equivalence of 12 yards is:
[tex]12 \ \text{yd}=12 \ \text{yd}\times\dfrac{3 \ \text{ft}}{1 \ \text{yd}}[/tex]
[tex]12 \ \text{yd}=12\times3 \ \text{ft}[/tex]
[tex]12 \ \text{yd}=36 \ \text{ft}[/tex]
Therefore, the length of the bed is 63 ft and the width is 36 ft.
Finally, the area of the bed (a rectangle) is calculated as follows:
[tex]\text{A}=\text{length}\times\text{width}[/tex]
[tex]\text{A}=63\times36[/tex]
[tex]\text{A}=2268 \ \text{ft}^2[/tex]
distributive property -3 square root 3 ( 2 + square root 6)
To distribute -3√3 to (2 + √6), we can use the distributive property:
-3√3 (2 + √6) = (-3√3 * 2) + (-3√3 * √6)
Next, we can simplify each term using the product rule of radicals:
(-3√3 * 2) = -6√3
(-3√3 * √6) = -3√(3
Therefore, when we distribute -3√3 to (2 + √6), we get:
-3√3 (2 + √6) = -6√3 - 9√2.
A cube wooden block measures 3 feet by 3 feet by 3 feet. Wedges 1 foot from each corner are cut out from the cube, the first cut of which is shown in the figure above. After all the wedges are removed, how many edges does the cube have?
Q27
Answer:
e
Step-by-step explanation:
[tex] \frac{ \sqrt{5} }{ \sqrt{5} + 2} [/tex]
express surd fraction with rational denominator
Answer:
Step-by-step explanation:
We will rationalize the denominator:
[tex]\frac{\sqrt{5} }{\sqrt{5} +2} =\frac{\sqrt{5} }{\sqrt{5} +2} \times \frac{\sqrt{5} -2}{\sqrt{5} -2}[/tex]
[tex]=\frac{\sqrt{5} (\sqrt{5} -2)}{(\sqrt{5} +2)(\sqrt{5} -2)}[/tex]
[tex]=\frac{5-2\sqrt{5} }{5-2\sqrt{5} +2\sqrt{5} -4}[/tex]
[tex]=\frac{5-2\sqrt{5} }{1}[/tex]
[tex]=5-2\sqrt{5}[/tex]
The area of the triangle below is 25/18 square meters. What is the length of the base? Express your answer as a fraction in simplest form
The length of the base with area 25/18 square meters is 5/3 meters. This answer is in its simplest form.
What is height of triangle?The height of a triangle is the length of the line segment that is drawn from the vertex of the triangle perpendicular to the base.
The area of a triangle is given by the equation
A = 1/2 * base * height.
Therefore, we can substitute the value of the area and the height of the triangle into the equation to solve for the base.
A = 1/2 * b * (5/3)
25/18 = 1/2 * b * (5/3)
We will divide left side of the equation by 5/3.
(25/18) / (5/3) = (1/2)*b
(25/18) * 3/5 = (1/2)*b
Now, we can solve for b by dividing the left side of the equation by 1/2
(5/6) / (1/2) = b
b = 5/6 * (2/1)
b = 5/3
Therefore, the length of the base is 5/3 meters. This answer is in its simplest form.
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Two pies are shared among 12 friends. How much did each friend recieve?
PLEASE HELP!!!!
Answer: 1/6 of a pie
Step-by-step explanation: each friend receives 1/6 of a pie because there are 2 pies being distributed to 12 friends. 2/12 = 1/6
Answer:
1/6 of the pie.
Step-by-step explanation:
We Know
Two pies are shared among 12 friends.
How much did each friend receive?
We take
2 / 12 = 1/6 of the pie
So, each friend receives 1/6 of the pie.