The area of a rug is 108 square feet and the length it it’s diagonal is 14 feet. what are the length and width of the rug. write a system of equations tk answer this equation
Answers
The system of equation is 7.71 feet, under the condition the area of a rug is 108 square feet and the length it it’s diagonal is 14 feet.
Now to solve this problem, we can use the formula for the area of a rectangle which is A = L x W . Therefore, we can write the equation 108 = L x W
Now the length of the diagonal is 14 feet. We can use this information to write another equation using the Pythagorean theorem which states that for any right triangle with legs of length a and b and hypotenuse of length c ,
a² + b² = c²
Since a rectangle is made up of two right triangles, we can use this theorem to find the length and width of the rectangle.
Let us assume the length of the rug L and the width of the rug W
L²+ W² = 14²
We have two equations with two unknowns
108 = L x W
L² + W² = 14²
We can solve for one variable in terms of another using substitution. From the first equation,
W = 108 / L
Substituting this into the second equation gives:
L² + (108 / L)² = 14²
L² - 196L² + 11664 = 0
This is a quadratic equation in terms of L². We can solve for L²
L² = (196 ± √(196² - 4 x 11664)) / 2
L² = (196 ± √(38416)) / 2
L² = (196 ± 196) / 2
Taking the positive root gives:
L² = 196
So:
L = √(196) = 14
Substituting this back into one of our original equations gives:
W = 108 / L
= 108 / 14
≈ 7.71
Therefore, the length of the rug is 14 feet and its width is approximately 7.71 feet.
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Related Questions
A bakery sells mocha cupcakes and chocolate cupcakes. One day it sold 28 mocha and 52 chocolate . What percent of the cupcakes sold that they were mocha?
Answers
35%
1) Gathering the data
bakery
mocha cupcakes =28
chocolate = 52
2) To find the percentage let's add them first and then set a proportion.
52+28= 80
Mocha cupcakes
Cupcakes
80---------------------------- 100%
28---------------------------- x
Cross multiply
80x = 2800 Divide them by 80
x=35
3) So 35% of the sold cupcakes were mocha cupcakes
Please help me ASAP please please please
Answers
The quadrilateral is parallelogram because the opposite sides are parallel and congruent
What is a parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.
Since WZ and XY are congruent and XW and YZ are congruent and Also, WZ and XY are parallel and XW and YZ are parallel, we can therefore say that the quadrilateral obeys the property of a parallelogram.
parallel lines are two straight lines that can not meet at a point.
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A company i throwing an end of the year party for their employee with a budget of $30 per peron. If their total pending wa $1000 for the pace, $850 for food, and $250 for decoration, how many employee attended the party?
Answers
By solving for the number of employees, there were 70 employees at the party.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. An equation typically consists of two sides, with an equals sign (=) in between.
what is linear equation?A linear equation is an equation in which the highest power of the variable is 1. In other words, a linear equation is an equation that can be written in the form:
ax + b = 0
where a and b are constants and x is the variable.
To find out how many employees attended the party, you can set up the following equation:
Number of employees * $30 per employee = $1000 for space + $850 for food + $250 for decorations
You can then solve for the number of employees by dividing both sides of the equation by $30 per employee:
Number of employees = ($1000 for space + $850 for food + $250 for decorations) / $30 per employee
= $2100 / $30
= 70 employees
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what is the slope of the line? WILL GIVE BRAINLIEST
Answers
Answer:
1/3
Step-by-step explanation:
Answer:
1/3
Step-by-step explanation:
In this graph, the line rises 1 and runs 3.
Translation: every time the line goes up 1 unit, it moves to the right 3 units.
I hope this helped and please mark me as brainliest!
Answers these three questions please for 50
Answers
Answer:
look at the photo..........
I’m very bad a rounding help! What’s the number 451157873 rounded to the hundreds place?? Help ASAP!
Answers
Answer:
451157900
Step-by-step explanation:
Answer:
461127830
Step-by-step explanation:
if shaun plays 1 game with mike and then 1 game with tim, what is the probability that shaun loses both games
Answers
Answers did you ever get this awnser??
Step-by-step explanation:
Consider the right triangle below. Solve for x. Label the sides in the image as opposite, adjacent, or hypotenuse, then show your work on the sketchpad.
Answers
Answer: 11.9
Step-by-step explanation:
The opposite is across from the 35 degree angle and the ajacent is the side valued at 17.
Answer:
A. 11.9
Step-by-step explanation:
35° = opposite/adjacent
tan(35°) = x/17
tan(35) x 17 = 11.90352814
x = 11.90352814
x = 11.9
Convert 72 miles per hour into meters per second.
