Answer:
Based on the data in the table, we can set up a system of equations to represent the relationship between the number of imports (f(x)) and the number of exports (g(x)):
2x + 3y = z (Equation 1)
4x + 4y = z (Equation 2)
6x + 5y = z (Equation 3)
8x + 6y = z (Equation 4)
In this system, x represents the month number (January = 1, February = 2, etc.), y represents the number of exports, and z represents the total trade (exports plus imports). Each equation represents the data for a specific month.
To solve the system, we can use any method of solving systems of linear equations, such as substitution or elimination. However, we can also observe a pattern in the coefficients of the variables:
2 3 5 8
4 4 6 8
We can see that the coefficients of the x-term (the month number) increase by 2 each time, and the coefficients of the y-term (the number of exports) increase by 1 each time. This suggests that the equation for the nth month (where n is an integer between 1 and 4) can be expressed as:
2n + (n+2)y = z
We can test this by plugging in the values of n and y from any of the given months and verifying that the resulting value of z matches the actual value for that month. For example, if we use the data for March (n=3, y=5), we get:
2(3) + (3+2)(5) = z
6 + 25 = 31
And we can see that the actual value of z for March is indeed 31, which confirms that our equation works.
Using this equation, we can find the solution to the system for any given month by plugging in the appropriate values for n and y. For example, to find the total trade (z) for May (which would correspond to n=5), we can plug in n=5 and solve for z:
2(5) + (5+2)y = z
10 + 7y = z
To find the number of exports for May, we can plug in n=5 and solve for y:
2(5) + (5+2)y = z
10 + 7y = z
10 + 7y = 10 + 2y + 3
5y = -3
y = -3/5
However, since exports cannot be negative, this solution is not valid. This suggests that the data given in the table only applies to the months of January through April, and we cannot use this equation to find the solution for any month beyond April.
In summary, the system of equations represents the relationship between the number of imports and exports for each month from January to April. By observing the pattern in the coefficients of the equations, we can derive a general equation that can be used to find the total trade for any month between January and April. However, we cannot use this equation to find the solution for any month beyond April, as there is not enough data to determine the number of imports and exports for those months.
a line segment is drawn between (4,8) and (8,5). find it’s gradient.
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{4}}} \implies \cfrac{ -3 }{ 4 } \implies - \cfrac{3 }{ 4 }[/tex]
In 2002, the population of a state was 6.7 million people and was growing at a rate of about 0.32% per year. At this growth rate, the function f (x) = 6.7(1.0032)x gives the population, in millions x years after 2002. Using this model, find the year when the population reaches 7 million people. Round your answer to the nearest whole number.
The population will reach 7 million people approximately 21.67 years after 2002. Rounding to the nearest whole number, this corresponds to the year 2024.
The year when the population reaches 7 million can be determined using the population model given, f(x) = 6.7(1.0032)x, where x is the number of years following 2002.
When we solve for x while setting f(x) equal to 7, we obtain:
[tex]7 = 6.7(1.0032)^x[/tex]
By multiplying both sides by 6.7, we obtain:
[tex]1.04478 = 1.0032^x[/tex]
When we take the natural logarithm of both sides, we obtain:
ln(1.04478) = x * ln (1.0032)
After finding x, we obtain:
x = ln(1.04478) / ln (1.0032)
x ≈ 21.67
Hence, approximately 21.67 years after 2002, the population will reach 7 million. This corresponds to the year 2024 when rounded to the next whole number.
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12. The amount of money in a savings account earning yearly interest is represented by the
expression 750(1+0.012), where t is in years since the account was opened. What does
(1+0.012) represent?
A
B
C
D
The account earns $0.012 in yearly interest.
The account earns $1.20 in yearly interest.
The account earns 1.2% in yearly interest.
The account earns 12% in yearly interest.
Answer:
C. The account earns 1.2% in yearly interest.
Step-by-step explanation:
The expression 750(1+0.012) represents the amount of money in a savings account earning yearly interest after t years, where t is the number of years since the account was opened.
The expression (1+0.012) represents the interest rate as a decimal. The value 0.012 represents 1.2% in decimal form, which is the yearly interest rate earned by the account.
Therefore, (1+0.012) represents the account's yearly interest rate as a decimal, which is 1.2%.
