Answers
The value of matrix A is \(A =\left[\begin{array}{cc}0&4\\-8&12\end{array}\right]\)
How to determine the matrix A?The given parameters are:
\(\lambda_1 = 4\) at \(v_1 = \left[\begin{array}{c}1&1\end{array}\right]\)
\(\lambda_2 = 8\) at \(v_2 = \left[\begin{array}{c}1&2\end{array}\right]\)
The matrix A is calculated using:
A = S ∧ S⁻¹
Where:
\(S = \left[\begin{array}{cc}v_1&v_2\end{array}\right]\)
\(\lambda = \left[\begin{array}{cc}\lambda_1&0\\0&\lambda_2\end{array}\right]\)
\(\lambda =\left[\begin{array}{cc}4&0\\0&8\end{array}\right]\)
Next, we have:
\(S = \left[\begin{array}{cc}v_1&v_2\end{array}\right]\)
This gives
\(S =\left[\begin{array}{cc}1&1\\1&2\end{array}\right]\)
Calculate the determinant of S
|S| = 1 * 2 - 1 * 1
|S| = 1
So, the inverse of S is:
\(S^{-1} = \frac{1}{1} * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\\\)
Evaluate
\(S^{-1} = \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\\\)
Recall that:
A = S ∧ S⁻¹
So, we have:
\(A =\left[\begin{array}{cc}1&1\\1&2\end{array}\right] * \left[\begin{array}{cc}4&0\\0&8\end{array}\right] * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\)
Multiply the first two matrices
\(A =\left[\begin{array}{cc}1 * 4 + 1 * 0&1 * 0 + 1 * 8\\1 * 4 + 2 * 0&1 * 0 + 2 * 8\end{array}\right] * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\)
Evaluate
\(A =\left[\begin{array}{cc}4&8\\4&16\end{array}\right] * \left[\begin{array}{cc}2&-1\\-1&1\end{array}\right]\)
Evaluate the product
\(A =\left[\begin{array}{cc}4*2+8*-1&4 * -1 + 8 * 1\\4 * 2 + 16 * -1&4 * -1 + 16 * 1\end{array}\right]\)
Evaluate
\(A =\left[\begin{array}{cc}0&4\\-8&12\end{array}\right]\)
Hence, the value of matrix A is \(A =\left[\begin{array}{cc}0&4\\-8&12\end{array}\right]\)
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Related Questions
Find the volume of a sphere with a radius of 9 inches. Use 3.14 for π
.
Round your answer to the nearest hundredth.
Answers
Answer:
Answer = 3053.63
Step-by-step explanation:
The formula for finding the volume of a sphere is : V = 4/3 πr³
V = 4/3· π · \(9^{3}\)
≈ 3053. 62806
Rounded to the hundreths place is 3053.63.
the other answer might be better
explanation
Select the correct answer. Simplify the following algebraic expression. √45x^5 A. 9x²√5x OB. 91³√5x² О с. 3x²√5x OD. 3r³√5x²
please help me and can you explain how you got your answer
Answers
The simplified form of the given algebraic expression is 3x²√5x. The correct option is с. 3x²√5x
Simplifying an algebraic expressionFrom the question, we are to simplify the given algebraic expression.
The given expression is
√45x^5
First, we will write the given expression properly
The expression written properly is
√45x⁵
Simplifying
√45 × √x⁵
√9×5 × √x⁴×x
√9 × √5 × √x⁴ × √x
3 × √5 × x² × √x
3 × x² × √5 × √x
3x² × √5×x
3x² × √5x
3x²√5x
Hence, the simplified expression is 3x²√5x
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Solve for x leave your answer in simplest radical form
Answers
Answer:
X=11 trust me on my mom
what's the expression of 3M
Answers
Given expression is:
\((3m^{-4})^3(3m^5)\)The expression is solved as:
\(=(3^3m^{-4\times3})\times(3m^{5)}\)\(undefined\)HELP ME PLEASE IM CRYING SO BAD
Answers
Answer:
V'= ( 5,2 )
U'= ( 8,2 )
T'= ( 7,12 )
S'= ( 3,12 )
Answers:
S ' (3, 7)T ' (7, 7)U ' (8,2)V ' (5,2)Check out the diagram below
===================================================
Explanation:
When reflecting over horizontal lines like this, the x coordinate stays the same as the original point. Only the y coordinate changes.
To find what the y coordinate changes to, we need to measure the vertical distance from the point to the line. Point S has a y coordinate of y = -5 and the vertical distance to the line of reflection (y = 1) is |-5-1| = |-6| = 6 units. So we move 6 units up to go from point S to the line of reflection. We must move another 6 units to get to the location for S' where its reflected point would end up, which has y coordinate y = 7.
