The orthogonal complement of subspace S, denoted as S⊥, is equal to the null space (kernel) of the matrix A.
How is the orthogonal complement of subspace S related to the null space of matrix A?Given the subspace S in ℝ³ spanned by the vectors x = (x₁, x₂, x₃)ᵀ and y = (y₁, y₂, y₃)ᵀ, we want to find the orthogonal complement S⊥. To do this, we can determine the null space (kernel) of the matrix A.
Matrix A is formed by arranging the vector x and y as columns: A = [x y] = [(x₁, x₂, x₃)ᵀ (y₁, y₂, y₃)ᵀ].
To find the null space of A, we solve the homogeneous system of linear equations Ax = 0, where x = (x₁, x₂, x₃, y₁, y₂, y₃)ᵀ. The solutions to this system form the orthogonal complement S⊥.
Therefore, S⊥ = N(A), where N(A) represents the null space (kernel) of matrix A.
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What is the exponential of 1?
Exponential of 1 is equal to the number itself which means 1.
Exponent is usually described as the method of demonstrating large numbers in terms of powers. It means, exponent refers to the count, that how many times a number is multiplied to itself to calculate that exponent.
In accordance with the exponent rule, any number raised to power of 1 would always be equal to 1 that is because it doesn't matter how many times we multiply 1 to itself. It is going to yield 1. For example, multiplying 1 hundred times i.e. 1^100 also results in 1.
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A picture is 5 inches wide and 7 inches long. A photographer enlarges it so it is 17.5 inches wide and 24.5 inches long. What scale factor was used to enlarge the picture?
5 over 7
7 over 5
5 over 17.5
17.5 over 5
Select all figures for which at least one cross section is a circle.
1.) cylinder
2.) cone
3.) triangular pyramid
4.) sphere
5.) cube
6.) rectangular pyramid
7.) square pyramid
Answer: Cylinder, Cone, and Sphere
Step-by-step explanation:
Which is the correct first step in solving the inequality –4(2x – 1) > 5 – 3xanswers are?ADistribute–4 to get –8x + 4 > 5 – 3x.BDistribute –4to get –8x – 1 > 5 – 3x.CSubtract2xfrom both sides of the inequality.DAdd 1to both sides of the inequality
The correct first step in solving the inequality –4(2x – 1) > 5 – 3x is option A: Distribute –4 to get –8x + 4 > 5 – 3x.
This is because we are trying to solve for x, so we need to get x on one side of the inequality and all the other terms on the other side. In order to do this, we need to apply distributive property of multiplication over addition, which means we need to multiply the -4 with the 2x-1. By doing this we get -8x + 4 > 5 - 3x. This can help us to move forward in solving the inequality. This is the correct first step as it gets us closer to isolating the variable x on one side of the inequality.
After this step, we can further simplify the inequality by adding or subtracting similar terms to get the final solution.
It is important to remember that when solving inequalities we need to be careful with the signs, specially when dividing or multiplying by a negative number, as it might change the direction of the inequality.
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Use multiplication to find 1/4
If the two fractions are 1/4 and 1/6, then the two equivalent fractions are 2/8 and 2/12, respectively.
A fraction is what?The numerator, which is found at the top of the fraction number, and the denominator, which is found at the bottom of the fraction number, are its two constituent parts.
The percentage is= 1/4
In both the denominator and the numerator, multiply it by two= 2/8
A fractional equivalent of 2/8 is 1/4.
Similarly,
For 1/6= 2/12
The fraction 2/12 is equivalent to 1/6.
Therefore, if the two fractions are 1/4 and 1/6, the two equivalent fractions are 2/8 and 2/12, respectively.
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What is linear equation Class 8 example?
such pair of equation that have only one pair of solutions which satisfy both equation is linear equation
How much will you pay for a hat that costs $24.99 if tax is 7.5%?
Answer: It would be 29.01
dentify the function shown in this graph
A. y = −x + 3
B. y=-3x-3
C. y = 3x - 3
D. y=-3x+3
Answer:
B
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line
m = [tex]\frac{-3-0}{0-(-1)}[/tex] = [tex]\frac{-3}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = - 3x - 3 ← equation of line
PLS PLS HELP PLSSSSSSSSSSSSSSSSSSS
Answer:One minute let me find a answer
Step-by-step explanation:
Can triangle be constructed with 2cm 3cm 4.5 cm measurements of sides give reason?
