The system of equations can be represented as a vector equation A x = b, where A is the coefficient matrix, x is the variable vector, and b is the constant vector.
Using matrices and vectors, a system of linear equations can be expressed as a vector equation. Consider a set of n variables and m linear equations. It may be written as follows:
A x = b
where A is a m x n matrix of the coefficients of the variables, x is a n x 1 column vector of the variables, and b is a m x 1 column vector of the constants on the right-hand side of each equation.
To match the rows of the system of equations to the corresponding row of the matrix A and vector b in the vector equation, we can represent the system of equations as:
a 21 x 1 + a 22 x 2 +... + a 2n x n = b 2 a 11 x 1 + a 12 x 2 +... + a 1n x n = b 1
a mn x n = b m, where a m1 x 1 = a m2 x 2 +...
The vector form of this is as follows:
Beginning with "a 11" and "a 12," adding "cdots and a 1n," going on to "a 21" and "a 22," adding "cdots and a 2n," adding "vdots and vdots and ddots and vdots," ending with "a m1" and "a m2," adding "cdots and a mn,"
With A serving as the coefficient matrix, x serving as the variable vector, and b serving as the constant vector, the system of equations can thus be expressed as a vector equation, A x = b.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The population after 4 years is 1982.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have.,
Current population = 1652 people
The population triples every 10 years.
This means,
We can make a function for the number of population after m years.
y = 1652 x 3(m/10)
Where M is the number of years.
Now,
Substitute m = 4.
y = 1652 x 3(m/10)
y = 1652 x 3 (4/10)
y = 1652 x 3 x 2/5
y = 1982.4
y = 1982
Thus,
1982 is the population after 4 years.
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A satellite orbits earth at a speed of 12700 feet per second (ft/s). Use the following facts to convert this speed to miles per hour (mph).
1 mile = 5280 ft
1 min = 60 sec
1 hour = 60 min
The speed of the satellite around the earth in miles per hour is 8659.09 miles per hour.
What is meant by Measurements?Measurement is the method of comparing the properties of a quantity or object using a standard quantity.
Measurement is important to determine the quantity of any object.
A same quantity can have more than one type of measurement which can be converted to each other.
Given,
Speed of the satellite in feet per second = 12700 feet per second (ft/s)
We have,
5280 feet = 1 mile
1 feet = 1/5280 mile
12700 feet = 12700/ 5280 miles
Also,
60 minute = 1 hour
1 minute = 1/60 hour
60 seconds = 1 minute = 1/60 hour
1 second = 1/3600 hour
12700 feet per second = 12700/ 5280 miles ÷ 1/3600 hour
= 8659.09 miles per hour.
Hence the speed converted is 8659.09 miles per hour.
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Michelle is buying a 95,000 dollar home. She has been approved for a 4.95% APR, 30 year mortgage. She made a 15% down payment and will be closing on April 8th. How much should she expect to pay in prepaid interest at the closing
Answer:
b
Step-by-step explanation:
because u can tell
At the closing of her home purchase, Michelle should expect to pay prepaid interest of $6,934.50. This amount represents the interest accrued from April 8th to the end of the month.
The monthly payment for Michelle's mortgage is calculated as follows:
Principal and interest payment = (95,000 - 15,000) x 0.0495 / 12
This equals a monthly payment of $420.63.
Michelle's total interest over the life of the loan is $119,750. This amount is the sum of her prepaid interest and the total interest she pays over the life of the loan.
Consider the following data: x −2 −1 0 1 2 P(X=x) 0.1 0.1 0.2 0.2 0.4 Step 3 of 5 : Find the standard deviation. Round your answer to one decimal place.
The answer is the expected value is - 2. The equation for expected value is the sum of the values times their probabilities.
for what values of k can 2x^2 kx 5 be factored as the product of two linear factor with integer coefficents
The values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.
What is a linear factor?
A linear factor is a polynomial of degree one, which means it has one variable raised to the first power and a constant coefficient. In other words, it is an expression of the form ax + b, where a and b are constants and x is the variable.
We can factor the quadratic 2x² + kx - 5 into the product of two linear factors with integer coefficients if and only if its discriminant is a perfect square.