Lube used to 9 cups of milk for a pancake recipe to drink another 394 cups of milk how about about how much milk did Luke is using on
To find the total amount of milk used, we simply add the amount of milk used for the pancake recipe and the amount used for drinking. So we add 9 cups and 394 cups together, giving us a total of 403 cups of milk.
We can calculate the total amount of milk that Luke used for the pancake recipe and the additional amount he used for drinking.
For the pancake recipe, Luke used 9 cups of milk.
For drinking, Luke used an additional 394 cups of milk.
Total amount of milk used = Milk used for pancake recipe + Milk used for drinking
= 9 cups + 394 cups
= 403 cups of milk.
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The complete question is:
Lube used to 9 cups of milk for a pancake recipe to drink another 394 cups of milk how about about how much milk did Luke is using on the recipe?
Mr stoves is investing $1500 on a bank account that would give him 3. 7% compounded monthly. What would be his final balance after 10 years?
Mr stove's final balance after 10 years if he invested 1500 on a bank account that would give him 3. 7% compounded monthly is $2,170.37
What would be his final balance after 10 years?A = P(1 + r/n)^nt
Where
P = $1500
r = 3.7% = 0.037
n = monthly = 12
t = 10 years
So,
A = P(1 + r/n)^nt
A = 1,500.00(1 + 0.037/12)^(12×10)
A = 1,500.00(1 + 0.0030833333333333)¹²⁰
A = $2,170.37
Ultimately, Mr stove will have $2,170.37 as his balance after 10 years.
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Calculate the perimeter of the trapezoid in millimeters
Answer:
135 mm
Step-by-step explanation:
The perimeter is found by adding all sides together. Since the answer is to be in millimeters, two side lengths must be converted.
1 centimeter = 10 millimeters
1.5 x 10 = 15 mm
6 x 10 = 60 mm
Now, add all sides together:
60 + 15 + 20 + 40 = 75 + 60 = 135 mm
Please help me with this math problem!! Will give brainliest!! :)
According to a recent survey of students about the juice they preferred, 20% of the students preferred cranberry juice, 40% preferred orange juice, 20% preferred grapefruit juice, and the remaining students preferred tomato juice. If each student preferred only 1 juice and 250 students preferred tomato juice, how many students were surveyed?
Answer: 1250 students
Step-by-step explanation:
20% + 40% + 20% = 80%
100% - 80% = 20%
If 250 is 20%, then it's just 250 x 5 = 1250
100 points hurry and mark brainly
Jennifer bought three of the same shirt and paid $63 after the 30% discount. What was the original price of each shirt? Show your work or explain in words how did you get the answer.
The graph below shows the variation in the average temperature of Earths surface from 1950-2000, according to one source
The years 1960–1965 saw the greatest change in temperature variation per unit of time.
What is Slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The graph for average temperature variation v/s time is given.
To find during which year maximum temperature variation with time:
We have to find the year with maximum magnitude of slope |m|.
Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}\\[/tex]
Consider m for year 1950-1955:
m = 0 [line parallel to x-axis]
Consider m for year 1955-1960:
[tex]\frac{-0.05-0}{1955-1960}\\\\= 0.01[/tex]
Consider m for year 1960-1965:
[tex]\frac{-0.15-0}{1965-1960}\\\\= -0.03[/tex]
Consider m for year 1965-1970:
m = 0.01 {same as of 1955-1960}
Consider m for year 1970-1975:
m = 0 [line parallel to x-axis]
Consider m for year 1975-2000:
[tex]\frac{0.4-(-0.1)}{2000-1975}\\\\= 0.02\\[/tex]
|m| is maximum for year 1960-1965
Hence, the temperature variation changed the most per unit time in the year 1960-65.
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we can descirbe 3x-2 as an expression
Answer: In each of the terms 3x 2 and 7x, x is a variable, and in both terms, we are multiplying a number by the variable. In the first term, 3x 2, 3 is being multiplied by the variable, so 3 is a coefficient. In the second term, 7x, 7 is being multiplied by the variable, so 7 is a coefficient.
Step-by-step explanation:
New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $205 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $54. A. What is the probability that a hotel room costs $227 or more per night (to 4 decimals)?
