Multiplication and division properties of equality are stated below.
What is Multiplication and Division?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Multiplication property of equality states that if a real number has been multiplied with the expressions on both sides of the equation, then the expressions on both sides remains equal to each other.
That is, if x = y, then ax = ay, where a is a real number.
Division property of equality states that if a real number has been divided by the expressions on both sides of the equation, then the expressions on both sides remains equal to each other.
That is if x = y, then x/a = y/a.
Hence the multiplication and division property of equality has been stated.
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75 POINTS WILL GIVE BRAINLIEST
A zoologist recorded the speed of two cheetahs. Cheetah A ran 18 miles in 16 minutes. Cheetah B ran 54 miles in 50 minutes. Which statement is correct?
Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is greater than 54 over 50.
Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is less than 54 over 50.
Cheetah B has a higher ratio of miles per minute than Cheetah A because 18 over 16 is greater than 54 over 50.
Both cheetahs have the same ratio of miles per minute.
Answer: C. Cheetah B has a higher ratio of miles per minute than Cheetah A because 18 over 16 is greater than 54 over 50.
Step-by-step explanation:
Answer:
Step-by-step explanation:
C. Cheetah B has a higher ratio of miles per minute than Cheetah A because 18 over 16 is greater than 54 over 50.
Bob buys some apples for $16.50. If bob buys 4.4 pounds of apples, what is the price per pound
Answer: The price per pound of apples is $3.75.
Step-by-step explanation:
determine if the subset of consisting of vectors of the form , where is a subspace.
The subset of consisting of vectors of the form is indeed a subspace.
A subspace is a special type of set within a vector space that has the same properties as the larger vector space.
In order to determine if a subset of a vector space is a subspace, we must check if it satisfies certain conditions.
The first condition is that the subset must contain the zero vector.
The second condition is that the subset must be closed under addition.
The third condition is that the subset must be closed under scalar multiplication.
Now, let's apply these conditions to the subset of consisting of vectors of the form . It is clear that the zero vector satisfies this condition, as.
The subset is also closed under addition, as adding two vectors of the form and will result in a vector of the form.
Finally, the subset is closed under scalar multiplication, as multiplying a vector of the form by a scalar will result in a vector of the form .
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Question 3(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the following table represents a linear or nonlinear function?
x −2 −1 0 1 2
y −4 −2 0 2 4
The table represents a nonlinear function because there is not a constant rate of change in the input values.
The table represents a nonlinear function because there is not a constant rate of change in the output values.
The table represents a linear function because there is a constant rate of change in the input and output values.
The table represents a linear function because there is not a constant rate of change in the input and output values.
Question 4(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the following graph represents a linear or nonlinear function?
coordinate plane with a graph that passes through the points negative 3 comma 0 and negative 1 comma 4 and 1 comma 4 and 3 comma 0
The graph represents a nonlinear function because there is a constant rate of change.
The graph represents a nonlinear function because the rate of change is not constant.
The graph represents a linear function because there is a constant rate of change.
The graph represents a linear function because the rate of change is not constant.
Question 5(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the data in the following table represents a linear or nonlinear function?
x y
−4 4
−1 2.5
0 2
4 0
The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
The table represents a linear function because the graph shows a rate of change that is increasing.
The table represents a nonlinear function because the graph does not show a constant rate of change.
The table represents a linear function because the graph shows a constant rate of change.
Question 6(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the equation y = 3x2 represents a linear or nonlinear function?
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a linear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are on a straight line.
The equation represents a nonlinear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are not on a straight line.
Question 7(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which of the following tables represents a linear function?
x −2 −1 0 1 2
y 5 2 1 2 5
x −2 −1 0 1 2
y 5 3 1 −1 −3
x 3 3 0 3 3
y −2 −1 0 1 2
x 0 1 2 3 4
y 0 −1 2 −3 4
A graph of linear function is a straight line.
Linear function in a slope-intercept form: y = mx + b: Equation 3: y = 12x + 17.
