We find the inverse of a 2x2 matrix on a calculator using formula
A⁻¹ = Adjoint of A / determinant of A
Where, adjoint of A = [ d -b]
[-c a]
and, determinant of A = 1/ ad - bc
What is inverse of a 2X2 matrix?A real number's inverse is a number that, when multiplied by the inputted number, yields the multiplicative identity, which is 1, or 1. A matrix's inverse, represented by A⁻¹ in matrices, is a matrix that, when multiplied by A, yields the identity matrix I, or A.A⁻¹ = A⁻¹.A = I
The formula (adj A)/(det A) can be used to determine the inverse of a matrix A, where "adj A" stands for "adjoint of A" and "det A" for "determinant of A".
Let A is a 2x2 matrix such that, A = [a b]
[c d]
then, A⁻¹ = Adjoint of A / determinant of A
Where, adjoint of A = [ d -b]
[-c a]
and, determinant of A = 1/ ad - bc
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How do you do two step inverse operations?
How do you convert this equation into vertex form?
Answer:
Below
Step-by-step explanation:
Filter out the - 2
y = -2 ( x^2 - 5/2 x) - 1 Now 'complete the square'
y = -2 ( x^2 - 5/2x + 25/16) + 50/16 -1 Now simplify:
= -2(x-5/4)^2 + 34/16 This will have vertex at 5/4, 34/16
PLEASE HELPP. FINALS DAY. BRAINLIEST ANSWER WILL BE MARKED!!
Rotation would be the first answer...Your second answer would be dilation. If this is wrong, I'm so sorry
Which types of transformations change the shape of a graph?
Dilation
By maintaining the object's orientation or shape, this type of translation either expands or contracts the object. This is referred to as resizing.
What is Graph Transformation?
A graph can be transformed to produce a different version of the one that came before it. The x-y plane can be used to translate or shift the graphs. In addition to these modifications, they may also be stretched.
Types of Stretching of Graphs
Stretching out VerticallyConsider the case where we need to lengthen a graph by a factor of 2. Next, change the y value. Now, each point of the function F's form (x, y) shifts to the point (x, 2y)*
Stretching out horizontallyAdjust the x value if a graph needs to be stretched horizontally by a factor of two. The point (2x, y) in function F is now the new location for all points with the form (x, y) in function F.
Types of Translation in Graphs
Moving HorizontallyA graph is horizontally translated by moving the base graph to the left or right in relation to the x-axis. Consider that if we want to move a graph horizontally by 1 unit, we would also need to change the x value.
Moving VerticallyA graph's base graph is moved up or down in the y-axis direction when it is vertically translated. Each point on a graph is moved b units vertically to translate the graph in that many directions.
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What is the inverse of 3?
The Additive Inverse of the number 3 is -3 that is "Negative 3".
The Inverse (Additive) of the number is defined as the number which when added to original number the result is zero .
the number is given as "3" ,
We let the additive inverse be = "a" ;
According to above definition of additive inverse ,
we get ;
3 + a = 0 ;
On simplifying further ,
we get ;
a = -3 .
the sum of 3 and -3 is written as 3 +(-3) ⇒ 3 - 3 = 0 .
Therefore , the additive inverse is "-3" .
The given question is incomplete , the complete question is
What is the additive inverse of the number 3 ?
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on dividing 2272 as well as 875 by 3 digit number n we get the same remainder The sum of the digits Of n is
Answer:
10
Step-by-step explanation:
2272-875=1397
Factors of 1397: 1, 11, 127, 1397
Where's the three-digit number? ==> 127 is the three-digit number
875/127 = 6.889
1397/127=11
2272/127=
(875+1397)/127=
875/127 + 1397/127= ==> substitute 11 for 1397/127 and 6.889 for 875/127
6.889 + 11 = 17.889
Hence, 2272/127=17.889
Hence, 2272 and 875 have the same remainder when divided by 127.
