A bed measures 40 inches by 75 inches.
What is the distance between opposite corners of the bed?
Answers
Therefore, the distance between opposite corners of the bed is 85 inches.
What is triangle?A triangle is a three-sided polygon that is formed by connecting three non-collinear points. It is a simple closed figure with three sides and three angles. Triangles are classified according to the relative lengths of their sides and the measure of their angles. There are several types of triangles, including equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles.
Here,
The distance between opposite corners of a rectangle can be found using the Pythagorean theorem, which states that for a right triangle with legs of length a and b and hypotenuse of length c, c² = a² + b².
In this case, the length and width of the bed form the legs of a right triangle, and the distance between opposite corners is the length of the hypotenuse.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c² = 40² + 75²
c² = 1600 + 5625
c² = 7225
c = √(7225)
c = 85
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Related Questions
The rate of change of function fis
the same from x = -2 to x = 1 as it
is from x=1 to x=4. Is the
function linear quadratic or
exponential?
Answers
If the rate of change of a function f is the same from x = -2 to x = 1 as it is from x = 1 to x = 4, then the function is linear.
Linear function explained.
In mathematics, a linear function is a type of function that can be represented by a straight line on a graph. Linear functions have the form:
y = mx + b
where x and y are variables, m is the slope of the line (i.e., the rate of change), and b is the y-intercept (i.e., the value of y when x = 0). The slope of a linear function determines how much the output (y) changes for a given change in the input (x), and the y-intercept determines where the line crosses the y-axis.
Linear functions are commonly used to model relationships between two variables that have a constant rate of change.
If the rate of change of a function f is the same from x = -2 to x = 1 as it is from x = 1 to x = 4, then the function is linear.
This is because a linear function has a constant rate of change, which means that the change in the output (y) for a given change in the input (x) is the same throughout the entire domain of the function.
In contrast, a quadratic or exponential function has a changing rate of change, which means that the change in the output for a given change in the input varies at different points along the domain of the function.
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Determine how large the number a has to be so that ∫[infinity]a1x2+1dx<0.001
Integrals of Inverse Trigonometric Functions
The derivative of a function f(x) is given by
ddxf(x)=g(x)
Then the integration of g(x) is given by
∫g(x)⋅dx=f(x)+C∫
We can differentiate trigonometric functions , so we can also integrate trigonometric functions.
∫1x2+1dx=tan−1x+C∫12+1=tan−1
Inverse function value of tan−1xtan−1 :
tan−1([infinity])=π2
Answers
The number a has to be greater than 636.6197723675814 for the integral ∫[infinity]a1x2+1dx to be less than 0.001.
To determine how large the number a has to be so that ∫[infinity]a1x2+1dx<0.001, we can use the formula for the integral of inverse trigonometric functions:
∫1x2+1dx=tan−1x+C
We can substitute the limits of integration into this formula:
∫[infinity]a1x2+1dx=tan−1([infinity])-tan−1(a)
Since tan−1([infinity])=π2, the formula becomes:
π2-tan−1(a)<0.001
We can rearrange this inequality to solve for a:
tan−1(a)>π2-0.001
Taking the inverse tangent of both sides of this inequality gives us:
a>tan(π2-0.001)
Using a calculator, we can find that:
a>636.6197723675814
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I need help simplifying this
Answers
Answer:-8
Step-by-step explanation:
Write a multiplication and division equation that matches the following statement: How many 4/55 are in 12 ? Multiplication: 132⋅54−37+54=2523=1253 Division: ∣72=57÷54=41⋅45−2035÷5÷47
Answers
The multiplication and division equation that matches the statement are 12 * (55/4) = 165 and (12/1) ÷ (4/55) = 165.
Writing multiplication and division equationGiven the statement "how many 4/55 are in 12?"
The multiplication equation can be written thus,
12 ÷ (4/55) = 12 * (55/4)
= 165
Therefore, there are 165 4/55 in 12.
Division equation:
12 ÷ (4/55) = (12/1) ÷ (4/55)
= (12/1) * (55/4)
= 165
Therefore, 12 divided by 4/55 is equal to 165.
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Find the slope of the line that passes through (3, 7) and (6, 8).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer:
Slope = 1/3
Step-by-step explanation:
Step 1: Define general form of equation of line
An equation of a straight line on two-dimensional plane could be represented in form of: y = Mx + b, with M is slope and b is y-intercept
Step 2: Set up the system to solve for slope M of equation of line
That equation passes 2 points, which are represented in form of (x, y), (3, 7) and (6, 8).