The probability that a hotel room costs $227 or more per night in New York City is 0.3406.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Lets standardize the value of $227 per night using the formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean of the distribution, and σ is the standard deviation of the distribution. Substituting the given values, we get:
z = (227 - 205) / 54
z = 0.4074
We need to find the probability that a hotel room costs $227 or more per night, which is equivalent to finding the probability that a standardized value is greater than or equal to 0.4074.
Using a standard normal table, we find:
P(Z ≥ 0.4074) = 1 - P(Z < 0.4074)
P(Z ≥ 0.4074) = 1 - 0.6594
P(Z ≥ 0.4074) = 0.3406
Therefore, the probability that a hotel room costs $227 or more per night in New York City is approximately 0.3406.
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The probability that a hotel room costs $227 or more per night is 0.3446
What is probability distribution?Probability distribution yields the possible outcomes for any random event. It is also defined based on the underlying sample space as a set of possible outcomes of any random experiment. These settings could be a set of real numbers or a set of vectors or a set of any entities. It is a part of probability and statistics.
Random experiments are defined as the result of an experiment, whose outcome cannot be predicted. Suppose, if we toss a coin, we cannot predict, what outcome it will appear either it will come as Head or as Tail. The possible result of a random experiment is called an outcome. And the set of outcomes is called a sample point. With the help of these experiments or events, we can always create a probability pattern table in terms of variables and probabilities.
GIven,
The mean hotel room rate ( [tex]\mu[/tex]) is $205 per night and standard deviation ([tex]\sigma[/tex]) of $54. A.
p( x > 225 )
we can't this to standard normal using [tex]z =\frac{X- \mu}{\sigma}[/tex]
[tex]z=\frac{227-205}{54} \approx0.4074[/tex]
p (z > 0.4074 ) = area to the right at 0.4074
p( x > 225 ) = p (z > 0.4074 ) = 1 - p (z < 0.4074)
= 1 - 0.6554 (from z table)
= 0.3446
Hence, probability that a hotel room costs $227 or more per night (to 4 decimals) 0.3446
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help plssssssssssssssssssssssssssss
Answer: First Picture 100:60 = The answer is A. 5:3 | The Second Picture K/12=8/24 the answer is A. k=4 | Third Picture is A. 4 | Fourth Picture answer is B. 4 teachers for every 64 students | And Final Picture answer is D. 9.33 miles per hour, Wendy Was Faster. | Hope this helps out today!!
Step-by-step explanation: Its simple math its just either x2 or what's it divided off
Does anyone know the answer?
Answer:
33.7°
Step-by-step explanation:
the direction angle is calculated as
tanΘ = [tex]\frac{y}{x}[/tex] ( Θ is the direction angle ) , then
tanΘ = [tex]\frac{-4}{-6}[/tex] = [tex]\frac{2}{3}[/tex]
Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{2}{3}[/tex] ) ≈ 33.7° ( to the nearest tenth )
7. Higher Order Thinking Point N has
coordinates (3, 4). On a quiz yesterday, Ari
incorrectly claimed that if you rotate N 180°
about the origin, the coordinates of N' are
(-4, 3). What are the correct coordinates
for N'? What was Ari's likely error?
The correct coordinates of N' is (-3, -4).
What is Rotation:Rotation of coordinates involves changing the orientation of a point or object in a plane about a fixed point called the center of rotation.
This process can be accomplished by applying a set of transformation rules to the original coordinates of the object.
When a point (x, y) rotated about the origin at 180° then the coordinates resultant point are (-x, -y).
Here we have
Point N has coordinates (3, 4)
Given that the point N is rotated about 180°
As we know when the point (x, y) rotated about the origin at 180° then the resultant point is (-x, -y)
Here (3, 4) is rotated about 180°
The resultant point N' is (-3, -4)
Therefore,
The correct coordinates of N' is (-3, -4).
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PLEASE HELP :(
Isabella is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $20, and her grandmother has pledged $2 per kilometer. If Isabella walks a certain distance, the two donors will end up owing the same amount. What is that distance?
Write a system of equations, graph them.