Now add the digits:
1+2+7=10
ABC Corporation, a large software developer, is Involved in the creation and sales of custom billing software for companies. The figure shows their quarterly sales figures for the last four years. The company's profit is Its total sales minus the cost of pay for salespeople and typical business costs. If salespeople earn 10% of their sales in pay and typical business costs account for 20% of the value of each sale, how much more profit was earned in 2010 than in 2007?
O exist4.0 million
O exist4.2 million
O exist5.0 million
O exist6.0 million
O exist6.4 million
Answer:
theans its a= exist 4.0million
What are the SSS SAS and AAS congruence criteria?
The definition of SSS, SAS, and AAS congruency conditions is shown.
SSS condition:
In accordance with the SSS rule, two triangles are considered to be congruent if their corresponding three sides are equal on both triangles.
SAS condition:
The two triangles are congruent if two sides and the included angle of one triangle match those of a second triangle by two sides and the included angle.
AAS condition:
The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
Therefore, the definition of SSS, SAS, and AAS congruency conditions is shown.
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Solve this system of equations by graphing. First graph the equations, and then type the solution.
According to question,
Given data,
2x-3y=-12……… (1)
Y=-5x/3-3……… (2)
3y= -5x-9………… (3)
Solving the equation,
(1) and (3)
5x-3y=-9
2x-3y=-12
To solve both equation
3x=3
x=1
the value of x, putting equation 1
5x-3y= -9
5×1-3y=-9
5-3y=-9
-3y=-9-5
-y=-14
y=14/3
y=4.6
the value of x=1 and y=4.6
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Q-find the greatest common factor.ab4c7,a7b4c.
We know that,
Greatest common factor= the greatest common factor is the greatest factor that divides both numbers.
According to question.
Given data,
Factor of a= a
Factor of b=b× b× b× b
Factor of c=c× c× c× c× c× c× c
Therefore,
Factor of a=a× a× a× a× a ×a ×a
Factor of b4=b ×b ×b× b
Factor of c=c
Greatest common factor=ab4c
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What is the relationship between the volumes of a cylinder and a cone both of which have equal radii and vertical heights?
The relationship between the volumes of a cylinder and a cone both of which have equal radii and vertical heights:
the volume of cone = 1/3 × volume of cylinder
In this question we need to find the relationship between the volumes of a cylinder and a cone both of which have equal radii and vertical heights.
Consider a cylinder with radius r and vertical height h.
We know that the formula for the volume of cylinder.
V1 = π × r² × h ..........(1)
Now consider a cone with radius r and vertical height h.
Using the formula for the volume of cone,
V2 = 1/3 × π × r² × h
From equation (1),
V2 = 1/3 × V1
the volume of cone = 1/3 × the volume of cylinder
Therefore, volume of cone = 1/3 × volume of cylinder
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How do you find the vertical and horizontal asymptotes of a function?
The vertical asymptotes can be simply found by equating the denominator of a function to zero and solving for x, but the vertical asymptotes requires consideration of the highest degrees of x in numerator and denominator.
What is veritcal asymptote?A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.
What is horizontal asymptote?A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph moves closer to the line as the inputs go closer to 0 or -1.
Find the x values where the function is undef for the purpose of determining a function's vertical asymptotes. Consider the degree of the numerator and the degree of the denominator while looking for a function's horizontal asymptotes. The horizontal asymptote is y = 0 if the degree of the numerator is smaller than the degree of the denominator. There is no horizontal asymptote if the degree of the numerator is higher than the degree of the denominator. The horizontal asymptote is y = the coefficient of the highest-degree term in the numerator divided by the coefficient of the highest-degree term in the denominator if the degree of the numerator and denominator are equal.
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What is the formula of variance and standard deviation of a probability distribution of a random variable?
For a given probability distribution, The random variable also contains discrete values, The variance and standard deviation are computed in terms of Expected values E(X).
What do you mean by random variable?The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a space of potential outcomes, commonly real numbers, to a space of measurement.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
for discrete probability distribution , E(x) = x*P(x)
for continuous probability distribution , E(x) = x *f(x)
Variance = [tex]E(X^2)-(E(X))^2[/tex]
standard deviation = [tex]\sqrt {Variance}[/tex]
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What is the quadrant of 3 1 on a graph?