2)
x|-1 | 0 | 1 | ? |
y| 4 | 7 |10| ? |
a slope: = (Change in y)/ (Change in x)
This means that (7-4)/(0--1) = 3/1 = 3
A slope intercept form is y-y₁ = m(x-x₁)
y-4 = 3[(x-(-1)]
Opening the brackets
y-4=3x+3
Rearrange
y=3x+7
substitute x = 2 to the equation (1):
This implies that y=3(2)+7
y=6+7 = 13
3) The slope is (4-7)/-5+2
S= 3/-3 = 1
If the slope is 1
Then the equation of the line is given as
y-y₁ = m(x-x₁)
y-7 = 1(x+2)
y-7=x+2
Collecting like terms we have
y=x+9
The conclusion: It's a linear function
It is a linear function because there is a constant rate of change in both the input and output values.
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On average shanth drinks 1/2 of a 6-ounce glass of water in 2/3 hour. How much water does she drink in an hour?.
On average Shanth drinks 4.5 ounces of water in an hour.
Multiplication is the process of taking one integer and multiplying it by a certain number of times. 5 multiplied by 4 is 5 + 5 + 5 + 5 = 20. We took the number 5 and multiplied it by four. This is why multiplication is often known as "times".
When we multiply a four-digit multiplied by a two-digit multiplier, we multiply the multiplied with the one place of the multiplier first, and then with the tens place of the multiplier.
As per the data given in the question,
As Shanth drinks 1/2 * 6 ounces = 3 ounces of water in 2/3 hour.
To find the average amount of water she drinks in an hour, we need to find the equivalent amount of water in an hour.
So, the equivalent amount of water in an hour will be
3 ounces * (1 hour / 2/3 hour)
= 3 ounces * (3/2)
= 4.5 ounces.
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How are diagonals and angle measures related in kites and trapezoids?
Answer: The diagonals of a kite are perpendicular to each other. Exactly one diagonal bisects the other.
Step-by-step explanation:
Determine whether the system of equations
is consistent or inconsistent and if it is
independent or dependent.
3x + 5y = -5
6y +15=-15x
Unresolved problems are referred to be inconsistent systems.
How to find the Equation?Find the solution to the system of equations by attempting to remove one of the variables to see whether there is a single solution, no solution, or never-ending options (If these two equations' lines all fall on the same line, then
By adding -2 to the first equation
-4x - 6y = -22
the second equation after that, adding it.
5x + 6y = 14
getting x = -8
Returning to either equation, plug in the following: the first one,
2(-8) + 3y = 11
-16 +3y = 11
3y = 27
y = 9
These two lines come together at one point since there is only one possible answer. They remain dependable.
The graphs of the equations yield two distinct lines, proving the independence of this system. Should the equations result in
In a same vein, they are interdependent.
They would have produced a constant equation, such as 0 = 0, if they had been the same line and had been solved for one variable.
Thus, (D) is still true because they are reliable and separate.
The Complete Question is :
Determine whether the system is consistent or inconsistent and whether the equations are dependent or independent.
2x + 3y = 11
5x + 6y = 14
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Zack's biology lab group is studying how quickly bacteria grow when exposed to sunlight. At the beginning of the experiment, Zack looked at the sample under a microscope and counted 5 bacteria. After the sample was exposed to sunlight for one hour, Zack looked again and counted 35 bacteria.
Answer: 5(7) over x
Step-by-step explanation:
carbon-14 has a half-life of 5,730 years. if a sample contains 80 mg originally, how much is left after 17,190 years?
Answer:
After 17,190 years, the amount of carbon-14 left would be approximately 5 mg.
The half-life of carbon-14 is 5,730 years, which means that every 5,730 years, half of the remaining carbon-14 decays. To calculate the amount of carbon-14 remaining after 17,190 years, we can use the formula:
A = A0 * (1/2)^(t/T)
where:
A0 is the initial amount (80 mg)
t is the time elapsed (17,190 years)
T is the half-life (5,730 years)
A = 80 * (1/2)^(17,190/5,730)
A = 80 * (1/2)^3
A = 80 * (1/8)
A = 10 mg * 1/2
A = 5 mg
what is the ones digit in the number 22006 ?
The ones digit number is 6 of the number 22006.
Now, According to the question:
In a two-digit number, the value of the digit depends on its position in that number. At one's place, the digit which is at the extreme right is known to be like one's, whereas the digit placed at the leftmost is known to be at ten's.
We have to find the ones digit in the number 22006
Now, Considering the number is 22006
So, the ones digit number is 6
It means the last digit is the ones digit number.
