The dimension which this rug should have is 23 feet × 13 feet.
How to calculate the dimensions of this rug?Mathematically, the area of a rectangle can be calculated by using this formula;
A = LW
Where:
A represents the area of a rectangle.l represents the length of a rectangle.w represents the width of a rectangle.Let x represent the width of this rug.
Also, the dimension of this rug is given by:
299 = (29 - 2x) × (19 - 2x)
299 = (29 - 2x)(19 - 2x)
Evaluating the equation, we have:
299 = 551 - 58x - 38x + 4x²
4x² - 58x - 38x + 551 - 299 = 0
4x² - 96x + 252 = 0
Dividing all through by 4, we have:
x² - 24x + 63 = 0
x² - 21x - 3x + 63 = 0
x(x - 21) - 3(x - 21) = 0
(x - 3)(x - 21) = 0
x = 3 or 21 feet.
Note: The plausible solution is x = 3.
Therefore, the width and length of this rug is given by:
Length = 29 - 2(3)
Length = 29 - 6
Length = 23 feet.
Width = 19 - 2(3)
Width = 19 - 6
Width = 13 feet.
In conclusion, the dimension of this rug is 23 feet × 13 feet.
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25 points plus brainliest
Answer:
i think b
Step-by-step explanation:
Answer:
B. y = 2x + 8
Step-by-step explanation:
14x - 7y = 1
7y = 14x - 1
y = 2x - 1/7
If two lines are parallel, their slopes are equal.
With m = 2, x = -2, y = 4
y = mx + b
4 = 2(-2) + b
4 = -4 + b
b = 8
so y = 2x + 8
The sum of Sharon's and John's ages is 70 . John is 4 times as old as Sharon.
If you let Sharon's age and John's age, then the problem can be represented by a system of equations. Which of the following shows a graph of this system and the solution to this problem?
Answer:
Graph A shows the system and solution to the system. Option A is correct.
The sum of Sharon's and John's ages is 70. Sharon is times as old as John. The system of equations regarding the problem is determined.
What is the equation?
The equation is the values of two expressions that are equal.
Let the age of Sharon's be x and Jhon's be y.
The sum of Sharon's and John's ages is 70.
x + y = 70 - - - - (1)
Sharon is times as old as John.
x = 4 y
Now put x = 4y in equation 1
4y + y = 70
5y = 70
y = 70/5
y = 14
Now put y = 14 in x = 4y
x = 4*14
x = 56
The solution of a system of equations is (14, 56) shown in graph 1.
Thus, graph A shows the system and solution to the system. Option A is correct.
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Step-by-step explanation:
Sharon is 14 years old and John is 56 years old.
The graph of the system of equations is given below where the solution is (14, 56).
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
Let x be Sharon's age and y be John's age.
From the first sentence, we know that:
x + y = 70
From the second sentence, we know that:
y = 4x
Substituting y = 4x into the first equation, we get:
x + 4x = 70
5x = 70
x = 14
Substituting x = 14 into y = 4x, we get:
y = 4(14) = 56
The graph of the system of equations is given below where the solution is (14, 56).
Therefore,
Sharon is 14 years old and John is 56 years old.
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fractional mathematics
Answer:
the numerator (the top number)/ Denominator (bottom number)
Step-by-step explanation:
you should know this
Answer:
Fractional mathematics have to do with dealing with certain amounts of a number and mathematical proportions. Fractions are amounts out of a whole number.
Write the number 86,360,000 using the number word "million" and then round to one decimal place.
million
M
The number 86,360,000 using the number word "million" and then round to one decimal place is Eighty-six million three hundred sixty thousand.
The writing style used to express numbers in India is known as the Indian numeral system. In this case, numbers are divided into several time periods or groupings. This numbering scheme uses ten distinct symbols, including the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The order of the digits when using the Indian number system is one, ten, hundreds, thousands, ten thousand, lakhs, lakhs, crores, and crores. The era and locations are shown in the table below according to the amount of digits in a number.
Given number: 86,360,000
Eighty-six million three hundred sixty thousand in numbers
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Georgia is on the prom committee. She wants to hang a dozen congruent triangles from the ceiling so that they are parallel to the floor. She sketched out one triangle on a coordinate plane with coordinates (0,4),(3,8) , and (6,0) . If each triangle is to be hung by one chain, what are the coordinates of the point where the chain should attach to the triangle?
The coordinates of the point where the chain should attach to the triangle are (3, 4).
Given that, a triangle is on a coordinate plane with coordinates (0,4), (3,8), and (6,0).
We need to find the coordinates of the point where the chain should attach to the triangle.
What is the centroid of the triangle?The centroid is the centre point of the object. The point at which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle formula is G = ((x1+x2+x3)/3 , (y1+y2+y3)/3).
Now, centroid = ((0+3+6)/3, (4+8+0)/4)
=(3, 4)
Therefore, the coordinates of the point where the chain should attach to the triangle are (3, 4).
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer:
c
Step-by-step explanation:
This was a question asked by someone else roughly a week ago, here's the answer to that question. It's the same as this question. I hope this helps.
Simplify an expression for the perimeter of the rectangle shown.
8.6x + 3
5.2
4
Write your answer with NO spaces:
The perimeter of the rectangle is P = (17.2x₊16.4).
Given that,
Length, l = 8.6x₊3
Width, b = 5.2
In the formula P=2l+2w, where l is the rectangle's length and w is its width, the perimeter P of a rectangle is determined. Using the formula A=l×w, where l is the length and w is the width, we can determine the area A of a rectangle.
We need to find the expression for the perimeter of the rectangle. The formula for the perimeter of the rectangle is given by :
P=2(l₊b)
Putting values of l and b in the above formula:
p = 2(8.6x ₊ 3 ₊ 5.2)
= 2(8.6x ₊ 8.2)
= 2(8.6x) ₊ 2(8.2)
= 17.2x ₊ 16.4
So, the required perimeter of the rectangle is 17.2x₊16.4.
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from a sample of 550 items, 52 were found to be defective. the point estimate of the population proportion defective will be:
The point estimate of the population proportion defective will be 0.0945
What is point estimateThe formula for calculating the point estimate is expressed as;
p = x/n,
where p is the proportion of successes in the sample
n is the total sample
Given the following
n = 550 items
x = 52
Substitute
p = 52/550
p = 0.0945
Hence the point estimate of the population proportion defective will be 0.0945
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Find the y-intercept of the line y = -8/5x -4
−8
5
y-intercept:
(0,−4)
Step-by-step explanation:
Heyy! Could you guys possibly help with the answer to this question? I’m stuck.
The codes of the countries are 34, 35 and 36
How to determine the codes of the countries?The given parameters are
Sum of codes = 105
Where the numbers are consecutive numbers
This means that
B = A + 1
C = A + 2
So, we have
A +A + 1 + A + 2 = 105
Evaluate the like terms
3A = 102
Divide through by 3
A = 34
So, we have
B = A + 1 = 34 + 1 = 35
C = A + 2 = 34 + 2 = 36
Hence, the codes of the countries are 34, 35 and 36
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NEED HELP
Which of the following is and isn't a function? ( There may be more than one answer ). Explain Clearly
Using the function concept, we have that:
Items, a, and d are functions.Item b and c are not functions.When does a relation represents a function?A relation represents a function when each value of the input is mapped to only one value of the output.
On a graph, it means that each value of x is mapped to only one value of y, that is, there are no vertically aligned points on the graph.
For this problem, relation c does not represent a function, as there are multiple values of x are related to two values of y, and there are vertically aligned points on the graph.
In item b, when x = 6, there are two values of y, hence this is also not a function. For items a and d, each value of x is mapped to only one value of y, hence they are functions.
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Amir has a collection of 936 trading cards. He wants to put them
in boxes with 25 trading cards in each box. How many boxes will
Amir fill? How many trading cards will be left over?
Answer:
He will fill 37 boxes and 11 cards will be left over
Step-by-step explanation:
A cyclist completes a journey of 500 m in 22 seconds in two parts. The first part with the speed of 10m/s and remainder of it in 50m/s, how far did she travel in each speed
Using the relation between velocity, distance and time, it is found that she traveled 15 seconds at 10 m/s and 7 seconds at 50 m/s.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
For the first part, we have that she cycled a distance of d m in t seconds, at a velocity of 10 m/s, hence:
10 = d/t
d = 10t.
For the second part, we have that she cycled a distance of 500 - d meters, in 22 - t seconds, at a velocity of 50 m/s, hence:
50 = (500 - d)/(22 - t).
