The area of a rectangle is represented by the expression x^2-9x+14 units^2. Find the expressions that could represent the length and width of the rectangle
Answers
The expressions that could represent the length and width are (x - 2) units and (x - 7) units respectively.
To find the expressions that represent the length and width of the rectangle, we need to factor the given expression.
x² - 9x + 14 = (x - 2)(x - 7)
The length and width of the rectangle are represented by two factors of the expression.
To find the length and width of the rectangle, we need to understand the formula for the area of a rectangle, which is length multiplied by width. The given expression x²-9x+14 represents the area of the rectangle. To find the expressions that represent the length and width, we need to factor the given expression.
We can do this by finding two numbers that multiply to 14 and add up to -9. These numbers are -2 and -7. Therefore, we can factor the given expression as (x - 2)(x - 7). From this, we can see that the length of the rectangle is represented by the factor (x - 2) units and the width is represented by the factor (x - 7) units.
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Related Questions
R 5 100 000 Bond Costs ✓ LOAN INFORMATION Deposit: 15% Interest rate: 11,2% Loan period: 20 years the information above to answer questions that follow. Define the term "Deposit" according to the given contex Write down the price of the house in words. Calculate the monthly repayment and the real cost of t If the length of this loan was 25 years, with the same I
Answers
Answer: Based on the provided information, it appears that the questions are incomplete. The term "Deposit" is mentioned, but there is no specific context given to define it. Additionally, the price of the house and the interest rate for a 25-year loan are missing. Therefore, I cannot accurately answer the questions without complete information. Please provide all the necessary details, and I will be happy to assist you further.
Step-by-step explanation:
A company constructing electric fans finds that the total cost of producing x fans, in dollars, is approximately
Using marginal cost, approximate the cost (in dollars) of producing the 100th fan.
C(x)=127+217x-0.88x2 Please round to two decimal places.
Answers
The approximate cost of producing the 100th fan is $41.
The marginal cost represents the rate of change of the total cost with respect to the number of fans produced, which can be found by taking the derivative of the cost function with respect to x.
The cost function C(x) = 127 + 217x - 0.88x^2, we can differentiate it to find the marginal cost function:
C'(x) = 217 - 1.76x
To approximate the cost of producing the 100th fan, we substitute x = 100 into the marginal cost function:
C'(100) = 217 - 1.76(100)
= 217 - 176
= 41
Therefore, the approximate cost of producing the 100th fan is $41.
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Multiplying mateices
Answers
Answer:
uhhhh
Step-by-step explanation:
4. Your first six-month auto insurance premium was $729.00. Based on your good
driving record, your renewal premium is $648.81. What percent decrease did you see
in your premium? (2 points)
I
Answers
Answer: 11%
Step-by-step explanation:
729-648.81=80.10
What percent is 80.10 of 729
%/100 = is/of (this may help you)
X/100 = 80.10/729 (cross multiplication)
(80.19*100)/729 =
11%
Name:
Date:
Bell: Homework 5: Multi-Step & Compound
Inequalities
** This is a 2-page documenti **
Directions: Solve, graph, and write the solution to each inequality in interval notation,
1.-7a - 11 <1-10
2. 5-9(8 - 2x) = 2x - 115
Interval Notation:
3.-2(7 + y)2 -8(y + 1)
Interval Notation:
4.-5(k+ 4) 2-(3k + 6)
Interval Notation:
Interval Notation:
3(2x + 7)
> x+1
-3
6. r + 10 S-3(2r - 3) + 6(r + 3)
5.
Interval Notation:
Interval Notation:
7.-8m - 12 > -5(m - 8) - 3(m - 7)
8. 18(9-3)=-2{q+7)
Interval Notation:
Interval Notation:
O Gina Wilson (All Things Algebra
Answers
Step-by-step explanation:
what you have written I can't send one thing on
a radio station claims that the amount of advertising each hour has a mean of 12 minutes and a standard deviation of 1.5 minutes. you listen to the radio station for 1 hour and observe that the amount of advertising time is 5 minutes. calculate the z-score for this amount of advertising time. z
Answers
The z-score for 11 minutes of advertising time is approximately -0.667
Here we have given that a radio station claims that the amount of advertising each hour has a mean of 12 minutes and a standard deviation of 1.5 minutes. you listen to the radio station for 1 hour and observe that the amount of advertising time is 5 minutes.