In the Indian numeral system, the place values of digits go in the sequence of Ones, Tens, Hundreds, Thousands, Ten Thousand, Lakhs, Ten Lakhs, Crores and so on.
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The circumference of a circular garden is 75.36 feet. What is the diameter of the garden?
Answer:
24.12 feet.
Step-by-step explanation:
The formula to find the diameter of a circle from its circumference is:
diameter = circumference / π
Plugging in the given values:
diameter = 75.36 feet / π
diameter = 75.36 / 3.14
diameter ≈ 24.12 feet
So, the diameter of the circular garden is approximately 24.12 feet.
Anissa is considering buying her first home. The house she is interested in buying is priced at $125,000. Anissa qualifies for a 30-year mortgage at 6%. What will her monthly mortgage payment be?
A) $629. 53
B) $697. 87
C) $805. 23
D) $749. 44
Anissa's monthly mortgage payment will be $749.44.
The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also gets additional income in terms of the recipient, known as interest, taking into account the time value of money.
In this case, we need to find the EMI - Equated Monthly Installments, Anissa has paid.
EMI = P*(1+r)^n / [(1+r)^n -1]
The Principal amount is P = $125,000.
The interest rate is, r = 6% p.a. = 0.005 per month.
The number of periods is, n = 30 × 12 = 360
The monthly payment is:
EMI = P*(1+r)^n / [(1+r)^n -1] = 3764.11/5.023 = 749.4381 = 749.44(approximately)
Thus, Anissa's monthly mortgage payment will be $749.44.
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PLEASE HELP ASAP THANK YOU, I'LL GIVE BRAINLIEST
Rebecca sells cupcakes for $3.50 each and charges customers an automatic $2 charge for a cupcake box as well. A customer walks in with $44 dollars. Represent the number of cupcakes that the customer can buy as an inequality.
Write the solution to the inequality in interval notation below.
Answer: The amount of cupcakes Rebecca can buy can be represented as: x < 45
Step-by-step explanation:
Consider two binary variables X and Y having the following joint probability distribution: XlY 1/3 1/3 1/3 Evaluate the following entropies: H(X), H(Y), H(XIY), H(YIX); H(X,Y), and the mutual informa- tion Im(X,Y).
The following entropies are evaluated as H(X, Y ) = ∑p(x, y) log p(x, y), H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y)) .
We have the following joint probability distribution:
X/Y 0 1
0 1/3 1/3
1 0 1/3
The entropy of X is given by
H(X) = −p log p − (1 − p) log(1 − p) = H(p)
The entropy does not depend on the values that the random variable takes (0 and 1 in this case), but only depends on the probability distribution p(x).
The joint entropy is given by
H(X, Y ) = ∑p(x, y) log p(x, y).
The joint entropy measures how much uncertainty there is in the two random variables X and Y
taken together.
The conditional entropy of X given Y is
H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y))
The conditional entropy is a measure of how much uncertainty remains about the random variable
X when we know the value of Y.
For two variables, the chain rule becomes:
H(X, Y ) = H(X|Y ) + H(Y ) = = H(Y |X) + H(X).
Thus, the following entropies are evaluated as H(X, Y ) = ∑p(x, y) log p(x, y), H(X|Y ) = ∑p(x, y) log p(x|y) = −E[ log(p(x|y)) .
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Let ff be the function given by f(x)=17x7−76x6+3x5−54x4−163x3+6x2f(x)=17x7−76x6+3x5−54x4−163x3+6x2. Which of the following statements is true?f′(−1.1)Answer A: f prime of negative 1.1, is less than f prime of 0.5, which is less than f prime of 1.4Af′(−1.1)Answer B: f prime of negative 1.1, is less than f prime of 1.4, which is less than f prime of 0.5Bf′(0.5)Answer C: f prime of 0.5, is less than f prime of 1.4, which is less than f prime of negative 1.1Cf′(1.4)
The correct statement is that f′(−1.1) is less than f′(0.5) which is less than f′(1.4).