Substitute these values of x and y into the original equation in step 1:
7 = 3M + b
8 = 6M + b
Step 3: Solve the system of equations in step 2 for M
Subtract 1st equation from 2nd equation:
8 - 7 = 6M - 3M + b - b
Simplify both sides:
1 = 3M
Divide both sides by 3:
=> M = 1/3
Hope this helps!
:)
Answer:
\(slope = \frac{1}{3} \)
Step-by-step explanation:
\((3 \: \: \: ,\: \: \: 7) = > (x1 \: \: \: ,\: \: \: x2) \\ (6 \: \: \: ,\: \: \: 8) = > (y1 \: \: \: \: , \: \: \: y2)\)
\(slope \\ = \frac{y1 - y2}{x1 - x2} \\ = \frac{7 - 8}{3 - 6} \\ = \frac{ - 1}{ - 3} \\ = \frac{1}{3} \)
hope this helps
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good luck! have a nice day!
PLEASE HELP! The two-way frequency table below shows the preferred communication method of employees at a company, based on years of employment with the company. What percentage of employees with 8 or more years at the company reported that email is their preferred method of communication? A. 67.19 B. 48.84 C. 20.48 D. 44.79
Answers
Answer:
D. 44.79
Step-by-step explanation:
\(\frac{43}{96}\) who worked 8 or more years said that e-mail was their favorite communication method.
\(\frac{43}{96}\) ≈ \(\frac{44.79}{100}\)
So around 44.79% who have worked 8 years or more said that email were their preferred communication method. Our answer is D. 44.79.
Answer:
44.79%
Step-by-step explanation:
help can you help me I need your help please help me solve that I would really appreciate it
Answers
The factor form of the quadratic equations are listed below:
Case 13: (b - 4) · (b - 2)
Case 14: (n + 4) · (n + 2)
Case 15: 2 · (n + 9) · (n - 6)
Case 16: 5 · (n + 2)²
Case 17: 2 · (k + 5) · (k + 6)
Case 18: (a - 10) · (a + 9)
Case 19: (p + 10) · (p + 1)
Case 20: 5 · (v - 2) · (v - 4)
Case 21: 2 · (p + 2) · (p - 1)
Case 22: 4 · (v - 2) · (v + 1)
Case 23: (x - 10) · (x - 15)
Case 24: (v - 5) · (v - 2)
Case 25: (p + 6) · (p - 3)
Case 26: 6 · (v + 10) · (v + 1)
How to factor a quadratic equation
In this problem we find quadratic equations of the form a · x² + b · x + c, whose factor form is introduced below:
a · x² + b · x + c = a · x² + a · (- r₁ - r₂) · x + a · r₁ · r₂ = a · (x - r₁) · (x - r₂)
Where r₁, r₂ are real roots.
Now we proceed to present the factor form of each quadratic equation:
Case 13
b² - 6 · b + 8 = (b - 4) · (b - 2)
Case 14
n² + 6 · n + 8 = (n + 4) · (n + 2)
Case 15
2 · n² + 6 · n - 108 = 2 · (n² + 3 · n - 54) = 2 · (n + 9) · (n - 6)
Case 16
5 · n² + 10 · n + 20 = 5 · (n² + 2 · n + 4) = 5 · (n + 2)²
Case 17
2 · k² + 22 · k + 60 = 2 · (k² + 11 · k + 30) = 2 · (k + 5) · (k + 6)
Case 18
a² - a - 90 = (a - 10) · (a + 9)
Case 19
p² + 11 · p + 10 = (p + 10) · (p + 1)
Case 20
5 · v² - 30 · v + 40 = 5 · (v² - 6 · v + 8) = 5 · (v - 2) · (v - 4)
Case 21
2 · p² + 2 · p - 4 = 2 · (p² + p - 2) = 2 · (p + 2) · (p - 1)
Case 22
4 · v² - 4 · v - 8 = 4 · (v² - v - 2) = 4 · (v - 2) · (v + 1)
Case 23
x² - 15 · x + 50 = (x - 10) · (x - 15)
Case 24
v² - 7 · v + 10 = (v - 5) · (v - 2)
Case 25
p² + 3 · p - 18 = (p + 6) · (p - 3)
Case 26
6 · v² + 66 · v + 60 = 6 · (v² + 11 · v + 10) = 6 · (v + 10) · (v + 1)
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when a number is decreased by 3% the result is 80. what was the original number?