Answer:
Step-by-step explanation:
25 becuase 3 times 52 is that plus 32 is 73 and isabella with be rivher then ever than muh hahaha
In a group of 100 students, 60 liked mathematics and 50 liked science.If 10 did not like any of the subjects , by using Venn-diagram, find the numbers of students who like both the subjects
Answer:
Below
Step-by-step explanation:
See Venn diagram below :
If matrix A = [-4,k; -7,2]
for what value of k does the matrix have one eigenvalue of
multiplicity 2?
To find the value of k for which the matrix A has one eigenvalue of multiplicity 2, we can use the characteristic equation of the matrix. The characteristic equation is det(A-λI)=0. For a given matrix, this equation will yield a polynomial equation of degree equal to the dimension of the matrix.
In this case, the equation is (λ+4)(λ-2) = 0. Solving this equation gives us two distinct eigenvalues of λ= -4 and λ=2. This means that for any value of k, the matrix A will have two distinct eigenvalues, and thus cannot have one eigenvalue of multiplicity 2. Therefore, the matrix A cannot have one eigenvalue of multiplicity 2 no matter what value of k is used.
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Watch help video Use synthetic division to find the result when x^(3)-6x^(2)+13x is divided by x-1. If there is a remainder, express the result in the
The result is x^(2)-7x+20 with a remainder of -20. So the final answer is x^(2)-7x+20-20/(x-1).
To find the result of the division using synthetic division, we need to follow these steps:
Write the coefficients of the dividend in a horizontal line, leaving spaces for the divisor and the result. In this case, the coefficients are 1, -6, and 13.Write the constant term of the divisor in the first space. In this case, the constant term is -1.Bring down the first coefficient to the result line.Multiply the first term of the result by the divisor and write the product in the next space on the dividend line.Add the two numbers in the next column and write the sum on the result line.Repeat steps 4 and 5 until all the coefficients have been used.The last number on the result line is the remainder. If there is a remainder, express the result in the form of a fraction with the remainder as the numerator and the divisor as the denominator.The result is x^(2)-7x+20 with a remainder of -20. So the final answer is x^(2)-7x+20-20/(x-1).
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Power of test related to
A type 1 error
B type 2 error
C type 1 and type 2
D non of sbovr
Answer:
B
Step-by-step explanation:
The correct answer is Option C - Type 1 and Type 2. The power of a test is the probability of rejecting the null hypothesis when it is false; in other words, it is the probability of avoiding a type II error.
The power may also be thought of as the likelihood that a particular study will detect a deviation from the null hypothesis given that one exists. A Type 1 error occurs when a hypothesis test results in rejecting a true null hypothesis, and a Type 2 error occurs when a hypothesis test fails to reject a false null hypothesis.
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Solve the system of equations using a calculator and a
matrix
1. 3x-6y=12, 2x-4y=8
The solution to the system of equations using a calculator and a matrix (3x-6y=12, 2x-4y=8) is x = 12 and y = 8.
To solve the system of equations using a calculator and a matrix, you will need to follow these steps:
1. Convert the system of equations into a matrix. In this case, the matrix will be:
```
| 3 -6 | | 12 |
| 2 -4 | | 8 |
```
2. Use your calculator to find the inverse of the coefficient matrix (the matrix on the left). The inverse of the coefficient matrix is:
```
| -2/3 3/2 |
| -1/3 3/4 |
```
3. Multiply the inverse of the coefficient matrix by the constant matrix (the matrix on the right) to find the solution. The solution will be:
```
| -2/3 3/2 | | 12 | = | 12 |
| -1/3 3/4 | | 8 | | 8 |
```
4. Simplify the solution to get the values of x and y. The solution will be:
```
x = 12
y = 8
```
Therefore, the solution to the system of equations is x = 12 and y = 8.
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At a club fundraiser a group of students washed 60 cars in one weekend the rest of the weekend they washed
75 cars what was the percent of increase in the number of cars washed
given is the area of the region which is bounded by y = x^3, y =
8, and x = 0. find the volume generated when it is revolved about
the y-axis.