And we need to calculate the z-score for this amount of advertising time.
While we looking into the given question, we have identified that Z-scores measure the distance of any data point from the mean in units of standard deviations and are useful because they allow us to compare the relative positions of data values in different samples.
Here the z-score for any single data value can be found by the formula:
z = (data value- mean) / standard deviation
Here from the information given we know:
Data value = 11 minutes
Mean = 12 minutes
Standard deviation = 1.5 minutes
When we apply the values on the formula then we get,
=> z = (11 - 12) / 1.5 = -0.667
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Find the solution of the differential equation that satisfies the given initial conditions?
(Just give me tips, you don't have to do the whole thing)
a. yy'=x sin x and y(0)=−1
b. y'tan x=y+8, y(Ï€3)=8 and 0
c. xy'=y + x2 sin x and y(Ï€)=0
Answers
The solution for question a is ln |y| = (1/2) x²- cos x - 1. The solution for question b is y = -8 - (16/√3) sin x. The solution for question c is ln |y/x + x sin x| = ln |x| + ln |y(π)| - ln |π|. We can show the working in the following manner.
To solve a differential equation with initial conditions, we usually follow these steps:
Separate the variables and integrate both sides to get a general solution that contains an arbitrary constant.
Use the initial conditions to find the value of the arbitrary constant and obtain a particular solution.
Check the solution by verifying that it satisfies the differential equation and the initial conditions.
For the given differential equations with initial conditions:
a. yy' = x sin x and y(0) = -1
We can separate the variables:
y' / y = x sin x / y
Integrating both sides:
ln |y| = (1/2) x² - cos x + C
where C is the arbitrary constant.
To find the value of C, we use the initial condition:
ln |-1| = (1/2) (0)² - cos 0 + C
C = -1
Therefore, the particular solution is:
ln |y| = (1/2) x²- cos x - 1
b. y' tan x = y + 8, y(π/3) = 8
We can separate the variables:
y' / (y+8) = cot x
Integrating both sides:
ln |y+8| = ln |sin x| + C
where C is the arbitrary constant.
To find the value of C, we use the initial condition:
ln |8+8| = ln |sin π/3| + C
C = ln 16 - ln √3
Therefore, the particular solution is:
ln |y+8| = ln |sin x| + ln 16 - ln √3
Simplifying:
|y+8| = (16/√3) |sin x|
y+8 = ± (16/√3) sin x
y = -8 ± (16/√3) sin x
We use the initial condition to determine the sign of the constant:
y(π/3) = -8 ± (16/√3) √3/2
y(π/3) = 8/√3
Since y(π/3) = 8, we take the negative sign:
y = -8 - (16/√3) sin x
c. xy' = y + x^2 sin x and y(π) = 0
We can separate the variables:
y' / (y/x + x sin x) = 1/x
Integrating both sides:
ln |y/x + x sin x| = ln |x| + C
where C is the arbitrary constant.
To find the value of C, we use the initial condition:
ln |y(π)/π + π sin π| = ln |π| + C
ln |y(π)| = ln |π| + C
C = ln |y(π)| - ln |π|
Therefore, the particular solution is:
ln |y/x + x sin x| = ln |x| + ln |y(π)| - ln |π|
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1. Which quadratic has x-intercepts at (-3, 0) and (5, 0)?
a) f (x) = (x - 3)(x + 5)
b) f (x) = x^2 - 3x + 5
c) f (x) = (x + 3)(x - 5)
d) f (x) = x^2 + 3x - 5
Answers
Answer:
c
Step-by-step explanation:
Since the x-intercepts of the quadratic function are (-3,0) and (5,0), so its roots are \(x=-3\) and \(x=5\)
So, the quadratic function contains the linear factors \((x+3)\) and \((x-5)\). Then, the quadratic function in the factored form would be, where a is a real number:
\(f(x)=a(x+3)(x-5)\)
For simplicity, assume that \(a=1\) and the quadratic function becomes:
\(f(x)=(x+3)(x-5)\)
Write the slope-intercept form of the equation of each line.