The discriminant of the quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. In this case, a = 2, b = k, and c = -5. Therefore, the discriminant is:
b² - 4ac = k² - 4(2)(-5) = k² + 40
For the quadratic to be factored into two linear factors with integer coefficients, k² + 40 must be a perfect square.
One way to proceed is to list the perfect squares that are 40 greater than a square, and see if k is one of the corresponding values. We can do this by solving the equation:
k² + 40 = m²
where m is an integer. Rearranging, we get:
k² - m² = -40
This is a difference of squares, so we can factor it:
(k + m)(k - m) = -40
We now need to find integer values of k and m that satisfy this equation. We can do this by considering all possible pairs of factors of -40 and solving for k and m.
The pairs of factors of -40 are:
(-1, 40), (-2, 20), (-4, 10), (-5, 8)
For each pair, we can solve the system of equations:
k + m = a
k - m = b
where a and b are the two factors in the pair. Adding these equations, we get:
2k = a + b
Subtracting them, we get:
2m = a - b
Solving for k and m, we obtain:
k = (a + b)/2
m = (a - b)/2
We can now check if the values of k and m are integers and if they satisfy the original equation.
For example, if we take the pair (-1, 40), we get:
k + m = -1
k - m = 40
Adding these equations, we get:
2k = 39
This implies that k = 39/2, which is not an integer, so this pair does not work.
Trying the other pairs, we find that:
(-2, 20) gives k = 9 and m = 11, which works
(-4, 10) gives k = 3 and m = 7, which works
(-5, 8) gives k = 1 and m = 3, which works
Therefore, the values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.
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Find the measure of angle 1
Find the measure of angle 2
The measure of angle 1 and the measure of angle 2 are 45° and 90°.
What is square?A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other.
Given is a square,
We are asked to find the missing angles,
We know that, The diagonals of the square bisect each other at 90°,
The diagonal of a square bisects its internal angle,
Therefore, the measure of angle 1 = 45°
And,
The measure of angle 2 = 90°
Hence, the measure of angle 1 and the measure of angle 2 are 45° and 90°.
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6/cm
4 cm
Find the value of x.
X
x = [?] cm
The value of x is given as follows:
x = 3.
How to obtain the length of AC?Applying the secant-tangent theorem, we have that the following equation holds true:
4x² = 6².
Hence we can solve the equation for x to obtain the value of x, as follows:
4x² = 36
x² = 36/4
x² = 9
x = sqrt(9)
x = 3.
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A car was stopped at a red light. When the light turns green, the car reaches a speed of 47 miles per hour in 4 seconds. What is the acceleration, to 1 decimal place?
feet/s2.
Answer:
275.7 ft/s^2 appr.
Step-by-step explanation:
47mi*5280=248160 feet per hour.
4 seconds = 4/(60*60)=1/900 of an hour.
1/900*248160=275.7 feet/s^2 approx.
Answer:
The car's acceleration is 17.2 ft/s².
Step-by-step explanation:
First we need to do some unit conversions.
Unit Conversions
There is 60 seconds in 1 minute.
There is 60 minutes in 1 hour.
So therefore there is 3600 seconds in 1 hour.
There is 5280 feet in 1 mile.
Now we can create an expression convert mph to ft/s
Multiply the speed value in mph by [tex]\frac{5280}{3600}[/tex] to get the speed in ft/s
We can simplify [tex]\frac{5280}{3600}[/tex] to [tex]\frac{22}{15}[/tex].
Multiply the speed value in mph by [tex]\frac{22}{15}[/tex] to get the speed in ft/s.
We are given a speed of 47 mph.
[tex]47*\frac{22}{15}=68.93[/tex]
Numerical Evaluation of Acceleration
Now we can solve for the acceleration.
The formula for acceleration is
[tex]a=\frac{v_f-v_i}{t}[/tex]
In this example we are given
[tex]v_f=68.93\\v_o=0\\t=4[/tex]
Substituting our values into the equation for acceleration yields
[tex]a=\frac{68.93-0}{4}[/tex]
Evaluate [tex]\frac{68.93-0}{4}[/tex]
[tex]a=17.23[/tex]
Rounding to 1 decimal place gives us
[tex]a=17.2[/tex]
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suppose the profit function for a company selling x items if a product is given by p(x)=-6x^2+360x-2500.
what is number of units will maximize the company's profit for this product?
what is the maximum profit?