The derivative of a function, denoted by f′(x), is the rate at which the function value changes with respect to a change in the independent variable. In this case, the function is given by f(x) = 17x7 − 76x6 + 3x5 − 54x4 − 163x3 + 6x2. So, the derivative of this function can be computed as follows:
f′(x) = 119x6 − 456x5 + 15x4 − 216x3 − 489x2 + 12x
Now, let's evaluate the derivative for x = −1.1, 0.5, and 1.4. Firstly, for x = −1.1,
f′(−1.1) = 119(−1.1)6 − 456(−1.1)5 + 15(−1.1)4 − 216(−1.1)3 − 489(−1.1)2 + 12(−1.1)
= −1709.085
Next, for x = 0.5,
f′(0.5) = 119(0.5)6 − 456(0.5)5 + 15(0.5)4 − 216(0.5)3 − 489(0.5)2 + 12(0.5)
= 112.75
Finally, for x = 1.4,
f′(1.4) = 119(1.4)6 − 456(1.4)5 + 15(1.4)4 − 216(1.4)3 − 489(1.4)2 + 12(1.4)
= −914.56
Therefore, the correct statement is that f′(−1.1) is less than f′(0.5) which is less than f′(1.4).
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The table below shows the cost of renting a bicycle at Ike's Bikes. Based on the rate in the table, what is the cost for 9 hours?
The cost of renting a bicycle for 9 hours is $72. The result is obtained by multiplying the rate and time duration.
How to calculate the cost of rent?The cost of rent related to time of rent. It could be cost per hour or cost per day.
The table is in the attachment to complete question.
We have the cost of renting a bicycle at Ike's Bikes.
$16 for 2 hours.$32 for 4 hours.$48 for 6 hours.Find the cost for 9 hours!
We take a sample of the data to find the rate.
The rate is
= $16/2 hours
= $8 per hour
Another sample will have the same result.
To rent for 9 hours, the cost will be
= $8 × 9
= $72
Hence, to rent a bicycle for 9 hours, it will cost $72.
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A cell phone plan costs $19.80 per mouth for 500 minutes of talk time. It costs an additional $0.09 per minute for each minute over 500 minutes. To get e-mail access, it costs 20% of the price for 500 minutes of talk time. Your bill, which includes e-mail, is the same each mouth for 7 mouths. The total cost for all 7 mouths is $212.31. Write and solve an equation to find the number of minutes of talk time you use each mouth.
So you use 73.02 minutes of talk time each month.
What is a cell phone?Cell phone is a portable electronic device that allows you to make calls, send messages, and perform various tasks such as browsing the internet.
Let x be the number of minutes of talk time you use each month.
The cost for the talk time each month is 19.80 + 0.09(x - 500), and the cost for e-mail is 0.2 * 19.80 = 3.96.
So, the total cost each month is 19.80 + 0.09(x - 500) + 3.96 = 23.76 + 0.09x - 46.04.
The total cost for 7 months is 7 * (23.76 + 0.09x - 46.04) = 166.32 + 0.63x.
We want to find the value of x that makes the total cost equal to $212.31, so we write:
166.32 + 0.63x = 212.31
Solving for x, we have:
0.63x = 45.99
x = 73.02
So you use 73.02 minutes of talk time each month
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the region bounded by the graphs of y = in x, y = 0, and x = e is revolved about the y-axis. find the volume of the resulting solid.
The volume of the resulting solid as V = 2π(0)(in e)e = 2πe^2in. can be found by using the method of cylindrical shells.
This method involves calculating the volume of a series of infinitesimally thin cylindrical shells that, when added together, form the solid of interest. The formula for the volume of a single cylindrical shell is V = 2πrhΔx, where r is the radius, h is the height, and Δx is the change in x.
To find the volume of the solid, we must first find the integral of the area of the region bounded by the graphs of y = in x, y = 0, and x = e. This integral can be found by integrating the equation y = in x from 0 to e, which gives us the area of the region. Then, we can use the formula V = 2πrhΔx to find the volume of the solid by substituting the radius of the shell (the radius of the y-axis) for r, the area of the region for h, and the change in x (e - 0) for Δx. This gives us the final volume of the solid as V = 2π(0)(in e)e = 2πe^2in.
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Natalie has $300 in a savings account that earns 15% interest per year. How much interest will she earn in 4 years?
Answer: 480
Step-by-step explanation:
300 In Account
15% of 300 = 45
45x4= 180
300+180= 480
Answer:
If Natalie had simple interest: $180
If Natalie had compound interest: $224.70
Step-by-step explanation:
Simple Interest.