-5-4-3-2-1
=-3x+4
A) y =
4
C) y=x+4
5
8
B) y=-x+4
5
D) y = 4x-
85
Answers
The slope-intercept form of the equation of each line is y=-x+4.
How should a slope-intercept form equation be written?When you know the slope of the line to be investigated and the specified point is also the y intercept (0,), you may apply the slope intercept formula, y = mx + b. The y value of the y intercept point is represented by b in the equation.Simply said, the slope-intercept form is the technique to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.The slope-intercept form of the equation of each line is y=-x+4.To learn more about slope-intercept refer to:
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PLEASE HELP WHATS THE ANSWER
Answers
Answer:
\(Domain: (-\infty, \infty)\)
\({\{x|x \in \R\}}\)
a lecture hall has 200 seats with folding arm tablets 30 of which are designed
Answers
There are number of 170 seats with folding arm tablets that are not designed for wheelchair users.
1. First we need to identify the total number of seats in the lecture hall which is 200.
2. Then we need to identify the number of seats with folding arm tablets that are designed for wheelchair users which is 30.
3. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats.
4. Therefore, 200 - 30 = 170, which means there are 170 seats with folding arm tablets that are not designed for wheelchair users.
The lecture hall in question has a total of 200 seats, with 30 of those seats having folding arm tablets that are designed for wheelchair users. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats. This means that 200 - 30 = 170, which means there are number of 170 seats with folding arm tablets that are not designed for wheelchair users.
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The Great Wall of China, built in the 7th century BCE, is about 1 x 10^4 miles long. The Panama Canal, built over 2 thousand years later, is about 5 x 10^1 miles long. Use these numbers to complete the sentence below. Write your answer in standarered form, without using exponets. The Great Wall of China is about ____ times longer then the Panama Canal what is the answer?
Answers
The Great Wall of China is about 200 times longer then the Panama Canal
How many times longer is the Great Wall of China?Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. An examples of 100 expressed in scientific notation is 1 x 10².
In order to determine the difference in the length of the great wall of China and the Panama Canal, divide the length of the Great wall of China by the length of the Panama Canal.
(1 x \(10^{4}\)) ÷ (5 x \(10^{1}\))
(1/5) x \(10^{4 - 1}\)
0.2 x \(10^{3}\)
2 x \(10^{3 - 1}\)
2 x10² = 200
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Given that cosα=−2√2 and tanα<0, draw and use a diagram to find the value of all six trig functions.
Answers
Given:
\(\begin{gathered} \cos \alpha=-\frac{\sqrt[]{2}}{2} \\ \tan \alpha<0 \end{gathered}\)To find the six trigonometric functions:
Since,
\(\cos \alpha<0\text{ and }\tan \alpha<0\)So, the angle lies in the second quadrant.
Let us draw the diagram.
Using the Pythagoras theorem,
\(\begin{gathered} AB^2=AC^2+BC^2 \\ 2^2=AC^2+(\sqrt[]{2})^2 \\ 4=AC^2+2 \\ AC^2=2 \\ AC=\sqrt[]{2}\ldots\ldots\ldots(1) \end{gathered}\)Next, find the six trig functions.