Answer:
$2700
Step-by-step explanation:
The x-coordinate of the vertex can be found using the formula:
x = -b/2a
where a = -6 and b = 360, so we have:
x = -360/(2*(-6)) = 30
Therefore, the company will maximize its profit by selling 30 units of the product.
p(x) = -6x^2 + 360x - 2500
(x = 30 )
p(30) = -6(30)^2 + 360(30) - 2500 = 2700
So, the maximum profit for the company is $2700.
In Hillsdale, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 15 miles and the
distance between the courthouse and the city pool is 25 miles, how far is the library from the
community pool?
The library is 20 miles from the community pool as calculated after performing mathematical operations.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, In Hillsdale, the library is due south of the courthouse and due west of the community swimming pool.
Also given,
The distance between the library and the courthouse is 15 miles.
The distance between the courthouse and the city pool is 25 miles,
Using the Pythagorean theorem, we have:
x = 25² - 15²
x² = 625 - 225
x = 400
Taking the square root of both sides, we get:
x = 20
Therefore, the library is 20 miles from the community pool
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√2x = 3 solve for x?
Answer:
9/2
Step-by-step explanation:
The point (7,-9) lies on a circle. What is the length of the radius of this circle if the center is located at (5,-7)
I think the radius would be 2
ACCOUNTING! HELP! Analyze DISH network.
The Account receivable turnover for Year 1 is 21.04.
The Account receivable turnover for Year 2 is 20.86.
What is account receivable turnover?The average number of the times a company collects its accounts receivable balance is measured by the accounts receivables turnover ratio. It is a measurement of how well a business manages its line of credit process and collects unpaid balances from customers. A company's accounts receivable turnover ratio is higher for an efficient business and lower for an inefficient one.
For year 1:
Account receivable turnover:
= Net sales / Average account receivable
= 13,612 / ((654 + 640)/2)
= 13,612 / 647
= 21.0386398764
= 21.04
For year 2:
Account receivable turnover:
= Net sales / Average account receivable
= 12,808 / ((640+588)/2))
= 12,808 / 614
= 20.8599348534
= 20.86
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Which of the following functions is graphed below?
20
15
10.
-10-
-15-
-20
OA. y - x² +3,x>1
x+6, x≤ 1
OB. y-
√x² +3, x < 1
x+6, 21
OC. y.x²+3,x≤1
x+6, x>1
The equation of the graphed function is y = x + 4, x ≥ 4 and y = x² + 3, x < 4
How to determine the equation of the graphed functionA similar question is added as an attachment
From the attached, we can see that the function types are:
Linear functionQuadratic functionBased on the list of options, we have:
Linear function: y = x + 4Quadratic function: y = x² + 3Next, we look at the intervals (domain)
The domain of the linear function is x ≥ 4 because the values start from 4 (inclusive) and increases to the rightThe domain of the quadratic function is x < 4 because the values start from infinity and ends at 4 (exclusive)Read more about piecewise function at
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What is the value of x?
A. 18
B. 24
C. 26
D. 33
Answer:
Where is the question??
If S$1.00 = NRs 80.00 If Shyam wants to send NRs 20,000 to Nepal, how many S$ does he need?
Answer:
S$ 250
Step-by-step explanation:
we can solve this by dividing 20,000 NRs by 80 since S$1.00 = NRs 80
Which ot the following numbers is NOT divisible by 3?
300
321
241
8,910
Answer:
Which of the following numbers is NOT divisible by 3?
241Step-by-step explanation:
You're welcome.
Answer:
241
Step-by-step explanation:
300÷3=100
321÷3=107
241÷3=80.33
8,910÷3=2,970
Grady lists three different expressions below. Determine which expression is not equivalent to the others.
The third expression i.e. a(b) + a(c) is not equivalent to the other expressions. The solution has been obtained by using the algebraic expressions.
What is an algebraic expression?
A mathematical phrase is said to as "algebraic" if it contains variables, constants, and algebraic operations (addition, subtraction, etc.).
We are given three expressions.
The first expression is a + b+ c which represents the sum of the three variables.
The second expression is c + b + a which also represents the sum of the three variables but just the order of adding is different.