P(1 +rt)
300(1 + 0.15 x 4) = 480
480 - 300 = 180
Compound interest.
P(1 + r/n)^nt
300(1 + 0.15)^4 = 524.70
524.70 - 300 = 224.70
five people are passing a ball amongst themselves. the ball starts with alonzo. each person who has the ball passes it onto someone else. on the eighth pass, the ball returns to alonzo. find the number of possible sequences of passes.
The number of possible sequences of passes is 252.
When Alonzo has the ball for the first time, he has 4 people to pass it to. Then, for the next seven passes, each person has 3 people to pass it to. So, the number of sequences can be calculated as 4 x 3^7 = 252. This calculation is based on the principle of counting the number of combinations, where each person has a fixed number of options for passing the ball and the options change as the passes go on.
In this case, with 5 people, the total number of possible sequences of passes will be a function of the number of options available for each pass.
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Explain how to ue a table to write an equation that repreent the relationhip in the table
A table can be used to write an equation that represents the relationship in the table by using the values in the table to determine the coefficients of the equation.
Here's how you can use a table to write an equation:
1. Identify the dependent and independent variables in the table. The dependent variable is the value that depends on the independent variable.
2. Choose one of the variables as the dependent variable and write the equation in terms of the dependent variable.
3. Use the values in the table to find the coefficients of the equation. For example, if the independent variable is x and the dependent variable is y, you can use the values in the first column for x and the values in the second column for y to find the coefficients.
4. Write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The slope represents the change in y for a unit change in x, and the y-intercept represents the value of y when x is 0.
5. Substitute the coefficients from step 3 into the equation from step 4.
6. Check your equation by plugging in the values from the table and verifying that they match the corresponding values in the dependent variable column.
By using a table to write an equation, you can easily find the mathematical relationship between the variables and make predictions for new values of the independent variable.
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A table can be used to write an equation that represents the relationship in the table by using the values in the table to determine the coefficients of the equation.
Here's how you can use a table to write an equation:
1. Identify the dependent and independent variables in the table. The dependent variable is the value that depends on the independent variable.
2. Choose one of the variables as the dependent variable and write the equation in terms of the dependent variable.
3. Use the values in the table to find the coefficients of the equation. For example, if the independent variable is x and the dependent variable is y, you can use the values in the first column for x and the values in the second column for y to find the coefficients.
4. Write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The slope represents the change in y for a unit change in x, and the y-intercept represents the value of y when x is 0.
5. Substitute the coefficients from step 3 into the equation from step 4.
6. Check your equation by plugging in the values from the table and verifying that they match the corresponding values in the dependent variable column.
By using a table to write an equation, you can easily find the mathematical relationship between the variables and make predictions for new values of the independent variable.
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Balance of payments For each transaction in the table, indicate the current account component, cash flow position, and type of entry on the balance-of-payments account. US Cash Flow Position Entry on US Balance-of- Payments Account Component Transaction Consumers in Japan purchase baseball jerseys from their favorite US baseball teams. The jerseys are produced in the United States. An American investor owns stock in a Spanish company and receives a dividend payment from that company. The United States government provides foreign aid to another country after a natural disaster. Consider the case where a company in Spain purchases stock in a US-based company. This component of the financial account is known as 7. Factors affecting international capital flows A decrease in the tax rate on dividends in a country is likely to decrease portfolio investment in that country. An increase in the tax rate on corporate earnings in a country is likely to direct foreign investment (DFI) in that country.
For each transaction in the table, the current account component, cash flow position, and type of entry on the balance-of-payments account are as follows:
1. Consumers in Japan purchasing baseball jerseys from their favorite US baseball teams: Current account component: Imports; Cash flow position: Outflow of funds; Entry on US balance-of-payments account: Debit.
2. An American-based subsidiary remitting earnings to the parent company in Canada: Current account component: Investment income; Cash flow position: Outflow of funds; Entry on US balance-of-payments account: Debit.
3. France providing funds to the United States as a gift to be used for the construction of a large monument: Current account component: Gifts; Cash flow position: Outflow of funds; Entry on US balance-of-payments account: Debit.