\(\begin{gathered} \sin \alpha=\frac{AC}{AB} \\ =\frac{\sqrt[]{2}}{2} \\ co\sec \alpha=\frac{AB}{AC} \\ =\frac{2}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ =\frac{2\sqrt[]{2}}{2} \\ =\sqrt[]{2} \end{gathered}\)And,
\(\begin{gathered} \cos \alpha=-\frac{BC}{AB}(Since,II\text{ quadrant)} \\ =-\frac{\sqrt[]{2}}{2} \\ \sec \alpha=-\frac{AB}{BC}(Since,II\text{ quadrant)} \\ =-\frac{2}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ =-\frac{2\sqrt[]{2}}{2} \\ =-\sqrt[]{2} \end{gathered}\)Similarly,
\(\begin{gathered} \tan \alpha=-\frac{AC}{BC}(Since,II\text{ quadrant)} \\ =-\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ =-1 \\ \cot \alpha=-\frac{BC}{AC}(Since,II\text{ quadrant)} \\ =-\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ =-1 \end{gathered}\)Therefore, the answers are,
\(\begin{gathered} \sin \alpha=\frac{\sqrt[]{2}}{2} \\ co\sec \alpha=\sqrt[]{2} \\ \cos \alpha=-\frac{\sqrt[]{2}}{2} \\ \sec \alpha=-\sqrt[]{2} \\ \tan \alpha=-1 \\ \cot \alpha=-1 \end{gathered}\)
Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer. Choose the correct choice below.
A. The smaller the sample size, the smaller is the standard deviation of X, because x is averaging fewer values.
B. The larger the sample size the larger the range of values that could take on, and therefore the larger the standard deviation of x.
C. The sample size has no effect on the standard deviation of all possible sample means because x - for every sample, and so the standard deviation is just zero.
D. The larger the sample size, the smaller the standard deviation of X, because the denominator of the standard deviation of x contains the square root of the sample size.
Answers
The correct choice is:
D. The larger the sample size, the smaller the standard deviation of X, because the denominator of the standard deviation of x contains the square root of the sample size.
To explain this answer, let's consider the formula for the standard deviation of the sample means, which is:
The standard deviation of sample means = σ/√n
Here, σ is the population standard deviation, and n is the sample size. As you can see, the standard deviation of the sample means is inversely proportional to the square root of the sample size. This means that as the sample size (n) increases, the standard deviation of the sample means will decrease. Therefore, a larger sample size will lead to a smaller standard deviation of all possible sample means, as it will provide a more precise estimate of the population mean.
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A coin is flipped five times. find the number of possible sets of heads and tails that have 2 heads.
Answers
The number of possible sets of heads and tails that have 2 heads is 11.
Given,
There is one coin and it is flipped five times.
First, we have to list out the outcome when we toss the coin five times.
(HHHHH), (HHHHT), (HHHTT), (HHTTT), (HTTTT), (TTTTT), (TTTTH), (TTTHH), (TTHHH), (THHHH), (THTHT), (HTHTH), (THHTT), (THHHT), (HTTTH), (HTTHH), (HTHHH), (THTTT), (TTHTH), (TTTHT), (TTHHT), (HHTHH), (TTHTT), (HHTTH), (HHTHT), (HTHTT), (THTHH), (THTTH), (HTHHT), (HHHTH)
Now, we can list out the possible sets with 2 heads.
(HHTTT), (TTTHH), (THTHT), (HTTHT), (HTTTH), (THHTT), (TTHHT), (TTHTH), (HTHTT), (THTTH), (HTHTT)
So, the number of possible sets of heads and tails that have 2 heads is 11.
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The dimension of the row space of a 3 x 3 matrix A is 2. (a) What is the dimension of the column space of A? (b) What is the rank of A? (c) What is the nullity of A? (d) What is the dimension of the solution space of the homogeneous system Ax = 0?
Answers
a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.
(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.
(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.
(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:
nullity = number of columns - rank
nullity = 3 - 2 = 1
Therefore, the nullity of matrix A is 1.
(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.
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imagine that a survey of randomly selected people finds that people who used sunscreen were more likely to have been sunburned in the past year. which explanation for this result seems most likely?
Answers
Imagine that a survey of randomly selected people finds that people who used sunscreen were more likely to have been sunburned in the past year.
There are several possible explanations for the finding that people who used sunscreen were more likely to have been sunburned in the past year.
However, without additional context or data, it is difficult to determine the most likely explanation definitively. Here are a few possible explanations to consider:
1. Ineffective or improper use of sunscreen: It is possible that the individuals who reported using sunscreen did not apply it correctly or did not reapply it as recommended.