The third expression is a(b) + a(c) which represents sum of two variables multiplied with the third variable.
Hence, the third expression i.e. a(b) + a(c) is not equivalent to the other expressions.
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Beverly evenly shared a box of 24 cookies with three friends. Then, Beverly ate 5 of her cookies. Which equation shows how to find n, the number of cookies Beverly has left?
The equation that shows the number of cookies Beverly has left is n = 6 - 5.
What are whole numbers and integers?An integer is any positive or negative number, including zero, that has no decimal or fractional parts.
Natural numbers which start at 1, are categorised as whole numbers, along with 0 as well.
We can see that integers are a collection of numbers that include both positive and negative values as well as 0, whereas whole numbers are a set of numbers that include only positive numbers.
Given that, Beverly evenly shared a box of 24 cookies with three friends.
The number of cookies with Beverly = 24 / 4 = 6 cookies.
She ate 5 of her cookies.
Thus, the number of cookies Beverly has left is:
n = 6 - 5
n = 1
Hence, the equation that shows the number of cookies Beverly has left is n = 6 - 5.
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20x +1400-40x =1000 
Maureen has a Jump rope that is 62 inches long nancys jump rope is 10 inches longer how long is nancys jump rope?
Answer: 6 feet long
Step-by-step explanation:
1ft. = 12 in
62 inches = 5 feet and 2 inches
Break down 62 into 60 and 2
60 divided by 12 = 5 (12x5=60)
60in. = 5ft.
2in. = 2in.
5ft. and 2in.
10in.= 10in.
Add the inches
10in. + 2 in. = 12 in.
12in.= 1ft.
5ft. + 1ft. = 6ft.
Answer: Nancy’s rope is 6ft. long
Please help me with this question.
Answer:
pooooooooooooooooooooooooooop hope this helps
4x10^27 in standard form
Answer: 4,000,000,000,000,000,000,000,000,000
Step-by-step explanation:
4x10^27 is a number expressed in scientific notation. In standard form, it would be written as 4 followed by 27 zeros. This is because the exponent 27 indicates the number of zeros that should be added after the 4 to represent the value of the number.
So, the standard form of 4x10^27 is: 4,000,000,000,000,000,000,000,000,000
The graph of a linear system appears in a textbook. You can see that the lines do not intersect on the graph, but also they do not appear to be parallel. Can you conclude that the system has no solution? Explain.
Answer:
No. There is a solution.
Step-by-step explanation:
Pages aren't infinite, but lines are! Lines just keep going forever. If the lines aren't parallel, then they will intersect at some point. The point of intersection is the solution to the system. Just because its not on the page doesn't mean it doesn't exist. We just need a bigger page...or maybe, a bigger imagination...or maybe smaller scale on the graph...or maybe a computer graphing utility...or maybe a piece of paper and a pencil to solve the system algebraically!
The solution is out there!
see image
What is 25^(2x-3)=125^(x+1)?
The expression 25^(2x-3)=125^(x+1) has its solution to be x = 15
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
25^(2x-3)=125^(x+1)
Express 25 and 125 as exponent with a base of 5
So, we have the following representation
5^2(2x-3)=5^3(x+1)
By comparison, we have
2(2x - 3) = 3(x + 1)
Open the brackets
4x - 12 = 3x + 3
Evaluate the like terms
x = 15
HEnce, the value of x is 15
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Need help, thanks!
Last question
The maximum total deduction that can be claimed is OE. $17,100.
What is deduction ?
Deduction refers to the process of subtracting or taking away something. In the context of taxes, a deduction is a specific amount of money that a taxpayer is allowed to subtract from their income before calculating their tax liability. Deductions are one way to reduce the amount of taxes owed and can help to lower a person's overall tax burden.
There are two main types of deductions in the U.S. tax system: standard deductions and itemized deductions. The standard deduction is a fixed amount that varies depending on the taxpayer's filing status, while itemized deductions are specific expenses that a taxpayer can deduct from their taxable income. Some common examples of itemized deductions include mortgage interest, charitable contributions, medical expenses, and state and local taxes.
It's important to note that not all deductions are available to all taxpayers, and there are specific rules and limits that apply to each type of deduction. It's also important to keep accurate records and documentation to support any deductions that are claimed on a tax return.