The same applies for the other points as well. Point T also goes up 6 units to get to y = 1, then it moves another 6 units to get to y = 7
Points V and U only move up 1 unit to get to the green dotted line of reflection. So they'll move only one additional unit to have their reflected points have y coordinates of y = 2.
The diagram hopefully visually summarizes everything discussed so far. The mirroring line cuts the distance from S to S' in half, same for T to T', and so on.
What is y 6=2(y+2)
HELP ME PLEASE
Answers
-y=2-3
-y=-1
Answer is y=1
I need help asap, please rn
Answers
Answer:
g(f(- 5)) = - 31
Step-by-step explanation:
to calculate g(f(- 5)), evaluate f(- 5) and substitute the value obtained into g(x)
f(- 5) = (- 5)² + (- 5) - 12 = 25 - 5 - 12 = 25 - 17 = 8 , then
g(8) = - 2(8) - 15 = - 16 - 15 = - 31
Answer:
-31
Step-by-step explanation:
f(x)=x²+x-12
or,f(-5)=(-5)²+(-5)-12
=25-5-12
=25-17
=8
now, g(x)= -2x-15
= (-2)×8-15
= -16-15
=-31
4.6 > x + 3/4
X < 5 7/20
X > 5 7/20
X < 3 17/20
X > 3 17 20
Answers
x < 3 17/20
Step-by-step explanation:
yes
If M is the set of all square numbers less than 80 and N is the set of all non-negative even numbers that are under 30, Write the lists of all elements of M and N.
Answers
Answer:
The set M of all square numbers less than 80 is:
M = {0, 1, 4, 9, 16, 25, 36, 49, 64}
The set N of all non-negative even numbers that are under 30 is:
N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}
Answer:
All elements of the set M in ascending order are:
1, 4, 9, 16, 25, 36, 49, 64All elements of the set N in ascending order are:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28Step-by-step explanation:
A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.
The square numbers less than 80 are:
1, 4, 9, 16, 25, 36, 49, and 64.An even number is an integer that is divisible by 2 without leaving a remainder.
The non-negative even numbers that are under 30 are:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, and 28.Therefore:
All elements of the set M in ascending order are:
1, 4, 9, 16, 25, 36, 49, 64All elements of the set N in ascending order are:
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 2829.For n ≥ 3, a pattern can be made by overlapping n circles, each of circumference 1 unit, so that each circle passes through a central point and the resulting pattern has order-n rotational symmetry.
For instance, the diagram shows the pattern where n = 7.
If the total length of visible ares is 60 units, what is n?
Answers
The value of n can be determined by finding the number of visible arcs in the pattern, which is 30 in this case.
To determine the value of n, we need to find the relationship between the total length of visible areas and the number of circles (n).
In the given pattern, each circle contributes to the visible area twice: once as its circumference and once as the overlapping part with the adjacent circles. Since the circumference of each circle is 1 unit, the visible area contributed by each circle is 2 units.
Therefore, the total length of visible areas can be expressed as 2n. Given that the total length is 60 units, we can set up the equation:
2n = 60
Solving this equation, we find:
n = 60/2 = 30
Thus, the value of n is 30.
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In the situation below, indicate whether it makes more sense to use a relatively large significance level (such as α=0.10 ) or a relatively small significance level (such as α=0.01 ). Testing to see if a well-known company is lying in its advertising. If there is evidence that the company is lying, the Federal Trade Commission will file a lawsuit against them. Relatively large significance level Relatively small significance level
Answers
It makes more sense to use a relatively small significance level (such as α=0.01) in this situation. The reason is, the consequences of falsely accusing a well-known company of lying in their advertising could be significant, and filing a lawsuit is a serious action.
Therefore, it is important to have a high level of confidence in the evidence before taking such a step. A small significance level would ensure that the evidence gathered is statistically significant, reducing the likelihood of making a false accusation. On the other hand, a relatively large significance level (such as α=0.10) would increase the chances of a Type I error, which is the incorrect rejection of a true null hypothesis, potentially leading to false accusations and legal repercussions.
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PLEASE HELP ME WITH THIS
Answers
Answer:
there is no correct answer given
Step-by-step explanation:
look at image
Carns Company is considering eliminating its Small Tools Division, which reported a loss for the prior year of $205,000 as shown below. Segment Income (Loss) Sales $ 1,430,000 Variable costs 1,295,000 Contribution margin 135,000 Fixed costs 340,000 Income (loss) $ (205,000) If the Small Tools Division is dropped, all of its variable costs are avoidable, and $119,000 of its fixed costs are avoidable. The impact on Carns’s income from eliminating the Small Tools Division would be: Multiple Choice
Answers
The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.
To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.
The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.