Inadequate application or failure to follow proper sunscreen usage guidelines could result in insufficient protection from the sun's harmful rays, leading to sunburn.
2. Self-selection bias: It is possible that individuals who have previously experienced sunburns may be more likely to use sunscreen. They may be more aware of the potential risks and take precautions, including using sunscreen.
This could create an association between sunscreen use and sunburn, even though sunscreen itself is intended to prevent sunburn.
3. Recall bias: The survey responses may be subject to recall bias, where individuals may inaccurately remember or report their sunscreen use and sunburn experiences.
Memory limitations or subjective perceptions of sunburn severity could influence the reported data and the observed association between sunscreen use and sunburn.
4. Confounding factors: There may be other factors or variables at play that are related to both sunscreen use and sunburn. For example, individuals who engage in activities that increase sun exposure or who have certain skin types may be more likely to both use sunscreen and experience sunburn.
It is important to note that further investigation, including more detailed surveys, data collection and statistical analysis, would be necessary to determine the most likely explanation for the observed association between sunscreen use and sunburn.
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ben plays basketball every 6 times in 3 weeks. at this rate how many times does he play basketball in 10 weeks
Answers
Answer:
20
Step-by-step explanation:
because he plays 2 times in one week
Please help!!! WILL GIVE BRAINLIEST
Answers
The removable discontinuity of the function is x-2/(x-2)(x+4).
Given, we have the following functions:
a. x-2/(x-2)(x+4)
separate the terms:
= x-2/x-2 × 1/x+4
cancel the like terms:
= 1 × 1/x+4
hence x-2/(x-2)(x+4) has a removable discontinuity.
A point on the graph that is undefinable or does not fit the remainder of the graph is referred to as a removable discontinuity. A detachable discontinuity can be generated in one of two ways. The function can be defined to have a blip, or it can have a common factor in both the numerator and the denominator.
When the two-sided limit at c exists but isn't equal to f(c), the discontinuity at c is referred to as detachable.
Hence the from the given functions the function which have a removable discontinuity is x-2/(x-2)(x+4)
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2 3/4÷4 1/2
What is the value of the expression, in simplest form?
I need help
Answers
The value of the expression, in simplest form is 11/18.
The given expression is:
2 3/4 ÷ 4 1/2
We have to determine the value of the expression, in simplest form.
To solve the expression we first convert the mixed fraction in the form of improper fraction.
To convert 2 3/4 in the form of improper fraction multiply 2 by 4 then add the result of multiplication of 2 and 4 with 3.
So the improper form of 2 3/4 = 11/4
To convert 4 1/2 in the form of improper fraction multiply 4 by 2 then add the result of multiplication of 4 and 2 with 1.
So the improper form of 4 1/2 = 9/2
Now the simplest form of the expression is:
= 11/4 ÷ 9/2
We can write the expression as
= 11/4 × 2/9
After simplifying
= 11/2 × 1/9
= 11/18
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Pls help question about total pay
Show working out
Answers
\(7\frac{1}{2}\implies 7.5\hspace{5em}1\frac{1}{4}\implies 1.25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Monday through Friday} }{\stackrel{ days }{(5)}\stackrel{ rate }{(10.80)}\stackrel{ hours }{(7.5)}}~~ + ~~\stackrel{ Saturday }{\stackrel{ days }{(1)}\stackrel{ rate }{(10.80)(1.25)}\stackrel{ hours }{(7.5)}} \\\\\\ 405~~ + ~~101.25\implies \text{\LARGE 506.25}\)
PLS HELP THIS IS IMPORTANT OFFERING 20 POINTS
The exponential function f intersects the x-axis at the point (2,0) and intersects the y-axis at the point (0,-5.25)
If g(x) = 3x - 2, which statement is true over the interval [0, 2]?
A.
The average rate of change of g is equal to the average rate of change of f.
B.
The average rate of change of g is greater than the average rate of change of f.
C.
The average rate of change of f cannot be determined using the information given.
D.
The average rate of change of g is less than the average rate of change of f.
Answers
Answer:
A.