The point (3,-1) is situated in the fourth quadrant.
Define quadrants.The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes. The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.
Given
Quadrant of (3, -1)
Due to the fact that x is positive and y is negative, the point is situated in the fourth quadrant.
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What is the x-coordinate of the ordered pair for the solution of the system of equations {y = −x + 102x + 6y = 8?
The x-coordinate of the ordered pair for the solution of the system of given equations is 10.4.
To find the solution to a system of equations, we need to find the values of the variables that make both equations true at the same time.
In this case, we are looking for the x-coordinate of the solution. To find this, we can solve the system of equations by eliminating one of the variables.
We can start by eliminating y from the equations by substituting the expression for y in the first equation into the second equation:
x + 6(-x + 10) = 8
x - 6x + 60 = 8
-5x + 60 = 8
-5x = -52
x = 10.4
The x-coordinate of the solution is 10.4.
This solution tells us that the x-coordinate of the point where the two lines intersect is 10.4, and the y-coordinate can be found by substituting this value into either of the original equations and solving for y.
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x + 6(-x + 10) = 8
x - 6x + 60 = 8
-5x + 60 = 8
-5x = -52
x = 10.4
The x-coordinate of the solution is 10.4.
This solution tells us that the x-coordinate of the point where the two lines intersect is 10.4, and the y-coordinate can be found by substituting this value into either of the original equations and solving for y.
For what values of k the roots of the equation x² 4x?
The equation x² + 4x = 0 has no real roots for any value of k.
The equation x² + 4x = 0 can be solved by using the Quadratic Formula. We can rearrange the equation to be in the form of ax² + bx + c = 0. In this case, a = 1, b = 4 and c = 0. We can then plug these values into the Quadratic Formula to find the roots of the equation.
The Quadratic Formula is x = [-b ± √(b² - 4ac)] / 2a
Plugging in our values of a, b, and c we get: x = [-4 ± √(-4² - 4(1)(0))] / 2(1)
Simplifying this equation we get: x = [-4 ± 0] / 2
The equation simplifies to: x = [-4 / 2] and x = [0 / 2].
Since both of these roots are imaginary, the equation x² + 4x = 0 has no real roots for any value of k.
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20. Let g be a twice-differentiable, increasing function of t. If g(0) 20 and g(10) 220, which of the following must be true on the interval 0 < 10 ? (A) g'(t) 0 for some t in the interval. (B) g) 20 for some t in the interval. (C) g"(t) 0 for some t in the interval. (D) g"(t) > 0 for all t in the interval
For given function the correct solution is g'(t) = 20 for some t in the interval.
A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
For a given function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function and if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function.
Given that g(10)= 220
g(0)= 20
So putting values in condition of differentiation for increasing function we get:
[tex]\frac{g(10)-g(0)}{10-0}[/tex]
= [tex]\frac{220-20}{10}[/tex]
=20
Hence as we can see that the correct solution for given function is g'(t) = 20 .
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A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Given that g(10)= 220
g(0)= 20
So putting values in condition of differentiation for increasing function we get:
= 220-20/2
=20
Which is arranged in order from least to greatest?
When numbers are arranged in ascending order, they are done so from least to largest.
What is the Ascending order?When numbers are arranged in ascending order, they are done so from least to largest.
We must first compare the numbers before we may arrange them in any order.
Compare first, then order.
Numbers arranged in ascending order: Determine how many digits each number has.
Numbers can be arranged in ascending order, from the least value to the highest value.
The arrangement is left to right.
Increasing order is another name for ascending order.
An ascending sort will organize numbers from smallest to largest and text from A to Z because ascending signifies moving upward.
For numbers, descending is going from largest to smallest, and for text, it's from Z to A.
Therefore, when numbers are arranged in ascending order, they are done so from least to largest.
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If the simple interest on $3,000 for 9 years is $1,350, then what is the interest rate?