Answers
Answer:
82.47
Step-by-step explanation:
.93n = 80
n = 80/.93
n = 82.47
Simplify. Your answer should only contain exponents. Please explain how to do this.
Answers
Answer:
\(1. \: \frac{8v {}^{5} }{u} \)
\(2. \: 32 {}^{6} y {}^{8} \)
Step-by-step explanation:
\(2vu {}^{ - 4} .4u {}^{3} v {}^{4} = 8.(v {}^{1} \times v {}^{4} ).(u {}^{ - 4} \times u {}^{3} ) = 8.v {}^{5} .u {}^{ - 1} = 8.v {}^{5} . \frac{1}{u} = \frac{8v {}^{5} }{u} \)
\(4x {}^{3} y {}^{2} .2y {}^{4} .4x {}^{3} = (4 \times 2 \times 4).(x {}^{3} \times x {}^{3} ).(y {}^{2} \times y {}^{4} ) = 32.x {}^{3 + 3}.y {}^{2 + 6} = 32x {}^{6} y {}^{8} \)
HELP ASAP I give brainliest!
1. I just signed up for Ugly Produce (a food delivery service for Ugly Fruits & Vegetables). My first box of apples arrived today. 2/5 of the apples were red. 3/4 of the remaining apples were green and the rest of the apples were yellow.
a. What percent of the apples were yellow?
b. Now that I have so many apples, I decided to make a giant apple pie. The recipe calls for 3 cups of sugar and 4 cups of flour but I only have 2 cups of sugar. How much flour should I use?
(set up a ratio/table or proportion and solve).
Answers
2. That’s the only answer I have, sorry.
Carla has a rectangular garden in her backyard. The width of the garden is 9 meters. The area of the garden is 360 square meters. What is the length of the garden? Show your work.
Answers
Answer:
l = 40 m
Step-by-step explanation:
The formula for area of a rectangle is
A = lw, where
A is the area in square units,l is the length,and w is the widthStep 1: Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):
360 = 9l
Step 2: Divide both sides by 9 to solve for l
(360 = 9l) / 9
40 m = l
Optional Step 3: We can check our answers by checking that the product of 40 and 9 is 360
40 * 9 = 360
360 = 360
A contractor records the areas, in square feet, of a small sample of houses in a neighborhood to determine data about the neighborhood. They are:
2,400; 1,750; 1,900; 2,500; 2,250; 2,100
Which of the following represents the numerator in the calculation of variance and standard deviation?
(225)2 + (–425)2 + (–275)2 + (325)2 + (75)2 + (–75)2 = 423,750
(650)2 + (–150)2 + (–600)2 + (250)2 + (150)2 + (–300)2 = 980,000
(250)2 + (–400)2 + (–250)2 + (350)2 + (100)2 + (–50)2 = 420,000
What is the variance?
What is the standard deviation, rounded to the nearest whole number?
Answers
The representation is the numerator in the calculation of variance and the standard deviation is 225)2 + (–425)2 + (–275)2 + (325)2 + (75)2 + (–75)2 = 423,750.
What is a variance?Variance = sum of (data value - mean)² / number of data values
To find the numerator, we need to calculate the mean of the data values first:
Mean = (2400 + 1750 + 1900 + 2500 + 2250 + 2100) / 6 = 2150
Then, the numerator for the variance calculation is:
(2400 - 2150)² + (1750 - 2150)² + (1900 - 2150)² + (2500 - 2150)² + (2250 - 2150)² + (2100 - 2150)²
= 250² + (-400)² + (-250)² + 350² + 100² + (-50)²
= 62500 + 160000 + 62500 + 122500 + 10000 + 2500
= 372500
Using the formula for variance:
Variance = 372500 / 6 = 62083.3333
To find the standard deviation, we take the square root of the variance:
Standard deviation = √62083.3333 ≈ 249
Therefore, the correct option is (A) 372500, the variance is 62083.3333, and the standard deviation is approximately 249.
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Answer:
C: (250)2 + (–400)2 + (–250)2 + (350)2 + (100)2 + (–50)2 = 420,000.84000.290.Step-by-step explanation:
Isabella went to taco stand. She got 2 tacos and 4 drinks for $11.60. Lucas went to the same stand and got 3 tacos and 1 drink for $8.40.
1. Write an equation on how you can found out how much 1 taco and 1 drink is.
2. Solve
Answers
2x + 4y = 11.60
x represents the price of tacos and y represents the price of drinks
For Lucas:
3x + 1y = 8.40.