Step-by-step explanation:
The circumference C of a circle is 2 17 inches. Use the formula C = 2rr to find the radius r of the circle. in.
Answers
Answer: r ≈ 34.54
Step-by-step explanation:
You have your circumference which is 217.
Plug this into your equation.
217 = 2πr
Divide both sides by 2π to make r by itself.
After you do this, you get r ≈ 34.54
7.
Write the equation of the piecewise function ƒ that is represented by its graph.
A.) \(f(x)=\left \{{{x^{3}, if x\ \textless \ 1} \atop {x, if x \geq 1}} \right.\)
B.) \(f(x)=\left \{{{x^{3}, if x\ \textless \ 0} \atop {x^{2}, if x\geq 0}} \right.\)
C.) \(f(x)=\left \{{{x^{3}, if x\ \textless \ 0} \atop {x, if x\geq 0}} \right.\)
D.) \(f(x)=\left \{{{x, if x\ \textless \ 0} \atop {x^{3}, if x\geq 0}} \right.\)
![7. Write the equation of the piecewise function that is represented by its graph.A.) [tex]f(x)=\left](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/pZ1v0LQq1pwKc72C3A9sofXLhvaNmOhp.png)
Answers
The piecewise function that represent the graph is A)f(x)=\(\left \{{ x^3 ,if{x < 1} \atop x,if {x\ge1}} \right.\).
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
In considering the definition of any piecewise function, the domain descriptions in the function definition must match the pieces shown in the graph.
Here, the right segment has no upper bound, so x > 1 is an appropriate description of its domain.
The left segment also has no upper bound , so x\(\ge\) 1is an appropriate description of its domain.
The one answer choice that combines these domain descriptions is
A)f(x)=\(\left \{{ x^3 ,if{x < 1} \atop x,if {x\ge1}} \right.\)
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Tasha has foam blocks stored in a box that measures 214 ft long by 2 ft wide by 2 ft tall.
Each foam block is a cube with 12ft edge length.
How many blocks can fit into the box?
Answers
If 50 is 20% of a value, what is that value?
Answers
Divide 50 by 20%
50/20% = 50/0.20 = 250
Answer: 250
14. Solve for x. (show work pls)
Answers
The value of the variable 'x' by simplifying the equation (x + 12) / (x + 5) = (x + 5) / x will be 12.5.
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 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Then the equation is given as,
(x + 12) / (x + 5) = (x + 5) / x
Simplify the equation, then we have
(x + 12) / (x + 5) = (x + 5) / x
x² + 12x = (x + 5)²
x² + 12x = x² + 10x + 25
12x - 10x = 25
Further, simplify the equation, then we have
2x = 25
x = 25/2
x = 12.5
The value of the variable 'x' by simplifying the equation (x + 12) / (x + 5) = (x + 5) / x will be 12.5.
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what is 3x+12 can u guys help me solve this
Answers
Step-by-step explanation:
x=4. Step-by-step explanation: 3x=12. Divide each term in by 3x=12 by 3. 3x = 12. 3 3. Cancel the common factor of 3. Cancel the common factor. 3x = 12.
Find value of x 4(x+6)° (5x+11)°
Answers
Value of x = 13°
Hope it helps you...
The congruence relation is used to define __________ . finite groups greatest common divisor lowest common divisor residue classes
Answers
The congruence relation is used to define residue classes.
Congruence is an important idea in algebra that is often used to describe equivalence classes of integers modulo some integer n. A congruence relation on a set of integers is a binary relation that reflects equality modulo some integer n. Specifically, if a and b are two integers, then we say that a is congruent to b modulo n, or a ≡ b (mod n), if a - b is divisible by n.
The congruence relation is used to partition the set of integers into equivalence classes that are referred to as residue classes. Each residue class is represented by a single integer that is congruent to all the other integers in the class. In other words, a residue class is a collection of integers that have the same remainder when divided by n. There are exactly n residue classes modulo n, each of which is represented by a unique integer from 0 to n-1. Residue classes are used extensively in number theory and algebraic geometry, where they are used to study systems of equations and algebraic curves.
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