4. A US-based company purchasing stock in a French company: This component of the financial account is known as Foreign Direct Investment (FDI). It is defined as an investment made to acquire lasting interest in enterprises operating outside of the economy of the investor.
With regards to the balance of payments, FDI is considered a capital account item, so there will be no entry on the balance of payments account. This is because FDI does not involve any money entering or leaving the economy.
In conclusion, when a transaction is made, it is important to be aware of the current account component, cash flow position, and type of entry on the balance-of-payments account that is associated with it.
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Complete question is shown in figure.
A school is constructing a rectangular play area against an exterior wall of the
school building. It uses 120 feet of fencing material to enclose three sides of the
play area. Write an equation to represent A, the area in square feet, as a function
of w, the width in feet. *
An equation to represent A, the area in square feet, as a function of w, the width in feet is A = 120W -2W²
According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.
Substitute into the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
We know that the area of a rectangle is l × w
When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000
When w = 20, length = 120 - 40 = 80, area = 80 x 20 = 1600
When w = 40, length = 120 - 80 = 40. area = 40 x 40 = 1600.
So, the completed table will be
Width Length Area
10 100 1000
20 80 1600
40 40 1600
w 120 - 2w (120 - 2w) w
In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have;
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
A = 120W -2W²
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Enter the correct answer in the box.
Write the inverse of the cube root function used to represent the situation in
Model 2:
"Jack owns a company that manufactures a product that we’ll call product A. After producing and selling x units of product A, the profit his company made is represented by the cube root function [tex]f (x) = \sqrt[3]{(x+4)^{2} }[/tex]"
The inverse of the cube root function used to act for the situation in model is f⁻¹(x) = √x³ - 4
Inverse of the cube root function f(x)
f(x) = ∛ (x + 4) ²
To find the inverse function, let f(x) = y
So, y = ∛ (x + 4) ²
Taking the cube of both sides, we have
y³ = [∛ (x + 4) ²] ³
y³ = (x + 4) ²
Taking square root of both sides, we have
√y³ = √ (x + 4) ²
√y³ = (x + 4)
Subtracting 4 from both sides, we have
√y³ - 4 = x + 4 - 4
√y³ - 4 = x
change y with x, we have
√x³ - 4 = y
Replacing y with f⁻¹(x), we have
f⁻¹(x) = √x³ - 4
So, the inverse of the cube root function used to represent the situation in model is f⁻¹(x) = √x³ - 4
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Sandy ha 26 meter of brown wire and 20 meter of red wire. She need to cut both wire into maller piece o that all of the maller piece are the ame length and there i no wire leftover. The length of each piece mut be a whole number of meter. What i the longet he can make each maller piece of wire? Give your anwer in meter
Each malleable piece of wire he can produce has a length of 2 metres.
How to calculate length?When given an area A and a width w, the length w is calculated using the formula h = A/w. Its length can be calculated using h = P/²w if you know its perimeter (P) and width (W). Its length is h = (d²w²) if you have a diagonal d and a width w.The definition of length is the distance or measurement between two points. In other terms, the largest two or highest three dimensions of a geometric shape or item. As an illustration, the length and width of a rectangle are its dimensions.The number of digits in the base-numerical for, as determined by the formula, determines a number's base length. A vector's magnitude (length), which is a scalar and determined by the square root of the sum of the squares of its components, is called a scalar vector. This is an exception to the general rule that the Euclidean distance in n-space between any two places is equal to the square root of the sum of the squares of the elemental differences.Prime factorization
26 = 2 × 13
20 = 2² × 5
HCF = 2
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Rectangle PQRS is dilated by a scale factor of 5 to form rectangle '. Side QR measures 5. What is the measure of Q'R'?
The length of Q'R' is 5 * 5 = 25.
Dilating Rectangle MeasurementThe steps to find the measure of Q'R' are:
Start with the length of QR, which is given as 5.Apply the dilation factor of 5 to find the length of Q'R'.The length of Q'R' is obtained by multiplying the length of QR by the scale factor: 5 * 5 = 25.So, the measure of Q'R' is 25.
This method is applicable for finding the length or width of a dilated figure when the original length or width and the scale factor are given. The formula to find the length (or width) of a dilated figure is: length (or width) of dilated figure = scale factor * length (or width) of original figure. The formula for finding the length or width of a dilated figure is a basic concept in geometry and is widely used in solving related problems.