Answer:
5%
Step-by-step explanation:
To solve this problem, we need to use the formula for simple interest, which is I = PRT, where I is the interest earned, P is the principal amount, R is the interest rate, and T is the length of time the money is invested. We know that I = 1350, P = 3000, and T = 9, so we can rearrange the formula to solve for R: R = I / (P * T) = 1350 / (3000 * 9) = 0.05. Therefore, the interest rate is 5%.
Answer: 5% per year
Step-by-step explanation:
First, take 1350 divided by 3000, then times 100% = 45% for 9 years
Then take 45 divided by 9 = 5% per year
What is the slope of 4x Y =- 1?
The slope of 4x - Y = -1 is 4.
We know that the general form of the equation of a straight line is:
y = mx + c,
where y represents the y intercept of the straight line, m represents the slope and c is the constant in it.
Let us re-arrange the given equation 4x - Y = -1 into Y = 4x + 1.
Now we compare this equation Y = 4x + 1 with the general equation of a straight line y = mx + c.
We conclude that here, m = 4 and c = 1.
Hence, we get that the slope of the given equation Y = 4x + 1 is 4.
The question is incomplete, the complete question is:
What is the slope of 4x - Y = -1?
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answer this question on trigonometry
The length of the sides a and b with one decimal place value are 9.4 cm and 12 cm.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Applying the Pythagorean theorem.
a² = 8² + 5²
a² = 64 + 25
a = √89
a = 9.4 cm
17² = b² + 12²
289 = b² + 144
b² = 289 - 144
b² = 145
b = √145
b = 12 cm
Thus,
The length of side a is 9.4 cm.
The length of side b is 12 cm.
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in the computer lab, there are 14 desktops and 16 laptops. approximately whta percent of the computers are laptops
Answer:
about 43% or 43.3%
Step-by-step explanation:
First, add up the total amount of computers in the computer lab:
14 + 16 = 30
We are told that 16 of the 30 computers are laptops so we can think of this percentage problem as its own equation
13 is what percent of 30
13 = % x 30
now to solve by dividing 13 by 30 using a calculator:
13/30 = 0.433...
This approximates to 43% or 43.3%
Franklin National Life Insurance Company purchased new computers for $300,000. If the rate at which the computers' resale value changes is given by the function V'(t) = 5700(t − 10) where t is the length of time since the purchase date and V'(t) is measured in dollars per year, find an expression V(t) that gives the resale value of the computers after t years. V(t) = dollars How much would the computers sell for after 5 years? (Round your answer to the nearest dollar.) $
To find an expression for V(t), we can integrate V'(t) with respect to t. Doing so, we have:
V(t) = ∫V'(t) dt = ∫5700(t − 10) dt = 5700 ∫(t − 10) dt = 5700 [t^2/2 - 10t] + C
Since V(t) is the resale value of the computers, the constant of integration C should be the initial value of V(t), which is the cost of the computers. Therefore, we have:
V(t) = 5700 [t^2/2 - 10t] + 300000
Now, to find the value of the computers after 5 years, we can substitute t = 5 into the expression for V(t):
V(5) = 5700 [5^2/2 - 10*5] + 300000 = 5700 [25/2 - 50] + 300000 = 5700 [-12.5] + 300000 = -67500 + 300000 = 232500
Thus, the computers would sell for approximately $232,500 after 5 years.
Explanation: The function V'(t) gives the rate at which the resale value of the computers changes with time. In other words, it gives the slope of the function V(t) at any point in time. To find the function V(t) itself, we need to integrate V'(t) with respect to t. The constant of integration C is added to the result of the integration to ensure that the initial value of V(t) is equal to the cost of the computers. Once we have the expression for V(t), we can find the value of the computers at any point in time by substituting the appropriate value for t into the expression. In this case, we found that the value of the computers after 5 years is approximately $232,500.
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The following rectangle is formed by four squares as shown below. The perimeter of this rectangle is 30 inches. What is the area of the rectangle?
The area of the rectangle formed by 4 squares is 36 sq inches.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the perimeter of any plane figure is the sum of the lengths of all the sides.
Let each side of this square be 'a'.
∴ (a + a + a + a) + a + (a + a + a + a) + a = 30.
4a + a + 4a + a = 30.
2(4a + a) = 30.
2(5a) = 30.
10a = 30
a = 3.
So, the length of the rectangle is 4a and the width is a.
∴ The area of the rectangle is (4a×a) = 4a².
= 4(3)².
= 4(9).
= 36 sq inches.
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the question is in the picture
Answer:
15 weeks
Step-by-step explanation:
read the graph at the number of words correct
those past 15.words count the weeks in the y.axis
How much extra do you get for limited capability for work?
You get £354.28 a month extra for limited capability for work.
If you have a "restricted capability for work-related activity," £354.28 per month (the higher rate) is included in your award. An evaluation of one's "work capability" is what determines this. In some cases, the work capability amount cannot be included in your award right away; instead, there is typically a three-month "waiting period." When you submit supporting medical documentation to the Department of Work and Pensions, this will ordinarily start. You should take the work capacity evaluation while you're waiting.
A lesser rate of the work capability amount of £132.89 might have been included in your award prior to April 3, 2017, if you were only determined to have a "limited capability for work" during this assessment (and not a limited capability for job-related activity).
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What are the roots of the quadratic equation 2x² 5x 3 0?
The roots of the quadratic equation 2x² + 5x + 3 = 0 are x = -3 and x = -1/2.
To find the roots of a quadratic equation, we must first convert the equation into the standard form ax² + bx + c = 0. In this case, the given equation is already in this form, so we can proceed with solving. To solve, we use the quadratic formula, which is x = (-b ± √(b² - 4ac))/2a.So, we have x = (-5 ± √(25 - 4(2)(3))/2(2). Simplifying, we get x = (-5 ± √(13))/4. The quadratic formula yields the values x = -3 and x = -1/2. Therefore, the roots of the quadratic equation 2x² + 5x + 3 = 0 are x = -3 and x = -1/2.
x = (-5 ± √(25 - 4(2)(3))/2(2)
= (-5 ± √(13))/4
= -3, -1/2
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The difference between two numbers is 60. If the large is divided by the smaller number the quetient is 3 and the remender is 12 find two number
The two numbers we have to find are 24 and 84.
So, we have been given that there are 2 numbers, and the difference between them is 60.
Let the two numbers be x and y. Let the larger number be x and the smaller number be y.
x-y = 60
When x is divided by y, the quotient is 3 and the remainder is 12.
By division lemma, we can clearly say x= 3y + 12
Now, we have two equations -
x-y=60 and x=3y+12
=>60+y=3y+12
=> y=24
If y=24 and we know x-y=60. This implies that x is equal to 84.
Hence the two numbers 24 and 84.
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What is the mean of 5 7 9 11?
The mean of the following data is 8.
To find: Mean of given numbers.
Given data is 5, 7, 9, 11
Mean: It is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Mean=[tex]\frac{Sum of all observations}{Number of observations}[/tex]Here, sum of observations is 5+7+9+11=32
Sum of observations is 32
Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data
Total number of observation is 4
The number of observations provides information on the total number of values that are contained in the Dataset. This property is intended to provide an indication of the size of a Dataset.
Substituting values in above formula,
=[tex]\frac{32}{4}[/tex]
=8
Therefore, the mean is 8.
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Solve for x.
(x+16)
(4x-5
7
11
13
9
Answer:
soln:
x+16=4x-5
16+5=4x-x
21/3=x
Therefore x=7
What is the slope of the linear equation 2y 3x − 1?
Let m s the slope of the given equation 2y+3x-1. So m=-3/2.
What is meant by slope?A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively. Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is
m =Δy/Δx = change in y/change in x
where "m" represents a line's slope.
Write alternative way to write slope.Slope can also be written as
tanθ = Δy/Δx
The given equation is:
2y+3x-1=0
Separate y
2y= -3x+1
y= -3/2x +1/2
Comparing it with equation of line y=mx+c where m is the slope we conclude that slope of the given equation is m=-3/2.
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