The maximum total deduction that can be claimed is OE. $17,100, because that is the sum of the deductible expenses and the standard deduction.
The question is asking for the maximum total deduction that can be claimed, given certain deductible expenses and a standard deduction.
The standard deduction for the tax year is $6,100, and the deductible expenses are $6,000 in mortgage interest and $5,000 in charitable contributions.
Since the deductible expenses ($6,000 + $5,000 = $11,000) are less than the standard deduction of $6,100, it makes sense to use the standard deduction instead of itemizing deductions.
Therefore, the maximum total deduction would be the sum of the deductible expenses and the standard deduction:
$11,000 + $6,100 = $17,100
So, the maximum total deduction that can be claimed is OE. $17,100.
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Find non-invertible matrices A,B such that A+B is invertible. Choose A,B so that (1) neither is a diagonal matrix and (2) A,B are not scalar multiples of each other.A = [_____ _____][_____ _____]B = [_____ _____][_____ _____]
Matrices A and B are non-invertible matrices that can be added together to form an invertible matrix. To find these matrices, we can use the following steps:
Step 1: Choose a matrix A that is not a diagonal matrix and is not invertible. One example of such a matrix is
[tex]A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right][/tex]
Step 2: Choose a matrix B that is not a diagonal matrix, is not invertible, and is not a scalar multiple of matrix A. One example of such a matrix is
[tex]B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right][/tex]
Step 3: Add the matrices A and B together to form the matrix A+B. This matrix will be invertible, as shown below:
[tex]A+B = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right]+\left[\begin{array}{ccc}0&0\\1&1\end{array}\right]=\left[\begin{array}{ccc}1&1\\1&1\end{array}\right][/tex]
Step 4: Verify that the matrix A+B is invertible by finding its determinant. The determinant of a 2x2 matrix is given by:
det(A+B) = (1)(1) - (1)(1) = 0
Since the determinant of the matrix A+B is not equal to zero, the matrix is invertible.
Therefore, the matrices [tex]A = \left[\begin{array}{ccc}1&1\\0&0\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}0&0\\1&1\end{array}\right][/tex] are non-invertible matrices that can be added together to form an invertible matrix [tex]A+B =\left[\begin{array}{ccc}1&1\\1&1\end{array}\right][/tex].
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the right isosceles triangle pqr has vertices p(3,3),, q(3,1) and r(x,y) and is rotated 90 degress counterclowise about the origin. find the missing vertex of the triangle.
The right isosceles triangle PQR has vertices p(3,3), q(3,1) and r(x,y) and is rotated 90 degrees counterclockwise about the origin. the missing vertex of the triangle is r (5, 1)
What is isosceles triangle?An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Properties are:
In a triangle, the angles that face the two equal sides are likewise equal.
An isosceles triangle has one base and two equal sides, which are known as the legs and the base, respectively.
Since the triangle is isosceles, the two legs have equal length. The coordinates of two vertices are given:
P(3,3)
Q(3,1)
Assuming that PQ and QR are the legs of equal length, the distance between Q and R must be the same as the distance between P and Q
d = √[(3-3)² + (3-1)²
d = 2
Therefore, the coordinates of r is: (5, 1)
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Jordan is taking out a two-week payday loan for $600. He will be charged $95 interest for the two-week loan. What is the
APR for this loan? Round your answer to the nearest whole number.
A rock climber climbs at a rate of 720 feet per hour. Write and solve an equation to find the number of minutes $m$ it takes for the rock climber to climb 288 feet.
An equation that represents this situation is
.
It takes 24
minutes for the rock climber to climb 288 feet. I got the minutes but I need the equation. THE y=12x IS INCORRECT! I HAVE ONE CHECK LEFT!!! PLEASE HELP!!!
it takes 24 minutes for the rock climber to climb 288 feet.
How to determine?
The correct equation to represent this situation is:
$$\frac{720}{60}m=288$$
Here, we first convert the rate from feet per hour to feet per minute by dividing by 60. Then, we set up the equation where the product of the rate and the time in minutes equals the distance climbed.
Simplifying this equation, we get:
$$12m=288$$
Dividing both sides by 12, we get:
$$m=24$$
Therefore, it takes 24 minutes for the rock climber to climb 288 feet.
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