It is possible to construct a triangle whose sides are 2 cm 3 cm and 4.5 cm because the sum of two sides are smaller than third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 2 cm 3 cm and 4.5 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.
To check this we firstly add the 2 and 3
2 + 3 > 4.5
5 > 4.5
Now we add 2 and 4.5
2 + 4.5 > 3
6.5 > 3
Now we add 3 and 4.5
3 + 4.5 > 2
7.5 > 2
It is possible to construct a triangle whose sides are 2 cm 3 cm and 4.5 cm because the sum of two sides are smaller than third sides.
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find the length of the hypotenuse if both legs of the right triangle are 3
Answer:
h = 3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 legs.
let h represent the hypotenuse , then
h² = 3² + 3² = 9 + 9 = 18 ( take square root of both sides )
h = [tex]\sqrt{18}[/tex] = [tex]\sqrt{9(2)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex] ← exact value
or h ≈ 4.24 ( to 2 decimal places )
What are solutions 3 properties?
A solution is a homogeneous mixture of two or more components in which the size of particle is smaller than 1 nm.
Normal examples of solutions are sugar in water and salt in water solutions, soda water, etc. In a solution, all the components emerge as a single phase. There is particle similarity i.e., particles are evenly allocated.
This is why a whole bottle of soft drink has the same flavors throughout.
Following are the property of solution:
1. It is a homogeneous mixture.
2. Its particles are too small and have a diameter of less than 1 nm.
3. Particles do not scatter a beam of light passing through it and so, the path of the light is not visible.
4. Solutes are indissoluble from the mixture and do not sediment.
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I need help with this, i am so confused on what to do
Answer: so the column on the left are expressions, you simplify them by combining like terms, in this case, the variable x. And the row across the top are the simplified expressions. Once you finished simplifying it, you check mark the simplified expression it matches under the column.
Step-by-step explanation:
For example, the first one you’d do this;
The simplified version of 1/3x + 1/4 -2/3x is -1/3x + 1/4
Pls help. Thank you.
The following is a basic formula to find the scale factor of a dilated figure is: : Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
What's the scale factor of the dilation?Sizing Factor (Dilation) The image's size will depend on the scale factor, which is used to dilate a mathematical entity (compared to the original object). An expansion happens when the scaling factor's absolute value exceeds one.
What is Dilation Geometry?Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.
In geometry, dilation math is used to enlarge and reduce two- or three-dimensional figures.
The Scale FactorA scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is the ratio of the original figure's and dilated figure's sizes.
You can use r or k to represent the scaling factor.
If the scale factor is more than 1 (k > 1), the image is expanded.
If the scale factor is less than 1 (0 k 1), the image is condensed.
If the scale factor is 1 (k = 1), the image doesn't change.
It should be noted that the scale factor's magnitude is taken into account and that it cannot be 0.
Scale Factor FormulaAn object's size can change depending on the scale factor, either growing or shrinking. The following is a basic formula to determine a dilated figure's scale factor:
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.Another approach to express this formula that aids in determining the new shape's dimensions is as follows:
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Please show working
When Corey buys a bottle of
water alone he spends $80.00.
When he buys a bottle of water
and 2 packs of peanut, he
spends $200.00.
How much would it cost to purchase 4 bottles of water and
four packs of peanut?
Answer:
560
Step-by-step explanation:
A bottle of Water is x=80
A Pack Of Peanuts is y=?
x+2y=200
y= 200-80 divided by 2 =60
4x+4y= 4x80 + 4x60 = 560
determine the serious of transformation that would map figure G onto figure H
The series of transformation that would map the quadrilateral in figure G to the quadrilateral in figure H are A reflection about the y-axis and A translation of three units left.
What is a transition in geometry?A geometric figure can undergo a geometric transformation by changing its position, size, orientation, or any combination of these.
The potential polygon in the question, which was produced in MS Excel using data from a related web question, is attached;
The polygon's vertices are;
Figure G's vertices' coordinates are (-2, 7), (-6, 3), (-1, 5), and (-1, 1)
Figure H's corresponding vertices' coordinates are (5, 7), (9, 3), (4, 5), and (9, 3). (4, 1)
Figures G and H have identical y-values, but their x-values have different values and signs.