A. 9/8 pi
B. 96/5 pi
C. 45/7 pi
D. 34/7 pi
Given y = x³, y = 8, and x = 0, we need to find the volume generated when it is revolved about the y-axis.To solve this problem, we will use the washer method. We will draw the region to better understand it. Area that is bounded by y = x³, y = 8, and x = 0, volume comes as 45/7 pi. The correct answer is option C
Now, let's draw the region we want to rotate around the y-axis. Below is the graph of the region after shading it. region which is bounded by , y = 8, and x = 0. We can see from the graph above that the region is between y = x³ and y = 8.
Thus the radius of our washer would be : R = 8 - x³ The height of the washer is dx (infinitesimal thickness). The width of the washer is given. We can now write the integral for the volume generated by the region V. Thus the volume generated when it is revolved about the y-axis is 45/7 pi. Therefore, the correct option is C.
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Give an example of a linear function that has a minimum value but no maximum value. Specify the domain and whether the function is increasing or decreasing.
Select all linear functions with a minimum value but no maximum value.
The decreasing function f(x)=10−3x over the domain x≤9 has a minimum value but no maximum value .
The decreasing function f(x)=5x−1 over the domain x≥−7 has a minimum value but no maximum value.
The increasing function f(x)=2x+5 over the domain x≥ 5has a minimum value but no maximum value .
The increasing function f(x)=7−2x over the domain x≥10 has a minimum value but no maximum value .
The two linear functions that have a minimum value but no maximum value are:
f(x) = 10 - 3x over the domain x ≤ 9
f(x) = 5x - 1 over the domain x ≥ -7
Determining linear functions that have minimum value but no maximum valueFrom the question, we are to determine the linear function that have minimum value but no maximum value
The decreasing function f(x) = 10 - 3x over the domain x ≤ 9 has a minimum value but no maximum value.
Domain: x ≤ 9
This function is decreasing since the slope is negative.
The minimum value occurs at x = 9, where f(9) = 10 - 3(9) = -17.
Since the slope is negative, the function continues to decrease without bound as x approaches negative infinity.
The decreasing function f(x) = 5x - 1 over the domain x ≥ -7 has a minimum value but no maximum value.
Domain: x ≥ -7
This function is increasing since the slope is positive.
The minimum value occurs at x = -7, where f(-7) = 5(-7) - 1 = -36.
Since the slope is positive, the function continues to increase without bound as x approaches positive infinity.
Hence, the functions are:
f(x) = 10 - 3x over the domain x ≤ 9
f(x) = 5x - 1 over the domain x ≥ -7
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x^2-8x+5=25 solve by completeing the square
We have the following response after answering the given question: As a result, the following are the answers to the equation: [tex]x = 4 + 6 = 10[/tex] and [tex]x = 4 - 6 = -2[/tex]
What is equation?In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.
We may use the completing the square method to solve the equation x2 - 8x + 5 = 25 by doing the following steps:
[tex]x^2 - 8x + 5 - 25 = 0\\x^2 - 8x - 20 = 0\\(-8/2)^2 = c\\16 = c\\x^2 - 8x + 16 - 16 - 20 = 0\\(x - 4)^2 - 36 = 0\\(x - 4)^2 = 36\\x - 4 = +6\\x = 4 + 6[/tex]
As a result, the following are the answers to the equation:
[tex]x = 4 + 6 = 10[/tex]
[tex]x = 4 - 6 = -2[/tex]
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5. (3 marks) Determine the area of the parallelogram formed by the following vectors:
u = (1,2,2) , v = (4.4.0)
The area of the parallelogram formed by the vectors u and v is 12.
The area of a parallelogram formed by two vectors u and v can be determined by finding the cross product of the two vectors and then taking the magnitude of the resulting vector.
First, we need to find the cross product of u and v:
u × v = [(2)(0) - (2)(4), (2)(4) - (1)(0), (1)(4) - (2)(4)] = [-8, 8, -4]
Next, we need to find the magnitude of the resulting vector:
|u × v| = √((-8)² + (8)² + (-4)²) = √(64 + 64 + 16) = √144 = 12
Therefore, the area of the parallelogram formed by the vectors u and v is 12.
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Jeff and Ella use a payment plan to buy new furniture. Jeff writes the equation y = –108x + 2240 to represent
the amount owed, y, after x payments. The graph shows how much Ella owes after each payment.
Whose furniture costs more, Jeff's or Ella's? Explain
Therefore, after 10 payments, Jeff owes $1160.
Since $1160 is less than $2200, we can conclude that Jeff's furniture costs less than Ella's.
What roles do equations play?A mathematical equation, such as 6 x 4 = 12 x 2, can be used to compare two amounts or values. a significant noun. An equation is employed when it's required to integrate two or more elements in order to understand or fully explain a situation.
To determine whose furniture costs more, we need to compare the amounts owed by Jeff and Ella for the same number of payments.
Jeff's equation is y = -108x + 2240, which gives the amount owed after x payments.
Ella's graph does not have an equation provided, but we can see that after 10 payments, she owes approximately $2200.
To compare the amounts owed after 10 payments, we can substitute x = 10 into Jeff's equation:
y = -108(10) + 2240
y = -1080 + 2240
y = 1160
Therefore, after 10 payments, Jeff owes $1160.
Since $1160 is less than $2200, we can conclude that Jeff's furniture costs less than Ella's.
Answer: Ella's furniture costs more than Jeff's.
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The mean earnings of a university undergraduate student is enrolled in a Business program is $28,000 per year. Assume that the average salaries follow a normal distribution with a standard deviation of $2,500.
Required
a. Find the probabilities that a student makes more than $30,000?
b. What is the probability that a student would make between $27,000 and $32,000?
c. What is the probability that a student would make less than $23,150?
a. The probability that a student makes more than $30,000 is 0.0668.
b. The probability that a student makes between $27,000 and $32,000 is 0.9545.
c. The probability that a student makes less than $23,150 is 0.0062.
Probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various events. Statistics is the study of occurrences that follow a chance distribution.
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DefineT:R2→R2byT(x)=T−([x1x2])=[3x1−−2x22x2]- a) Letu=[u1u2]andv=[v1v2]be two vectors inR2and let c be any scalar. Prove thatTis a linear transformation. - b) Find the standard matrixAofT. - c) Is T one-to-one? Prove your answer using the matrix A.
a)T(u) + T(v) T is a linear transformation
b)[3 -2 ; 2 0]
c)T is one-to-one.
a) To prove that T is a linear transformation, we need to show that it satisfies two conditions.
1. Additivity: T(u + v) = T(u) + T(v)
Let u = [u1, u2] and v = [v1, v2], then
T(u + v) = T([u1 + v1, u2 + v2]) = [3(u1 + v1) - 2(u2 + v2), 2(u2 + v2)]
= [3u1 - 2u2 + 3v1 - 2v2, 2u2 + 2v2]
= [3u1 - 2u2, 2u2] + [3v1 - 2v2, 2v2]
= T(u) + T(v)
2. Homogeneity: T(cu) = cT(u)
Let u = [u1, u2] and c be any scalar, then
T(cu) = T([cu1, cu2]) = [3cu1 - 2cu2, 2cu2] = c[3u1 - 2u2, 2u2]
= cT(u)
Therefore, T satisfies both conditions, and is a linear transformation.
b) The standard matrix of T is the matrix A = [3 -2 ; 2 0]
c) To determine whether T is one-to-one, we look at the matrix A. Since the matrix A has a non-zero determinant, which is equal to -4, then T is one-to-one.
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How to find a height of a trapezoid with phythagorean theorem
Height of a trapezoid with Pythagorean theorem is = √{Hypotenuse ^2 - Base ^2}
Trapezoid has two parallel sides and two non parallel sides. The length of the parallel sides are unequal but the length of the non parallel sides are equal.
Thus the trapezoid can be divided into three parts where one is rectangle ( which has length equal to the shortest length of the parallel sides) and two triangles which are equal ( having equal base, height and hypotenuse).
The Pythagoras theorem on the triangular part of the trapezoid can be stated as ,
Hypotenuse ^2 = Base ^2 + Height ^2
⇒ Height ^2 = Hypotenuse ^2 - Base ^2
⇒ Height = √{ Hypotenuse ^2 - Base ^2}
where, Height of the triangle is equal to that of the trapezoid it belongs to;
Hypotenuse of the triangle is the non parallel but equal side of the trapezoid;
Base of the triangle is = {(length of the longest side of parallel sides of trapezoid) - (length of the shortest side of parallel sides of trapezoid) }/2
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The volume of a sphere is 1230pi what is the radius