Answers
Answer:
72 Miles Per Hour = 32.18688 Meters Per Second
Step-by-step explanation:
hii can someone please help me, I don’t know the answer
Answers
Answer:maybe search up the meaanings
Step-by-step explanation:
the rectangle class is derived from square. in addition to a width, a rectangle has a height. define the constructor: rectangle(width, height).
Answers
The constructor for the rectangle class is defined as follows:
```python
class Rectangle(Square):
def __init__(self, width, height):
super().__init__(width)
self.height = height
```This constructor takes two arguments, `width` and `height`, and uses the `super()` function to call the constructor of the `Square` class with the `width` argument. It then sets the `height` attribute to the `height` argument. This creates a new `Rectangle` object with a `width` and `height` attribute. The `Rectangle` class is derived from the `Square` class, which means that it inherits the `width` attribute from `Square`. However, since a `Rectangle` has a `height` attribute in addition to a `width`, we need to define a new constructor that can handle both attributes. The `super()` function is used to call the `__init__()` method of the `Square` class, which initializes the `width` attribute. The `height` attribute is then set to the `height` argument.
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Patricia is 5 years older than Wyatt. The sum of their ages is 61. How old are Patricia and Wyatt?
(A) First write an equation you can use to answer this question. Use x as your variable.
The equation is_________
Answers
Answer
w+(w+5)=61
Step-by-step explanation:
Answer:
an answer could be Patricia is 33 and wyatt is 28 so x=33
Step-by-step explanation:
what is 56/60 as a percentage
Answers
Answer:
93.33%
Step-by-step explanation:
56/60 as a percentage:
56/60 = 0.93333
0.93333 as a percent:
0.93333 * 100 = 93.33%
The value of solution for a number 56/60 into a percentage is,
⇒ 93.33%
We have to given that,
To change a number 56/60 into a percentage.
Since, A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Hence, We can write as,
⇒ 56/60 × 100%
⇒ 5600/60
⇒ 93.33%
Therefore, The value of solution for a number 56/60 into a percentage is,
⇒ 93.33%
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Which equation can be solved using the one-to-one property?
3X = 10
4In x = 2
log x = 5
4* = 47x+2
Answers
Answer:
3x=10
Step-by-step explanation:
x=10-3
x=7
i hope this answer will help u
Answer:
4x = 47x+2
Step-by-step explanation:
Using the one–to–one property, you can set x = 7x + 2.
Segment AB is shown on the graph. Which shows how to find the x-coordinate of the point that will divide segment AB into a 2:3 ratio using the formula…
PLEASE HELP!!
Answers
Answer:
\(x=\dfrac{2}{5}\times (2+3)-3\)
Step-by-step explanation:
The given ratio is 2:3.
x₁ = -3, x₂ = 2
We need to find the x-coordinate of the point that will divide segment AB into a 2:3 ratio. The formula is as follows :
\(x=\dfrac{a}{a+b}(x_2-x_1)+x_1\)
Put all the values,
\(x=\dfrac{2}{2+3}(2-(-3))+(-3)\\\\=\dfrac{2}{5}\times (2+3)-3\)
Hence, the correct option is (d).
Answer: D
Step-by-step explanation:
I got it right on edge trust me :)
the median line AM of the triangle ABC is half the length of the side towards which it is drawn, line BC. prove that triangle ABC is a right triangle.
Answers
\(\\ \sf\longmapsto AM=\dfrac{1}{2}BC\)
\(\\ \sf\longmapsto AM=BM=CM\)
All points are equidistant from MIf it becomes a inscribed triangle
A,B,C will create a arc of 180°\(\\ \sf\longmapsto arcABC=180°\)
The measure of inscribed angle is half the inscribed arc\(\\ \sf\longmapsto <BAC=\dfrac{1}{2}arc ABC\)
\(\\ \sf\longmapsto <BAC=\dfrac{1}{2}180°\)
\(\\ \sf\longmapsto <BAC=90°\)
Hence ABC is a right angled triangle (Verified)
the median line AM of the triangle ABC is half the length of the side towards which it is drawn, line BC. prove that triangle ABC is a right triangle.
Write 6 1/5 as an improper fraction in its simplest
form
Answers
The mixed fraction in simplest improper fraction is 31/5.
Define the term improper fraction?A fraction that has the numerator higher than or equal to a denominator is said to be inappropriate.Proper fractions are those that are higher than 0 but a little less than 1. The numerator is lower than the denominator in appropriate fractions. An improper fraction is one that has a numerator that is greater or equal to the denominator.A wrong fraction is always bigger than or equal to one.For the stated mixed fraction;
6 1/5
To convert this in improper fraction;
= (6x5 + 1)/5
= (30 + 1)/5
= 31/5
This, the mixed fraction in simplest improper fraction is 31/5.