This is a systems of equation and can be solved by three methods. I’ll use the substitution method.
y = 8.40 - 3x … plug that into the top equation and solve for..
2x + 4(8.40-3x) = 11.60
.. simplify;
2x + 33.6 - 12x = 11.60
.. combine like terms;
-10x + 33.60 = 11.60
.. solve;
-10x = -19
.. solve;
divide by -10 on both sides of the equation..
-19/-10 = 1.9.. x = 1.9 ; this means that tacos cost $1.90. Let’s plug this into our original equations to figure out the price of each drink.
3(1.9)+y=8.40
.. simplify;
5.7 + y = 8.40
.. solve;
y = $2.70.. this means each drink costs $2.70.
We can work even further to double check our answers by plugging both numbers in the equations. Remember;
y = 2.70 (drinks)
x = 1.90 (tacos)
to factorize the following algebraic expression: 3x² + 6x + 4x + 8 Provide a three-step guide on how to factorize the expression.
Answers
Answer:
Check below:
Step-by-step explanation:
To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:
Step 1: Grouping
Group the terms in pairs so that you can factor out a common factor from each pair.
3x² + 6x + 4x + 8
(3x² + 6x) + (4x + 8)
Step 2: Factoring out the common factors
Factor out the common factors from each pair separately.
3x(x + 2) + 4(x + 2)
Step 3: Factoring out the common factor from the resulting expression
Notice that we have a common factor, (x + 2), in both terms.
(x + 2)(3x + 4)
Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).
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Evaluate the following expression: \[ 1.723 \times 10^{2}+7.38 \times 10^{3} \] Type answer:
Answers
The sum of expression \(1.723 \times 10^{2}\) and \(7.38 \times 10^{3}\) is \(7.5523 \times 10^{3}\). The numbers in scientific notation are added by summing the coefficients while keeping the exponent unchanged.
In scientific notation, numbers are expressed as a coefficient multiplied by a power of 10. To add numbers in scientific notation, we need to ensure that the powers of 10 are the same.
In this case, both numbers are already in scientific notation with powers of 10. We can directly add the coefficients while keeping the exponent the same.
Adding \(1.723 \times 10^2\) and \(7.38 \times 10^3\) gives us a sum of \(7.5523 \times 10^3\). The coefficient represents the numerical value, and the power of 10 indicates the magnitude.
Thus, the expression \(1.723 \times 10^2 + 7.38 \times 10^3\) evaluates to \(7.5523 \times 10^3\), indicating a significant increase in magnitude compared to the individual numbers.
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help me out please? it would mean a lot tysm
Answers
Answer:
0
Step-by-step explanation:
Graph Rate of Change:
(0,1) (1,3)
\(\frac{3-1}{1-0}\) = \(\frac{2}{1}\) = 2
Table Rate of Change:
(5,13) (7,17)
\(\frac{17 - 13}{7 - 5}\) = \(\frac{4}{2}\) = \(\frac{2}{1}\) = 2
2 - 2 = 0
In school ,there are 3 girls for every 2 boys . There are 650 students in total . How many students are girls ?
Answers
Answer:
Girls = 390
Step-by-step explanation:
Set up a proportion:
In a sample of 3:2, you have 5 kids in all.
So the the ratio of girls to kids in a sample of 5 is 2:5.
So set up a proportion:
(3/5) = (x/650)
5x = 650(3)
5x = 1950
x = 390
Answer:
390Step-by-step explanation:
Let number of boys be b and girls be g. Then we have:
g/b = 3/2g + b = 650From the first equation b is:
b = 2g/3Substitute b in the second equation
g + 2g/3 = 6505g/3 = 650g = 650*3/5g = 390Two equations are shown Y equals four over X +3 and Y equals negative 2X subtract four which statement best describes the graph of the two equations
Answers
The graph for the given system of equations is shown below
Graph of System of Linear equationsFrom the question, we are to determine the graph that describes the given system equations
First, we will graph the given system of linear equations.
The given equations are
Y equals four over X +3
and
Y equals negative 2X subtract four
That is,
y = 4/(x+3)
y = -2x -4
The graph for the given system of equations is shown below
The statement that best describes the graph of the two equations is the statement that describes the graph of the system of equations as shown below
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What is the probability that the battery life for an ipad mini will be at least 11 hours?
Answers
Answer:
0.2857
Step-by-step explanation:
We want to determine,
The probability that the battery life is at least 11 hours is 0.2857.
jerry has 3,572 live chickens in his poultry farm.if there are 38 boxes , how many chickens must go in each box?