Since d = 10t, and applying cross multiplication:
500 - 10t = 50(22 - t)
500 - 10t = 1100 - 50t
40t = 600
t = 600/40
t = 15.
22 - t = 22 - 15 = 7, hence:
She traveled 15 seconds at 10 m/s and 7 seconds at 50 m/s.
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total u.s. land area is 3.537 million square miles. what percentage of u.s. land is national park system land ?
The percentage of u.s. land is national park system land is approximately 41.8%
PercentageConvert acres to square miles
945,000,000 acres = 1476562.5 square milesPercentage of u.s. land is national park system land = national park system land / Total U.S. land area × 100
= 1476562.5 square miles / 3,537,000 square miles × 100
= 0.417461832061068 × 100
= 41.74618320610687%
Approximately,
41.8%
Therefore, the percentage of u.s. land is national park system land is approximately 41.8%
Complete question:
Total U.S. land area is 3.537 million square miles. Total U.S. national park system land occupies 954 million acres. What percentage of U.S. national park system land?
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What is the value of x in the equation 1/5x - 2/3y = 30, when y = 15?
4
8
80
200
Answer:
x = 200
Step-by-step explanation:
substitute y = 15 into the equation
[tex]\frac{1}{5}[/tex] x - ([tex]\frac{2}{3}[/tex] × 15) = 30
[tex]\frac{1}{5}[/tex] x - (2 × 5) = 30
[tex]\frac{1}{5}[/tex] x - 10 = 30 ( add 10 to both sides )
[tex]\frac{1}{5}[/tex] x = 40 ( multiply both sides by 5 to clear the fraction )
x = 5 × 40 = 200
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-6, 5) and (3,-7)
Answer: 15
Step-by-step explanation:
Distance formula: a^2+b^2=c^2 where c is the distance.
a^2=
(-6-3)^2=
(-9)^2=81
b^2=
(5-(-7))^2=
(5+7)^2=
12^2=144
c^2=81+144=225
If c^2=225, then what's c?
c=15
Write the composite function in the form f(g(x)). [identify the inner function u = g(x) and the outer function y = f(u).] y = 3 1 5x
Answer:
It's really hard to really solve cause I'm a student in learning.
the air quality index, or aqi, measures how polluted the air is in your city and assigns a number based on the quality of the air. over 100 is "unhealthy".the following quadratic regression equation gives us an estimate of n, which is the number of days the aqi exceeded 100 a particular year. we will use this equation to estimate the number of days the aqi was over 100 in the year 1995.n
Final answer:
The estimated number of days the aqi was over 100 in the year 1995 is calculated as 135 days.
Is linear regression quadratic regression ?
Simple linear regression is expanded upon in quadratic regression. While quadratic regression has the drawback of requiring more data points to ensure that your data falls into the "U" shape, linear regression can be carried out with as few as two points (i.e., enough points to draw a straight line).
In situations where the second differences are constant, a quadratic model is adequate. We can ascertain the degree of the model for the data by identifying variations between the dependent values. The model will be linear if the initial difference has the same value. The model will be quadratic if the second difference has the same value as the first.
Explanation:
The air quality index, or aqi, calculates a number depending on how clean or dirty the air. Then it is estimate n, the number of days the aqi exceeded 100 in a specific year is evaluated and calculated as it is actually as 135 days on edge.
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Use the graph of each function to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically.
f(x)=x^3-x^2-2x+3
It appears that from graph that the function is increasing in the interval (-∞,-1) and (1,∞). Also the function is decreasing in the interval (-1,1) and (0.0.5).The function is not constant anywhere.
To check if this is correct, we will find the relative extrema of the function,
f(x) = x³-x²-2x+3
Find it derivative f'(x) = 3x²-2x-2
f'(x) = 0
⇒ x = 2 ± √(4+24)/3
= 3.77 , -1.1
Find the second derivative f''(x) = 6x -2
f''(3.77) = 20.62>0
So the function has a relative minimum at x = 3.77.
f''(-1.1) = -8.6<0
So the function has a relative maximum at x = -1.1
Now we can conclude with the intervals where the function is increasing is before the relative maximum and after the relative minimum.
i.e., the intervals (-∞,-1) and (3.5,∞) [rounding to the nearest 0.5 unit]
So the interval in which the function is decreasing is between the relative maximum and minimum. i.e., the interval (-1, 3.5)
The function is nowhere constant.