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lim f(x) = 19, find the value of A and B, if the lim f(x) = Ax – 3B and lim f(x) = **+ B
X
1
A is
B is
Question is messed up so a photo of the question is below. Thanks in advance
Answers
Answer:
A = 4, B = 3
Step-by-step explanation:
In order for the limit to exist and have a value of 19, the left limit and the right limit must both have that value at x=7.
left limit = 19
right limit = 19
__
4A(7)/7 +B = 19
A(7) -3B = 19
Adding 3 times the first equation to the second gives ...
3(4A +B) +(7A -3B) = 3(19) +(19)
19A = 4(19) . . . . . simplify
A = 4 . . . . . . . . divide by 19
Substituting into the first equation gives ...
4(4) +B = 19
B = 3 . . . . . . . subtract 16
A is 4, B is 3.
State if the given functions are functions
Answers
y(x-(9-4y)) for x=4 and y=2
Answers
Answer:
6
Step-by-step explanation:
( 2 ) ( 4 - ( 9 - 4 ( 2 )))
2 ( 4- ( 9-8 ))
2 ( 4 - ( 1 ))
2 ( 3 )
6
Answer:
6Step-by-step explanation:
2(4-(9-4(2) )2 ( 4- (9-8)2(4 - 1)2(3)6Consider the t distribution with 5 degrees of freedom. (a) What proportion of the area under the curve lies to the right of t = 2.015?
Answers
The proportion of the area under the curve that lies to the right of t = 2.015 in a t-distribution with 5 degrees of freedom can be calculated using the t-distribution function in a statistical software package such as R.
The answer is approximately 0.9522. This means that 95.22% of the area under the curve lies to the right of t = 2.015. This indicates that the probability of observing a value of t greater than 2.015 is quite high.
This is because the t-distribution with 5 degrees of freedom has a larger spread than the normal distribution, which means that the probability of observing values further from the mean is greater.
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The circumference of a circle is 91.688 millimeters. what is the radius of the circle? use 3.14 for π. 29.2 mm 183.4 mm 14.6 mm 45.8 mm
Answers
Answer:
14.6mm
Step-by-step explanation:
The formula for finding the circumference of a circle is 2πr.
The circumference is 91.688 millimeters inorder to find the radius we have to do the opposite or inverse of multiplication which is division.
So we divide the circumference by 2 and pi which is 3.14 which will give us the radius
r = radius = 91.668 ÷ 3.14 ÷ 2 = 14.6
Answer: its c
Step-by-step explanation:
Solve: 3x - 3= x +5
please can someone solve this I will give brainiest
Answers
3x - 3= x + 5
=> 3x - x = 5 + 3
=> 2x = 8
=> x = 8/2
=> x = 4
Answer:
4
Step-by-step explanation:
3x - 3 = x+5
=> 3x = x+5+3 ( transposing method)
=> 3x-x = 5+3
=> 2x = 8
=> x = 8/2
=> x = 4
PLEASE HELPPPPP ITS URGENTTTTTTTTTTTTTTTTTTTTTTTT
Answers
Answer:
are this if its a function or not?
Answer:
NO
YES
YES
NO
Step-by-step explanation:
To solve this, plug the values into the functions.
4(6)+2(0)=18 FALSE
4(4)+2(1)=18 and (1)= -2(4)+9 TRUE
4(-5)+2(19)=18 and (19)= -2(-5)+9 TRUE
(-3)= -2(5)+9 FALSE
What is the value of x in the equation
1/3x - 1/2 = 18 1/2
a. 6
b. 15
c. 54
d. 57
PLEASE HELP I HAVE 5 MIN LEFT ON MY TEST
Answers
Answer:
D 57
Step-by-step explanation:
The value of X
A farmer goes to the market to sell a box of eggs. A clumsy horse steps on the box of eggs and breaks a lot of them. The horse’s rider offers to pay for all of the eggs in the box and asks the farmer how many eggs there were. The farmer does not remember the exact number, but when she took them out of the box two at a time, there was 1 egg left. The same thing happened when she took them out three, four, five and six eggs at a time, but when she took them out 7 at a time, there were no eggs left
Answers
The smallest number of eggs that could have been in the box is 1134
The problem is to find the smallest number of eggs that could have been in the box, given the remainder when taking them out by different numbers. Here are the moves toward tackling it:
Allow n to be the quantity of eggs in the container. Then we have the accompanying arrangement of congruences:
n ≡ 1 (mod 2)
n ≡ 1 (mod 3)
n ≡ 1 (mod 4)
n ≡ 1 (mod 5)
n ≡ 1 (mod 6)
n ≡ 0 (mod 7)
For this problem, we have k = 6 k = 6, a i = {1,1,1,1,1,0} a_i = {1,1,1,1,1,0}, M i = {1260,840,630,504,420,720} M_i = {1260,840,630,504,420,720}, and y i = {−1,−2,−3,-4,-5,-6} y_i = {-1,-2,-3,-4,-5,-6}.