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course 3 chapter 5 triangles and the pythagorean theorem answer key
In the given right triangle, the perimeter is 12 in.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the length of the two legs (a and b). Hence,
c^2 = a^2 + b^2
In the given triangle,
c = x in
a = 3 in
b = 4 in
Hence,
x^2 = 3^2 + 4^2
x^2 = 9 + 16
x^2 = 25
x = √25
x = 5
The perimeter of a geometric shape is the sum of all its side. Hence,
Perimeter = 3 + 4 + 5 = 12 in
Note: The question is incomplete. The complete question probability is: Using the Pythagorean theorem, find the perimeter of the triangle.
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let 4pqr be the equilateral triangle illustrated below. a unit vector in the direction of −→pq is 〈1,0〉.
Unit vectors for equilateral triangle sides: pq is 〈1,0〉, qp is 〈-0.5,√3/2〉, rq is 〈-0.5,-√3/2〉. Sum is zero vector.
a) The equilateral triangle has rotational symmetry of 120 degrees, so the unit vectors in the direction of each of the sides can be obtained by rotating the unit vector in the direction of pq by 120 degrees in the counter-clockwise direction.
Using 2D rotation matrix, the unit vector in the direction of qp can be obtained as 〈cos(120), sin(120)〉 = 〈-0.5, √3/2〉.
Similarly, the unit vector in the direction of rq can be obtained as 〈cos(240), sin(240)〉 = 〈-0.5, -√3/2〉.
b) To verify that the three unit vectors sum to the zero vector, we add up the vectors:
〈1,0〉 + 〈-0.5, √3/2〉 + 〈-0.5, -√3/2〉 = 〈0,0〉.
Thus, the three unit vectors sum to the zero vector as required.
Complete Question:
let 4pqr be the equilateral triangle illustrated below. a unit vector in the direction of −→pq is 〈1,0〉.
(a) Find unit vectors in the directions of and Qi)
(b) Verify that the three unit vectors you found in part (a) sum to the zero vector.
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for the matrices a = −3 2 1 4 and b = 5 1 0 −2 in m2,2, determine whether the given matrix is a linear combination of a and b. −19 4 3 16
The given matrix is non linear matrix combination of a and b matrix.
a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
An equation in which the maximum degree of a term is 2 or more than two is called a nonlinear equation.
Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix. Matrices have wide applications in engineering, physics, economics, and statistics as well as in various branches of mathematics.
Given that,
a = [tex]\left[\begin{array}{ccc}-3&2\\1&4\\\end{array}\right][/tex]
b = [tex]\left[\begin{array}{ccc}5&1\\0&-2\\\end{array}\right][/tex]
The given matrix is a linear combination of a and b
a - b = [tex]\left[\begin{array}{ccc}-3&2\\1&4\\\end{array}\right] - \left[\begin{array}{ccc}5&1\\0&-2\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
a - b = [tex]\left[\begin{array}{ccc}-3-5&2-1\\1-1&4-0\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
Therefore,
The given matrix is non linear matrix combination of a and b matrix.
a - b = [tex]\left[\begin{array}{ccc}-8&1\\0&4\\\end{array}\right][/tex] ≠ [tex]\left[\begin{array}{ccc}-19&4\\3&16\\\end{array}\right][/tex]
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What is the equation of the line that passes through the point (-1, 1) and has a
slope of -1?
The equation of the line that passes through the point (-1, 1) and has a slope of -1 is y = -x.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-1, 1), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -1(x - (-1))
y - 1 = -1(x + 1)
y = -x -1 + 1
y = -x.
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The equation of the line is y = -x
How to determine the equation of the lineThe general formula for the equation of a line is expressed with the equation;
y = mx + c
Given that the parameters are;
y is a point on the y-axis of the linem is the slope of the line of graphx is a point on the x-axis of the line of graphc is the intercept of the line on the y-axisFrom the information given, we have that;
slope, m =-1
The points are (-1, 1)
Now, let's substitute the values
1 = -1(-1) + c
expand the bracket
1 = 1 + c
collect like terms
c = 0
The equation of the line is y = -x
Hence, the equation is y = -x
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