Following a reflection about the y-axis, the coordinates of the point (x, y) are the point (-x, y)
The transformation that maps the image produced by the reflection and figure H are;
Transformation (5 - 3, 7 - 7) = (3, 0)
(9 - 6, 3 - 3) = (3, 0)
(4 - 1, 5 - 5) = (3, 0)
(4 - 1, 1 - 1) = (3, 0)
The transformation that maps the image of figure G to figure H is therefore T₍₃, ₀₎, which is a translation of 3 units to the right.
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Please help, will give brainiest
QUESTION 1.
Element X on Planet Qatar has three known isotopes: X-121 with a relative abundance of 43.2%, X-123 with a relative abundance of 53.1%, and X-129 with a relative abundance of 3.70%. What is the average atomic mass in amu of Element X given this information?
QUESTION 2.
How did Rutherford's experiment change the way scientists had previously viewed atomic structure? How did this pave the way for subsequent changes up to and including the currently accepted quantum mechanical atomic model?
QUESTION 3.
How is percent abundance related to average atomic mass?
a) The percentage abundance Shows us the amount of the substance in the element
b) The relative atomic mass for the element X has been obtained as 122.5 amu
c) The Rutherford's model explained showed the movement of the electrons.
What is the isotope?The isotopes of an elements are the atoms of the elements that have the same atomic number but do not have the same mass number. We know that the atoms of the isotopes of the element that we have are important as we try to determine the relative atomic mass of the element as we have the element X in this case.
Now we have that;
Relative atomic mass = Weighted average of all the isotopes
As such we have;
(121 * 0.432) + (123 * 0.531) + (129 * 0.0370)
52.27 + 65.31 + 4.773
=122.35 amu
The Rutherford model of the atom shed light on the manner in which the electrons move around the nucleus of the atom of the element that we have in the atom.
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2
Given the coordinates, classify AQRT by by its sides. Q(-2, -1), R(1, 5), T(-8,-4)
If necessary, round to the tenths place.
QR
Classify:
RT=
QT
To classify a quadrilateral by its sides, we need to calculate the distance between each pair of its vertices.
The distance between Q and R is the square root of ((1-(-2))^2 + (5-(-1))^2) = square root of (3^2 + 6^2) = square root of (9+36) = square root of 45 = 6.7
The distance between R and T is the square root of ((-8-1)^2 + (-4-5)^2) = square root of (9+81) = square root of 90 = 9.5
The distance between Q and T is the square root of ((-8+2)^2 + (-4+1)^2) = square root of (10+5) = square root of 15 = 3.87
If the quadrilateral is a rectangle, two sides of it have to be equal, so in this case, AQRT is not a rectangle.
If the quadrilateral is a rhombus, all four sides have to be equal, so in this case, AQRT is not a rhombus.
If the quadrilateral is a square, all four sides have to be equal, so in this case, AQRT is not a square.
If the quadrilateral is a trapezoid, two adjacent sides are parallel, so in this case, AQRT is not a trapezoid.
If the quadrilateral is a parallelogram, two pairs of opposite sides are parallel, so in this case, AQRT is not a parallelogram.
If the quadrilateral is a kite, two pairs of sides have the same length, so in this case, AQRT is not a kite.
So the only possible classification is that AQRT is a general quadrilateral.
so we have:
QR = 6.7
RT = 9.5
QT = 3.87
What is the value of the function y=2x-3 when x = −1?
0-5
0 -1
O2
O 3
Answer:
-5
Step-by-step explanation:
2(-1) - 3
-2 - 3
-5
Question 7 of 25
f(x)=√x-4. Find the inverse of f(x) and its domain.
O A. f¹(x) = x² + 4; x≥0
OB. f¹(x) = (x+4)²; x≥-4
O c. f¹(x) = x² + 4; x ≥-4
O D. f¹(x) = (x+4)²; x≥0
Answer:
Domain of inverse = Range of f = x>-4
Hence B
Francesca and her family traveled out of state to visit family members. The first day they drove 238 miles. The second day they drove 55 more miles than the first day. Francesca wants to find the number of miles, m, they drove ok the second day. What equation could francesca use?
The equation that Francesca could use will be T = 238 + 55. And the number of miles on the second day will be 293 miles.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Francesca and her family made a trip out of state to see relatives. On a primary day, they traveled 238 miles. On the second day, they traveled 55 additional miles than the principal day.