Plugging these values into the formula and simplifying modulo 5040, we get:
n = (−1260 + −1680 + −1890 + −2016 + −2100 + 0) mod 5040
n = (−8946) mod 5040
n = (−3906) mod 5040
n = 1134 mod 5040
Therefore, the smallest number of eggs that could have been in the box is 1134
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Someone plz help me I will give brainliest
Answers
Answer:
he greatest denominator for the both of the fractions is 24 so the fractions are 10/24 and 9/24 and the answer is 19/24
Step-by-step explanation:
the mean of five positive integers is 1.5 times their median. four of the integers are 8, 18, 36 and 62, and the largest integer is not 62. what is the largest integer?
Answers
The largest number of the five positive integers is 146.
Mean:
The mean is the mathematical average of a set of two or more numbers. The arithmetic mean and the geometric mean are two types of mean that can be calculated. The formula for calculating the arithmetic mean is to add up the numbers in a set and divide by the total quantity of numbers in the set.
Median:
The median is the middle value in a set of data. First, organize and order the data from smallest to largest. To find the midpoint value, divide the number of observations by two. If there are an odd number of observations, round that number up, and the value in that position is the median.
Here we have to find the largest integer.
Data given:
Four of the five integers are 8, 18, 36, and 62.
It is given that mean of five numbers 1.5 times their median.
mean = (8+18+36+62 + x)/5
median = 36
mean = 1.5 × median
(124 + x) / 5 = 1.5 × 36
124 + x = 5 × 54
x = 270 - 124
= 146
Therefore we get the largest number as 146.
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in the number 652.12, how does the value of the 2 in the hundredths place compare to the value of the 2 in the ones place?
Answers
In the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.
In the number 652.12, the value of the 2 in the hundredths place is much smaller than the value of the 2 in the ones place. In this number, the 2 in the hundredths place represents 0.02, which is two hundredths of a unit. On the other hand, the 2 in the ones place represents 2 units.
To understand the difference in value, consider that the decimal point separates the number into its integer part (to the left of the decimal point) and its fractional part (to the right of the decimal point). The place value of each digit depends on its position relative to the decimal point. The rightmost digit is the ones place, the digit to its left is the tens place, and so on. The place value of the digits to the right of the decimal point is determined by powers of 10 that are negative, starting from -1 for the hundredths place, -2 for the thousandths place, and so on.
Therefore, in the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.
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In the number 652.12, the 2 in the hundredth place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.
In the number 652.12, the value of the 2 in the hundredths place is much smaller than the value of the 2 in the ones place. In this number, the 2 in the hundredths place represents 0.02, which is two hundredths of a unit. On the other hand, the 2 in the ones place represents 2 units.
To understand the difference in value, consider that the decimal point separates the number into its integer part (to the left of the decimal point) and its fractional part (to the right of the decimal point). The place value of each digit depends on its position relative to the decimal point. The rightmost digit is the ones place, the digit to its left is the tens place, and so on. The place value of the digits to the right of the decimal point is determined by powers of 10 that are negative, starting from -1 for the hundredths place, -2 for the thousandths place, and so on.
Therefore, in the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.
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a person who does not ignore a sunk cost increases the probability that
Answers
A person who does not ignore a sunk cost increases the probability of making irrational decisions. This is because they are more likely to continue investing time, money, or effort into a project or situation that is not yielding positive results.
When we refer to a "sunk cost," we mean a cost that has already been incurred and cannot be recovered. Ignoring a sunk cost means not taking it into consideration when making decisions about the future. By not ignoring a sunk cost, individuals may feel a psychological attachment to their past investment, leading them to continue investing in something that may not be beneficial.
This can result in irrational decision-making and potentially wasting additional resources. For example, imagine a person who has spent a significant amount of money on a gym membership but rarely goes to the gym. Instead of accepting the fact that the money is already spent and may not be recouped.
They may feel compelled to continue paying for the membership in the hopes of eventually utilizing it. This decision is influenced by their failure to ignore the sunk cost and assess the situation rationally.
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