Answers
Answer: 94 live chickens go in each box.
Step-by-step explanation: 3,572 divided by 38 = 94 so 94 live chickens go in each box.
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Which equation represents a line that passes through (2, –left-parenthesis 2, negative StartFraction one-half EndFraction right-parenthesis.) and has a slope of 3?
y – 2 = 3(x + y minus 3 equals 2 left-parenthesis x plus StartFraction one-half EndFraction right-parenthesis.)
y – 3 = 2(x + y minus 3 equals 2 left-parenthesis x plus StartFraction one-half EndFraction right-parenthesis.)
y + y plus StartFraction one-half EndFraction equals 3 left-parenthesis x minus 2 right-parenthesis. = 3(x – 2)
y + y plus StartFraction one-half EndFraction equals 2 left-parenthesis x minus 3 right-parenthesis. = 2(x – 3)\
Answers
The distance between two points is a line. The equation of the line is y = 3x - 8
Equation of a line
The equation of a line in slope - intercept form is given as;
y = mx + b
where
m is the slope
b is the intercept
Given the following
slope 'm' = 3
Determine the y-intercept
-2= 3(2) + b
-2 = 6 + b
b = -8
Determine the equation
y = 3x + (-8)
y = 3x - 8
Hence the equation of the line is y = 3x - 8
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The method 100 students use to get to
school and their grade level is shown below.
Walk
Drive
Sophomore 2
Junior
13
Senior
25
P(AnB)
P(B|A) = P(A)
Bus
25
20
5
MN5
3
2
5
Find the probability a student drives,
given that they are a senior.
P(drive | senior) = [?]
Round to the nearest hundredth
Answers
The probability that a student drives to school, given that they are a senior, is approximately 0.71, rounded to the nearest hundredth.
How to find the Probability?
We can use Bayes' theorem to find the probability that a senior student drives to school, given that they are a senior.
First, we need to calculate the probability of a student being a senior:
\(P(senior) = \frac{25+5+5}{(2+25+3+13+20+2+25+5+5)} = \frac{35}{100} = 0.35\)
Next, we need to calculate the probability of a senior student driving to school:
P(drive ∩ senior) = 25/100 = 0.25
Now we can apply Bayes' theorem:
P(drive | senior) = P(drive ∩ senior) / P(senior)
P(drive | senior) = 0.25 / 0.35 ≈ 0.71
Therefore, the probability that a student drives to school, given that they are a senior, is approximately 0.71, rounded to the nearest hundredth.
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Which statement is true?
f 0.09>78
g 8.0×10-3>6%
h 78<8.0×10-3
j 6%<0.09
Answers
Answer:h
Step-by-step explanation:
Employees of the sports department at a television station want to measure the number of viewers for a particular exercise program. They call the homes of all the members of a nearby health club. Why might this be a biased sample?
A.The station does not include everyone in the viewing area.
B.The station does not include people all across the country.
C.People who belong to a health club may have many television sets in their homes.
D.People who belong to a health club may be more likely to watch an exercise program.
Answers
Answer:
d
Step-by-step explanation:
Please help grade depends on it
Answers
Answer:
C
Step-by-step explanation:
17/10 is correct
what’s the slope for this
Answers
Answer:
-2
Step-by-step explanation:
Which symbol correctly compares the two angles?
45° pi/3
Answers
Answer:
a pi = 3.14
Step-by-step explanation:
The symbol which compares the two angles is "< ".
What is an angle?
Angles around a point define the sum of angles that can be arranged together so that they construct a full arch. Angles around a point add to 360 °.
π/3 =180/3 = 60 degree
π/3 > 45 degree
45 degree < π/3
Therefore, the correct answer is option A. <.
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PLEASE HELP ASAP!!!!!
Answers
Answer:
Factored completely is: 3x^2 (x+3)(x-2)
according to your question - probs (x-2), no other choice
Step-by-step explanation:
have fun friend & have a good day friend :)
6) You go to dinner with some
friends. Your total bill was $56.32.
You have a coupon for 15%. How
much is your total cost if you leave
a 20% tip?
Answers
Answer:
$57.44
Step-by-step explanation:
1. subtract 15% from the bill with coupon:
$56.32 - ($56.32 x 0.15) = $47.87
2. add 20% to this new bill:
$47.87+(47.87 x 0.20) = $57.44
I need help with both of these questions.
Answers
X= 14 and x= -12
On the second one
X= 7 and x= -7