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What is the slope of the line that contains the points (-2, 2) and (3, 4)?
A. -5/2
B. 5/2
C. 2/5
D. - 2/5
If m∠ABD=84°, what are m∠ABC and m∠DBC? D A B C (5x+1)° (6x-5)°
The measures of angle ABC and DBC are 41 degrees and 43 degrees
How to find the measures of the angle ABC and DBC?The angles are given as
Angle ABC = (5x + 1) degrees
Angle DBC = (6x - 5) degrees
Angle ABD = 84 degrees
The angles add up to 84 degrees
So, we have:
ABC + DBC = 84
This gives
5x + 1 + 6x - 5 = 84
Evaluate the like terms
11x = 88
Divide both sides by 11
x = 8
Substitute x = 8 in Angle ABC = (5x + 1) degrees and Angle DBC = (6x - 5) degrees
Angle ABC = (5 x 8 + 1) degrees
Angle DBC = (6 x 8 - 5) degrees
Evaluate
Angle ABC = 41 degrees
Angle DBC = 43 degrees
Hence, the measures of angle ABC and DBC are 41 degrees and 43 degrees
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W
Which graph represents the solution of the system
{x² + y² = 4
x-y = 1
The graph is plotted in the following figure .
To plot a graph we need 2 pts .
First eqn is of a circle ( [tex]x^{2}[/tex] ) + ( [tex]y^{2}[/tex] ) = 4
Second eqn is of a line x - y = 1
The center of circle is ( 0 , 0 )
The circle passes through ( 2 , 0 ) , ( 0 , 2 ) , ( - 2 , 0 ) , ( 0 , - 2 ) .
The line passes through ( 0 , 1 ) , ( 0 , - 1 ) .
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1/3 ÷ 8 =
what s the answer
Answer:
0.0416¯
Step-by-step explanation:
after the 1 six is being repeated. Hope this helps! :)
The probability a d-link network server is down is 0.10. if you have three independent servers, what is the probability that at least one of them is operational?
The probability that at least one of them is operational is 0.999
Probability:
Probability means the possibility of happening the particular event. So, it can be written as the fraction of possible event by the total number of event.
Given,
The probability a D-Link network server is down is 0.10.
Here we need to find if you have three independent servers, what is the probability that at least one of them is operational.
Let D be an event that a D-Link network server is down.
It is given that the probability that a D-Link network server is down is
=> P(D) = 0.10
The number of independent servers
=> (n) = 3
The probability that none of the servers is working is
=>P(None) = P(D) x P(D) x P(D)
=> P(None) = 0.10 x 0.10 x 0.10
=> P(None) = 0.001
The probability that at least one of them is operational is given as
=> 1 - P(None)
=> 1 - 0.001
=> 0.999
Therefore, the probability that at least one of them is operational is 0.999.
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On a map where each unit represents 100 miles, two airports are located at P(1,17) and Q(12,10). What is the distance, to the nearest whole mile, between the two airports? A. 1,800 miles B. 1,304 miles C. 1,122 miles D. 900 miles
Using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.
How to Apply the Distance Formula?The distance formula is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the following locations:
P(1,17) = (x1, y1)
Q(12,10) = (x2, y2)
Use the distance formula to find the PQ:
PQ = √[(12−1)² + (10−17)²]
PQ = √[(11)² + (−7)²]
PQ = √170
PQ ≈ 13.04 units
1 unit = 100 miles
PQ = 13.04 × 100
PQ = 1,304 mils
Thus, using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.
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Answer: B. 1,304 miles.
2. Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i and .
Review Andrew’s work, identify the error and correct all work from that point forward that is affected by this error. Include at least one sentence explaining his error. Use proper mathematical vocabulary, appropriately
(x-3)(x+2+2i)(x+2-2i)=0
(x-3)(x^2+4x+8)=0
x^3+x^2-4x-24=0)
Using the Factor Theorem, Andrew's error was at the application of the minus signal to the complex roots, and the polynomial of degree 3 is of f(x) = x³ - 7x² + 20x - 24.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
For this problem, the roots are given as follows:
[tex]x_1 = 3[/tex].[tex]x_2 = 2 + 2i[/tex].[tex]x_3 = 2 - 2i[/tex].Hence the polynomial is given as follows, considering leading coefficient a = 1:
[tex]f(x) = (x - 3)(x - 2 - 2i)(x - 2 + 2i)[/tex]
His error was at the application of the minus signal to the complex roots.
Then:
f(x) = (x - 3)[(x - 2)² - (2i)²]
f(x) = (x - 3)(x² - 4x + 4 + 4)
f(x) = (x - 3)(x² - 4x + 8)
f(x) = x³ - 7x² + 20x - 24.
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In a set of geometric figures the mass of 4 pyramids and 2 cubes is 40 grams and the mass of 6 pyramids and 4 cubes is 68 grams
The mass of pyramid is 6 grams and the cube is 8 grams
Let's assume the mass of a pyramid is x gram and mass of a cube is y gram .
So, algebraic mass of 6 and 4 pyramids is 6x grams and 4x grams. and algebraic mass of 2 cubes and 4 cubes is 2y grams and 4y grams .
Total algebraic mass of 4 pyramids and 2 cubes are , 4x + 2y = 40 ;(equation 1)
and Total algebraic mass 6 pyramids and 4 cubes are , 6x + 4y = 68 ;(equation 2)
Now we have to use adoption method to solve this problem ,
we have to multiply equation (1) with 4 and equation (2) with 2 , and we will get ,
16x + 8y = 160 ; ( equation 3 )
12x + 8y = 136 ; ( equation 4 )
Now , we will substract equation ( 3 ) from equation ( 4 )
4x = 24 and x = 24/4 = 6
Let's put the value of x in equation ( 1 )
24 + 2y = 40 or, 2y = 16 or, y = 8
Here we can conclude , mass of pyramid is 6 grams and the cube is 8 grams.
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I need help I need it in 1 min please help 13 and 14
i) 9⁻⁴=1/6561
ii1/2⁻⁶=64
Positive exponent: An exponent defines the number of times a number is multiplied by itself. For example, 32. It means that the number 3 has to be multiplied twice. Here, the number 3 is a base number and 2 is an exponent. The exponent can be positive or negative.
Nagative exponent: We know that the positive exponent tells us how many times a number is multiplied by itself. Whereas, the negative exponent tells us how many times we have to divide the base number. In other words, the negative exponent describes how many times we have to multiply the reciprocal of the base. An example of negative exponents is 3-2.
Thus, x-2 is written as (1/x²).
i)Rewrite expression using a positive exponent 9⁻⁴
We know that positive exponent.
9⁻⁴=1/94
9⁻⁴=1/6561.
ii)Rewrite expression using a positive exponent 1/2⁻⁶
1/2⁻⁶=26
⇒1/2⁻⁶=64.
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Imagine that you are a teacher grading your students’ assignments. The following questions were turned in with incorrect answers. Trace through the process of solving them to discover where your students made a mistake in their order of operations. Which step of PEMDAS did they do out of order? Explain.
(6-2)^2+12-3^2
The correct answer is 19
student answer 97
The student did the subtraction step of PEMDAS out of order.
What is PEMDAS?PEMDAS is a rule regarding precedence of operations, given as follows, from highest to lowest precedence.
Parenthesis.Exponents.Multiplication/Division.Addition/Subtraction.In this problem, the expression is:
(6 - 2)² + 12 - 3².
The student reached an answer of 97 as follows:
(6 - 2)² + 9² = 4² + 9² = 16 + 81 = 97.
The student did the subtraction first, hence the student did the subtraction step of PEMDAS out of order.
The correct solution is:
(6 - 2)² + 12 - 3² -> Solve the Parenthesis.
4² + 12 - 3² -> Solve the Exponents.
16 + 12 - 9 -> Solve the Addition and Subtraction.
19.
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find the area and circumference of each circle. Use pi in your answer (example: radius = 8, or diameter = 14).
The area of the circle is 64π square unit and the circumference is 16π units
Calculating area and circumference of a circleFrom the question, we are to find the area and circumference of the circle
The area of a circle is given by the formula,
A = πr²
Where A is the area
and r is the radius
Using the parameter, radius = 8
Then,
A = π × 8²
A = 64π square unit
Calculating the circumference
The circumference of a circle is given by the formula
C = 2πr
Where C is the circumference
and r is the radius
Thus,
C = 2 × π × 8
C = 16π units
Hence, the area of the circle is 64π square unit and the circumference is 16π units
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