Let 'T' be the travel miles in a day. Then the equation is given as,
T = 238 + 55
T = 293 miles
The equation that Francesca could use will be T = 238 + 55. And the number of miles on the second day will be 293 miles.
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At target you will pay $32.00 for 20 packages of travel kleenex, how much will 1 package cost?
A. $2.00
B.$1.60
C.$1.00
D.$2.60
At target you will pay $32.00 for 20 packages of travel Kleenex. The correct answer is (option B)
What was the steps to get to this answer?We see here that we have 32 and 20 we are going to divide those numbers to get are answer:
→ 32/20
→ = ?
What does 32/20 equal?→ 32/20
→ = 1.6
→ 1 package will cost $1.60.
Therefore, at target you will pay $32.00 for 20 packages of travel Kleenex. The correct answer is (option B)
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A small farm has sheep and chickens, there are chickens as many as twice the sheep and there are 104 legs. What is the count of chickens?.
Answer:
56 chickens or 112 legs
Calculate the pay for the following day of a weekly time card given a wage of $16/hr
The Total Pay for the following Day is $136 in this algebra question.
What is a Time Card?A time card is a piece of cardboard with the hours worked by an employee for a given work week printed on it. The time an employee starts and stops working is often printed on the card when it is entered into a time clock. It is used by the payroll staff to calculate the hours for which an employee shall be paid.
On Monday Morning the work time is from 8:15 to 12:15 is equal to 4 hours.
On Monday Afternoon the work time is from 13:00 to 17:30 is equal to 4.5 hours.
So, total work time is = (4+4.5)hours = 8.5 hours
SInce the given wage is $16/hr
Therefore,
Total Pay for he following day is = 8.5 x 16=$136.
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6/4+3/6+2/3=????????
These would all add up to 8/3 and 8/3 would be turned into a mixed number which would be 2 2/3
what concept does the concentric circle model illustrate?
Answer:
This theory states that the concentric circles are based on the amount that people will pay for the land.
Step-by-step explanation:
I swear this is the answer because I had the same question and I think this was my answer .
The concentric circle model illustrates nested relationships or boundaries.
We have,
The concentric circle model illustrates the concept of nested or concentric circles.
It represents a series of circles that share the same center point but have different radii.
These circles are placed one inside the other, with each circle contained within the previous one.
The concentric circle model is often used to visualize or explain various concepts, such as:
- Levels of influence or impact
- Zones or boundaries
- Relationships or proximity
- Targeting or segmentation
Thus,
The concentric circle model helps visually represent hierarchical or nested relationships, boundaries, proximity, or segmentation in various contexts.
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On the first play of a game, the Eagles
26. Brett and Max are diving. Brett is 34 feet
running back lost three yards. On their next
below the surface and Max is 25 feet below
play, the quarterback was sacked for a loss the surface. How many feet above Brett is of fourteen yards. Find the total yards in
Max?
these two plays.
9 feet above Brett is Max.
What is surface in math?Surface in math is a two-dimensional object that can be defined by a set of points in three-dimensional space. It may have a single boundary or multiple boundaries, and can have curved, straight or irregular edges. Surfaces can be used to represent physical objects in mathematics, such as a sphere or a torus, and also to represent abstract objects such as a surface of revolution or a Riemann surface.
9 feet above Brett is Max. Since Brett is 34 feet below the surface and Max is 25 feet below the surface,
The difference is 9 feet.
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Jackie made a poster for the school advertising the Science Olympiad. She included sample statistics on the speed of the mousetrap cars from the previous years.
a. If one car raced 8 meters in 1.5 seconds, what was its speed?
what is a division problem that has a quotient of 17
Answer: 85 ÷ 5 = 17
Step-by-step explanation: We can simply find whatever division problem that has a quotient of 17 by multiplying 17 by something. So, I chose to do 17 * 5. That equals 85. Now to turn this into a division problem, we just take the product and divide it by a number other than 17 (5 in our case) so, it would look like 85 ÷ 5. That is 17. The way to check is by taking the 17 and multiplying it by the number in the middle (5). We get 85, making this statement true. I hope this helped!
What kind of word is geometry?
The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.
Who named geometry?The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.
The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.
The point, line, and plane are only a few of the many undefined terms in geometry. All other concepts in geometry may be defined from these three undefined terms.
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