To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:
Impact on income = Loss - Avoidable costs
Impact on income = $205,000 - ($1,295,000 + $119,000)
Impact on income = $205,000 - $1,414,000
Impact on income = -$1,209,000
The negative sign indicates a decrease in income.
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-15>-11+w solve inequality for W
Answers
Answer:
Starting with:
-15 > -11 + w
Add 11 to both sides:
-15 + 11 > w
Simplifying:
-4 > w
Therefore, the solution for the inequality -15 > -11 + w, when solved for w, is:
w < -4
Could someone help me out? I don't get it
Answers
(x-2)(x+1)(x+5)
(x^2-x-2)(x+5)
x^3-x^2-2x+5x^2+5x-10
So after simplifying this, you are left with
A.) x^3+4x^2-7x-10
Hope this helps!
Part A: Use the Pythagorean Theorem to derive the standard equation of the circle, with center at (a, b) and a point on the circle at (x, y). Show all necessary math work. (3 points)
Part B: If (a, b) = (5, –2) and c = 10, determine the domain and range of the circle. (4 points)
Part C: Is the point (10, 2) inside the border of the circle if (a, b) = (5, –2) and c = 10? Explain using mathematical evidence. (3 points)
Answers
According to the equation the given all necessary math work are:
\(A: (x -f)^2 +(y -g)^2 = h^2\)
B: domain: [-5, 11]; range: [-9, 7]
C: yes, inside
What is Pythagοras theοrem?The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.
Part A:
Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:
sum οf squares οf sides = square οf hypοtenuse
\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h
Part B:
The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.
dοmain: 3 ± 8 = [-5, 11]
range: -1 ±8 = [-9, 7]
Part C:
The distance frοm pοint (10, -4) tο (f, g) is ...
\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)
\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)
h = √58 < 8 . . . . the distance tο the pοint is less than h=8.
The pοint is inside the circle.
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What is x, the distance between points A and A'? D.15
Answers
The value of x that fills the coordinate are 7 or -5
Distance between two pointsThe formula for calculating the distance between two points is expressed as:
D = √(x2-x1)² +(y2-y1)²
Substitute the given coordinates
10 = √(15-7)² +(1-x)²
100 = 8² +(1-x)²
(1-x)² = 100 - 64
(1-x)² = 36
1- x = -6
x = 7 or -5
Hence the value of x that fills the coordinate are 7 or -5
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Complete question
If the distance between two points (x, 7) and (1, 15) is 10, find the value of x.
6. Create a probability distribution for a coin flipping game. That is, toss a coin at least 25 times and keep up with the number of heads and the number of tails. (8 points for each part) a. Compile your data into a probability distribution. Be sure to show that your distribution meets the properties for a probability distribution. Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Res. T H H H T H H H H T H H T H T H T T H T T H H T H H 15/25=3/5 T 10/25=2/5 3/5+2/5=1 Can anyone help with part a im lost!
Answers
Answer:
Event Probability
Heads \(\dfrac{3}{5}\)
Tails \(\dfrac{2}{5}\)
Step-by-step explanation:
If a coin is tossed 25 times, then from the given table it is clear that
Number of heads = 15
Number of tails = 10
Total number of tosses = 15+10 = 25
We know that,
\(Probability=\dfrac{\text{Favorable outcomes}}{\text{Total number of outcomes}}\)
\(P(H)=\dfrac{\text{Number of heads}}{\text{Total number of tosses}}=\dfrac{15}{25}=\dfrac{3}{5}\)
\(P(T)=\dfrac{\text{Number of tails}}{\text{Total number of tosses}}=\dfrac{10}{25}=\dfrac{2}{5}\)
So, probability distribution table is
Event Probability
Heads \(\dfrac{3}{5}\)
Tails \(\dfrac{2}{5}\)
According to the properties for a probability distribution, the sum of probability of all events is 1.
Since,
\(\dfrac{3}{5}+\dfrac{2}{5}=\dfrac{3+2}{5}=\dfrac{5}{5}=1\)
Hence, the distribution meets the properties for a probability distribution.
Who is most affected by a discrepancy in dosage
Answers
When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.
What is the discrepancy in dosageInsufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.
It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.
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e
value of x:
3/2 (x – 4) = 2(3x + 1)
Answers
3/2x-6x=6+2
-4.5x=8
X=-1.7
Answer:
Step-by-step explanation:
how many do they have
Answers
Answer:
333
335
355
555
533
553
353
535
so I think 8
Find the surface area of a cylinder with a height of 5 ft and a base radius of 4 ft.
Use the value 3.14 for x, and do not do any rounding.
Be sure to include the correct unit.
Answers
Answer:
A =281 ft^2
Step-by-step explanation:
A=2πrh+2πr^2
A = 2 (3.14) (4)(5) + 2 (3.14) (5)^2
A =281 ft^2
Jennifer has carpet in her square bedroom. She decides to also purchase carpet for her living room which is rectangular in shape and 9 feet longer than her bedroom.
The area of the carpet required in the living room is given by the quadratic expression below, where x represents the side length, in feet, of the carpet in the bedroom.
X^2 + 9X
Match each part of the expression with what is represents.
Answers
Answer/Step-by-step explanation:
Let's highlight the dimensions of the bedroom and living room using the information given in the question:
==>Squared Bedroom dimensions:
Side length = w = x ft
Area = x*x = x²
==>Rectangular living room dimensions:
width = side length of the squared bedroom = x
length = (x + 9) ft
Area = L*W = x*(x+9) = x² + 9x
Now let's match each given expression with what they represent:
==>"the monomial, x, a factor of the expression x² + 9x" represents "the width of the carpet in the living room"
As we have shown in the dimensions of the squared bedroom above.
==>"the binomial, (x + 9), a factor of the expression x² + 9x" represents "the length of the carpet in the living room" as shown above in the dimensions for living room
==>"the second-degree term of the expression x² + 9x" represents "the area of the carpet in the bedroom"
i.e. the 2nd-degree term in the expression is x², which represents the area of the carpet of the given bedroom.
==>"the first-degree term of the expression x2 + 9x" represents "the increase in the area of carpet needed for the living room".
i.e. 1st-degree term in the expression is 9x. And it represents the increase in the area of the carpet for the living room. Area of bedroom is x². Area of carpet needed for living room increased by 9x. Thus, area of carpet needed for living room = x² + 9x
with expression 1. the options are, 2 factors, 3 factors, 2 terms, 3 terms.
with expression 2. the options are, 2 factors, 3 factors, 2 terms, 3 terms.
its a multiple choice question ;-;
Answers
Consider the expression 4(8x + 5)
Complete 2 descriptions of the parts of the expression.
1. The entire expression is the product of 2 factors.
1 factor is 42 factor is (8x + 5)2. On its own, (8x + 5) is a sum with 2 terms.
1 term is 8x2 term is 5Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.9
years with a standard deviation of 0.8
years.
Step 2 of 2 : If a sampling distribution is created using samples of the ages at which 68
children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
The standard deviation of the sampling distribution of sample means will be 0.097.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
Assume that an investigation of primary school understudies reports that the mean age at which youngsters start perusing is 5.9 years with a standard deviation of 0.8 years.
The standard deviation of the sampling distribution of sample means is given as,
⇒ 0.8 / √68
⇒ 0.8 / 8.246
⇒ 0.097
The standard deviation of the sampling distribution of sample means will be 0.097.
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Write an exponential function in the form y=ab^x that goes through points (0,14) and (3,4802).
Answers
\(y = ab^x \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=14 \end{cases}\implies 14~~ = ~~ab^0\implies 14=a(1)\implies 14=a~\hfill \underline{y=14b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=4802 \end{cases}\implies 4802~~ = ~~14b^3\implies \cfrac{4802}{14}=b^3 \\\\\\ 343=b^3\implies \sqrt[3]{343}=b\implies 7=b~\hfill \underline{y=14(7)^x}\)
What values does the function f of x is equal to the square root of the quantity x plus 1 end quantity minus 3 have in its range that are not in the range of the graph of g(x)?
Polynomial function g of x decreasing from the left in quadrant 2 and passing through the point negative 3 comma 3 to a minimum at negative 2 comma 0 and then increasing to a maximum at 0 comma 2 and then decreasing to a minimum at 2 comma 0 and then increasing through the point 3 comma 3 to the right
(–∞, 0]
(–∞, 0)
[–3, 0)
(–3, 0)
Answers
Answer:
[-3, -1)
Step-by-step explanation:
Hope this helps:)
Answer:
[–3, 0)
Step-by-step explanation:
I took the test :)
Solve for x in the given interval.
CSC X= -1,, for 3pi < x < 4pi
A. 5pi/2
B.3pi
C.7pi/2
D.4pi
Answers
Answer:
7pi/2
Step-by-step explanation:
Given the expression cosec x = -1
I'm trigonometry csecx = 1/sinx
The equation becomes
1/sin(x) = -1
Sinx = -1
x = arcsin(-1)
x = -90°
x is negative in the third and 4th interval
Third interval;
x = 180+90
x = 270°
x = 3pi/2
Since the angle should be within 3pi < x < 4pi
Add 2pi to the angle
x = 2pi+ 3pi/2
x = 7pi/2
Hence the required angle is 7pi/2
Select the correct answer from the drop-down menu. The missing term in the denominator is
Answers
Answer: where is the answer choices
Step-by-step explanation:
Which figure shows a reflection of pre-image QRS over the line t?
1
2
or 3
Answers
Answer:
1
Step-by-step explanation: