When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The scaling factor for the eigenvector is the appropriate eigenvalue, frequently represented as lambda.
When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by.
Hence, characteristic polynomial of A and A^T are the same, therefore their eigenvalues are also same.
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Solve for the requested variable.
s varies directly as the square of t, and s = 80 when t = 4. Find s when t is 8.
Answer:
[tex]\huge\boxed{\sf s = 320}[/tex]
Step-by-step explanation:
Given that,
[tex]s \propto t^2[/tex]
Converting proportionality into equality and adding a constant.
s = kt² ----------------(1)
Given that, s = 80 when t = 4
Put in Eq. (1)
80 = k(4)²
80 = k(16)
Divide 16 to both sides
80/16 = k
5 = k
k = 5Now,
Put t = 8 in Eq. (1)
s = (5)(8)²
s = (5)(64)
s = 320[tex]\rule[225]{225}{2}[/tex]
While exploring a volcano, Zane heard some rumbling, so he decided to climb up out of there as quickly as he could.
Zane's elevation relative to the edge of the inside of the volcano (in meters) as a function of time (in seconds) is graphed.
A fourth quadrant coordinate plane. The horizontal axis is from zero to thirty-seven point five with a scale of two point five and is titled Time in seconds. The vertical axis is from negative thirty to ten with a scale of two point five and is titled Elevation in meters. The graph of the line is y equals five-sevenths x minus twenty-five. The graph ends at each axis.
A fourth quadrant coordinate plane. The horizontal axis is from zero to thirty-seven point five with a scale of two point five and is titled Time in seconds. The vertical axis is from negative thirty to ten with a scale of two point five and is titled Elevation in meters. The graph of the line is y equals five-sevenths x minus twenty-five. The graph ends at each axis.
How fast did Zane climb?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
252525 meters per second
(Choice B)
B
5775start fraction, 5, divided by, 7, end fraction meters per second
(Choice C)
C
7557start fraction, 7, divided by, 5, end fraction meters per second
(Choice D)
D
353535 meters per second
Zane's velocity climbing the volcano is given as follows:
B. 5/7 meters per second.
What is the linear function?The linear function in the context of this problem is defined as follows:
y = 5/7x - 25.
Hence the coefficients of the linear function are given as follows:
The slope is of m = 5/7.The intercept is of b = -25.The meaning of each of these coefficients is given as follows:
The slope of m = 5/7 means that each second, his position increases by 5/7, which gives his velocity climbing the volcano.The intercept of b = -25 means that at a time of 0, he was at a height of -25 meters, which was his initial height.Thus the correct option of Zane's velocity climbing the volcano is of option B.
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Diego states that diagonal WY bisects angles ZWX
and ZYX. Is he correct? Explain your reasoning.
The given statement that Diagonal WY bisects angles ZWX and ZYX has been proven below to be true.
How to prove bisection of angles?Bisection of an angle is simply defined as dividing an angle into two equal parts.
We are given that Diagonal WY bisects angles ZWX and ZYX.
Now, from the image attached, we can see that side XY is congruent to side ZY and so; XY ≅ ZY.
Similarly, XW is congruent to ZW and as such; XW ≅ ZW
Since XY is congruent to ZY and XW is congruent to ZW, then the statement that diagonal WY bisects angles ZWX and ZYX is true
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quadrilateral abcd is a rhombus with perimeter 52 meter. the length of diagonal ac is 24. what is the are in square meters of rhombus abcd?
The area of the Rhombus ABCD is 1.2 square meter.
What is Rhombus?
A quadrilateral with four equal-length sides is known as a Rhombus in plane Euclidean geometry. Another name for this shape is an equilateral quadrilateral because all of its sides are equal in length.
Let ABCD be the given Rhombus of Perimeter = 52 cm.
Since all the sides are equal to each other.
Therefore, each side of Rhombus measures = 13 cm
So,
AD = CD = 13 cm and AC = 24 cm.
Area of the triangle ACD = √[ s (s - a) (s - c) (s - d) ] ….. Heron’s Formula.
where s = semi-perimeter,
a, c, and d are side measures.
s = (1/2) [ 13 + 13 + 24 ] = 25
Area (A) = √[ 25 (25 – 13) (25 – 13) (25 - 24) ] = 60
Hence Area of the entire Rhombus = 2 * 60 = 120 cm²
Convert 120 cm^2 into meter square
⇒ 120 cm^2 = 1.2 m^2
Hence, the area of the Rhombus ABCD is 1.2 square meter.
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The density of some steel is 7.92/cm³
What is the mass of 60cm³ of this steel?
Give your answer to 1 d.p.
Answer:
below
Step-by-step explanation:
density * volume = mass
7.92 g / cm^3 * 60 cm^3 = 475.2 g
One of the same side interior angles of two parallel lines is 20* less than the other same side interior angle. Find the measures of the two angles
The measure of both the angles will be x = 80° and y = 100°.
What is Parallelogram? What are parallel lines?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. Two lines are said to be parallel if they have same slope. These lines never intersect each other and have no common point of intersection.
Given is the same side interior angles of two parallel lines is 20° less than the other same side interior angles.
Same side interior angles are supplementary, we can write -
x + x + 20 = 180
2x = 160
x = 80°
Other angle will be -
y = x + 20 = 100°
y = 100°
Therefore, the measure of both the angles will be x = 80° and y = 100°.
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bailey has 5 skirts, 9 blouses, and 8 pairs of shoes. how many different skirt-blouse-shoe outfits can she wear? (assume that each item matches all the others, so she is willing to wear any combination.)
There are 360 different skirt-blouse-shoe outfits can she wear.
What is outfits?
A group of clothes that have been specifically chosen or designed to be worn together is known as an outfit. The term "outfit" can also refer to a business, an association, or a team of people who collaborate frequently. It can be used as a verb to mean "provide with the necessary gear."
A dress is different from a blouse and a skirt! So I'll rephrase this as how many ways can she dress, to wear one blouse, one skirt and one pair of matching shoes.
You just multiply the number of blouses, the number of skirts, and the number of pairs of shoes;
= 5*9*8 = 360
Hence, there are 360 different skirt-blouse-shoe outfits can she wear.
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Last year, Pinwheel Industries introduced a new toy. It cost $2500 to develop the toy and S25 to manufacture each toy. Fill in the blanks below as appropriate.
A.) Give a linear equation in the form Cmn + b that gives the total cost, C, to produce n of these toys Preview
B.) The total cost to produce n 3000 toys is S
C.) With $32500, a total of toys can be produced.
a)The linear equation is C=25n + 2500 to produce n 3000 toys, b) The total cost to produce 3000 toys is $77,500, c) With $32500, a total of 1200 toys can be produced in Pinwheel Industries.
What is meant by the term linear equation?An equation is a mathematical statement with an equal symbol (=) between the algebraic expression. Equations with a degree of one are called linear equations. It is the straight line's equation. Whenever values are substituted for the unknown values in linear equations, the solutions produce values that make the equation true. Since there is only one variable, there is only one solution. For instance, the equation x + 2 = 0 has just one solution, which is x = -2. In the case of the two-variable linear equation, however, the solutions are determined as the Cartesian coordinates of a point on the Euclidean plane.
The three different types of linear equations are: 1) Standard Form
2) The slope intercept form
3)Point Slope Form
How to solve?
A) Linear equation y=mx+b,
C (total cost) = y and n (number of toys) =x.
C=25n + 2500
B) Put n=1750
C= 25(3000) + 2500
C= $77,500
C)
32500= 25n +2500
30000=25n
n = 1200
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The probability of getting a six, when you are tossing a coin is ?
Solution needed ~
Answer: The possible outcomes are — 1, 2, 3, 4, 5, and 6. The probability of getting any of the outcomes is 1/6
Step-by-step explanation:
A bag contains 3 red, 6 blue, 5 purple, and 2 orange marbles. One marble is selected at random. What is the probability that the marble chosen is blue?.
Given that there are six blue marbles in the bag out of a total of 16, there is a 3/8 chance that the marble selected will be blue.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
Total number of marbles in bag,
=3+6+5+2
=16 marbles
Number of blue marbles=6
Probability of selecting blue marbles,
=6/16
=3/8
The probability that the marble chosen is blue will be 3/8 as the bag contains 6 blue marbles when total number of marbles is 16.
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what is $639 with a markup of 10%
Answer:
$63.90
Step-by-step explanation:
cost = $639
markup = 10%
cost * markup = $63.90
Refer to the previous question, the physics student used the regression model to predict that a force of 377.28N would be required to stretch the spring by 15cm. Remarkably, his prediction was horribly wrong. Can you explain why? (Check all that apply)
A. Correlation does not imply causation.
B. He made a prediction outside of the range of forces observed.
C. He made a prediction outside of the range of stretched distances measured.
D. He had outliers or influential points in his data.
E. None of the above
The physics student predicted that a force of 377.28N would be needed to stretch the spring by 15 cm using the regression model.
The relevant points from the regression model are
B. He predicted something that was outside the range of forces seen.
C. He predicted something that was outside the range of stretched distances that were observed.
D. His data contained outliers or significant points.
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Jakobe earns a bi-weekly mean gross pay of $1,592. 0. What percent of his total salary will he pay if his student loan payments are $130. 00 per month for 180 months? round to the nearest tenth. (4 points) 3. 9% 3. 8% 3. 6% 3. 7%
Answer:
Step-by-step explanation:
a pet store has 16 1/2 pounds of dry cat food. the manager divides the food into containers, putting 2 3/4 pounds in each container how many containers does the manager fill
what are three equations that are equivalent to 60% of 25
The equation which is equivalent to 60% of 25 is x = 0.6 * 25
1. Equivalent equations: Equivalent equations are algebraic equations that are having identical roots or solutions. By adding or subtracting the same number or expression to both side of an equation we get an equivalent equation. Also by multiplying or dividing both sides of an equation by the same non zero number we get equivalent equation.
2. How to find equivalent equation : Steps to find weather the equations are equivalent are:
Distribute the coefficients Combine any like term on both side.Arrange the term in same order.If all the terms in two expressions are same then the equations are equivalent.An equation is used to show the relationship between variables, numbers.
Let x represent the value of 60% of 25. Hence:
x = 60% of 25
x = 0.6 * 25
Hence the equation which is equivalent to 60% of 25 is x = 0.6 * 25
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Which of the following constructions can be accomplished with paper
folding?
Check all that apply.
A. Drawing a line through a given point parallel to a given line
B. Drawing a perpendicular line segment from a given point to a
given segment
C. Finding the midpoint of a segment
D. Drawing a perpendicular line segment through a given point on a
given segment
The steps are given in option B and option C are used in paper folding.
What is Paper Folding?When we simply fold the paper in such a manner that we can achieve our objectives, the method is called Paper Folding.
Now, WE get;
Option A can not be accomplished as we need the proper equipment to construct the circle.
Option B can be done by folding the paper along the point.
Option C can be done by folding the paper in the exact half measure.
Option D can not be done.
Hence, the steps are given in option B and option C are used in paper folding.
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Value of x?
-3(4x + 3)-4(5x + 1) = 79
Answer:
-2.875
Step-by-step explanation:
-12x-9-20x-4=79
-32x-13=79
-32x=92
92/-32= -2.875
Answer:
-23/8 OR 2.875Step-by-step explanation:
Split 「-3(4x + 3)-4(5x + 1)」 out into -3(4x+3) and -4(5x+1):-3(4x+3)= (-3)(4x)+(-3)(3) = -12x-9-4(5x+1)= (-4)(5x)+(-4)(1) = -20x-4Substitute it back to the formula:-12x-9-20x-4= 79 -32x-13= 79 -32x= 79+13 -32x= 92 x= 92/-32 x= -23/8 OR 2.875show that differentiation reverses parity: if f is even, then f' is odd, and if f is odd, then f' is even. hint: differentiate f (-x ).
Differentiation reverses the parity of a function, means if f(x), is an even function, then its derivative f'( x ) is odd which is true i.e f(x) is even function implies f'(x) is odd and if f(x) is odd function implies f'(x) is even .
First, let's we start with the definition of even and odd functions.
f is even if and only if f(x) = f(-x) --(1)
f is odd iff f(x) = -f(-x) ---(2)
If f is even and differentiating equation (1) we get,
f'(x) = f'(-x)× (-1) = -f'(-x).
f'(x) = - f'(-x).
Since, f'(x) is some function, then let
g(x) = f'(x) So, we see g(x) = -g(-x) which shows that the derivative of an even function is an odd function.
If f is odd then: f(x) = -f(-x)
differentiating above function with respect to x we get ,
f'(x) = -f'(-x)× (-1 ) = f'(-x).
Let g(x) = f'(x), then g(x) = g(-x) which shows that the derivative of an odd function is an even function.
Hence, Differentiation reverses the parity is hold.
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When rounded to the tens place, which of the numbers below round to 34,590? Select all that apply.
A) 34,587
B) 34,650
C) 34,594
D) 34,595
E) 35,005
Answer:
A), C)
Step-by-step explanation:
Let's round all numbers below to the nearest 10.
A) 34,590
B) 34,650
C) 34,590
D) 34,600
E) 35,010
Monica deposits $200 into a savings account that pays a simple interest rate of 3.7%. Paul deposits $300 into a savings account that pays a simple interest rate of 2.9%. Monica says that she will earn more interest in one year because her interest rate is higher, is she correct? justify your response.
Paul earns more interest than Monica does.
What is simple interest?Simple interest can be defined as a form of interest in which the percent rate is applied on the same principal for a given period of time.
Given that,
Money deposited by Monica is $200 at simple interest of 3.7%.
Money deposited by Paul is $300 at simple interest of 2.9%.
The expression to calculate simple interest is given as,
(P × r × t)/100
Substitute the corresponding values to obtain the simple interest for both cases as follows,
Interest gained by Monica is (200 × 3.7 × 1)/100 = $7.4.
Interest gained by Paul is (300 × 2.9 × 1)/100 = $8.7.
Hence, monica is not correct as the interest earned by Paul is greater than that of monica.
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*100/50 points* It's a timed question! (in attachment)
Answer: last one should be it
Step-by-step explanation:
Answer:
3rd one is correct.
Step-by-step explanation:
12 is 30% of what number?
Answer: 40
Step-by-step explanation: the answer is 40
Answer:
40
Step-by-step explanation:
12=[tex]\frac{30}{100}[/tex]*x
12=[tex]\frac{3}{10}[/tex]x
multiply both sides by 10/3
x=40
if an open rectangular box is to have a fixed volume v, what relative dimensions will make the surface area a maximum
Relative dimensions which will make the surface area a maximum is
x=y = \sqrt{area/3 }
z = 1/2( \sqrt{area/3 })
Volume = 2xh
Let the box have dimensions x,y,z>0.
The surface area is A=xy+2xz+2yz
The volume is V=xyz
The Lagrangian is L=V−λ(A−constant)=xyz−λ(xy+2xz+2yz−constant).
∂L∂x=yz−λ(y+2z)=0
∂L∂y=xz−λ(x+2z)=0
∂L∂z=xy−λ(2x+2y)=0
Hence, λ=yzy+2z=xzx+2z=xy2x+2y
On cross multiplication,
xyz+2yz2=xyz+2xz2which implies x=y.
Cross-multiplying the middle and the right expressions ,2x2z+2xyz=x2y+2xyzwhich implies z=12y.
So, optimal volume with fixed surface area is to have the width and the depth equal and the height to be half the width and depth.
To find x,y,z given a fixed surface area Area one would use x=y=2z in the equation
Area=xy+2xz+2yz=x2+x2+x2 so
x=y = \sqrt{area/3 }
z = 1/2( \sqrt{area/3 })
Volume is a measurement of three-dimensional space that is occupied. Numerous imperial units or SI-derived units, such as the cubic metre and litre, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.
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In exercises 4 and 6 tell whether the ordered pair is a solution to the linear inequalities.
Just Question 4 and 6.
Answer:
3
Step-by-step explanation:
if you look at the graph, you can see that the line intercepts where the points are
what is the area of the largest rectangle with lower base on the x axis and upper vertices on the curve y
4 square units will be the area of the largest rectangle.
Given,
First, let's build a rectangle ABCD, where A is the point at the bottom right corner and B,C, and D are the points designated in accordance with A.
Now,
Let A = (p, 0)
B = (-p, 0)
C = (-p, 3 - p²)
D = (p, 3 - p²)
Then the area of rectangle is given as: BA×AD
= 2p × 3 - p²
A = 6p - 2p³
Taking the derivative with respect to p, we have
A' = 6 - 6p²
Now,
A' =0
⇒ 6 - 6p² = 0
⇒ 6p² = 6
⇒ p² = 1
Since, we have to find the greater area, therefore we will take p = 1.
Now, substituting the value of p in (A), we have
Greater area = A= 6 - 2 x 1 = 4 square units
Therefore,
The area of the largest rectangle should be 4 square units.
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Question is incomplete. Completed question is given below;
What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 3 − x2?
What is the value of x in this triangle?
Enter your answer in the box.
x =
Answer:
37+82+x=180
119+x=180
x=180-119
x=61
what is the degrees of freedom for the t distribution? (round your answer down to the nearest integer.) (c) what is the p-value? (round your answer to four decimal places.) p-value
By using t distribution, it can be calculated that
b) Degree of freedom is 65
c) P value of 2.115 at 65 degrees of freedom = 0.0383
What is t-distribution?
t - distribution is used to find the distance between two sample means if the population standard deviation is unknown and it is assumed that the observation comes from a normally distributed population.
b) Here,
Degree of freedom =
[tex]=\frac{(\frac{s_1^2}{n_1} + \frac{s_1^2}{n_2})^2}{\frac{s_1^4}{n_1^2(n_1 -1)} + {\frac{s_2^4}{n_2^2(n_2 -1)}}}\\\\=\frac{(\frac{5.3^2}{35} + \frac{8.8^2}{40})^2}{\frac{5.5^4}{35^2(35 -1)} + {\frac{8.8^4}{40^2(40 -1)}}}[/tex]
= 65
c) The value of test statistic obtained is 2.115
P value of 2.115 at 65 degree of freedom = 0.0383
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Complete Question
The complete question has been attached
HELP ASAP! Linear function k has a zero at 3 and a y-intercept of 9. Which graph best represents k?
Suppose that y varies directly with x, and y= 8 when x = 2. find y when x is -5
The required value of y is -20, when x is -5.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given that,
y varies directly with x,
implies that,
y = k x (1)
Substitute the values x = 2 and y = 8,
8 = k x 2
k = 4
Substitute x = -5 and k = 4, to find the values of y,
y = -5 x 4
y = -20
The value of y is -20, when x is -5.
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-2/3^8
two thirds to the power of eight
pls help me
Answer: i think either 256/6561 or -256/6561
Step-by-step explanation: