Answers
Answer:
No, but you can graph them by converting to mx+b form
Step-by-step explanation:
The procedure for solving simultaneous linear equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.[4]
Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.
The first systematic methods for solving linear systems used determinants, first considered by Leibniz in 1693. In 1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy.[5]
In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester introduced the term matrix, which is Latin for womb.
Linear algebra grew with ideas noted in the complex plane. For instance, two numbers w and z in {\displaystyle \mathbb {C} }\mathbb {C} have a difference w – z, and the line segments {\displaystyle {\overline {wz}}}{\displaystyle {\overline {wz}}} and {\displaystyle {\overline {0(w-z)}}}{\displaystyle {\overline {0(w-z)}}} are of the same length and direction. The segments are equipollent. The four-dimensional system {\displaystyle \mathbb {H} }\mathbb {H} of quaternions was started in 1843. The term vector was introduced as v = x i + y j + z k representing a point in space. The quaternion difference p – q also produces a segment equipollent to {\displaystyle {\overline {pq}}.}{\displaystyle {\overline {pq}}.} Other hypercomplex number systems also used the idea of a linear space with a basis.
Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group. The mechanism of group representation became available for describing complex and hypercomplex numbers. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".[5]
Benjamin Peirce published his Linear Associative Algebra (1872), and his son Charles Sanders Peirce extended the work later.[6]
The telegraph required an explanatory system, and the 1873 publication of A Treatise on Electricity and Magnetism instituted a field theory of forces and required differential geometry for expression. Linear algebra is flat differential geometry and serves in tangent spaces to manifolds. Electromagnetic symmetries of spacetime are expressed by the Lorentz transformations, and much of the history of linear algebra is the history of Lorentz transformations.
The first modern and more precise definition of a vector space was introduced by Peano in 1888;[5] by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra. The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.[5]
Vector spaces
Main article: Vector space
Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract.
A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. The second operation, scalar multiplication, takes any scalar a and any vector v and outputs a new vector av. The axioms that addition and scalar multiplication must satisfy are the following. (In the list below, u, v and w are arbitrary elements of V, and a and b are arbitrary scalars in the field F.)[7]
Related Questions
60 PTSA grocery store finds that the number of boxes of a new cereal sold increases each week. In the 1st week, 26 boxes of the cereal were sold. In the 2nd week, 58 boxes of the cereal were sold and in the 3rd week 90 boxes of the cereal were sold. The number of boxes of cereal sold each week represents an arithmetic sequence.
Show all work!
A) State the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in week n.
B) Use this rule to calculate how many boxes of cereal will be sold during the 9th week.
Answers
Answer:
aₙ = 31n - 5
Step-by-step explanation:
The terms of your sequence are.
26, 57, 88, …
This is an arithmetic sequence, because there is a constant difference of 31 between consecutive terms.
The explicit formula for the nth term of an arithmetic sequence is
aₙ = a₁ + d(n - 1 )
a₁ is the first term, and d is the difference in value between consecutive terms. Thus,
aₙ = 26 + 31(n - 1) = 26 + 31n - 31
aₙ = 31n - 5
The explicit rule for the arithmetic sequence is aₙ = 31n - 5.
what would be the answer
Answers
Answer:
B= 21.195
Step-by-step explanation:
Inner circle area = 3.14×1.5×1.5=7.065
Outer circle area = 3.14× 3×3 = 28.26
3 is the radius of the outer circle
Area of the shaded portion is = area of outer circle - area of inner circle
28.26-7.065=21.195
Answer B= 21.195
The elevator at the state capital has a maximum weight capacity of 2000 pounds. If there are 3
people already on the elevator with a combined weight of 428 pounds, write an inequality to express
the possible weights that may be added to the elevator,
Part A: Define your variable
Part B: Write the inequality
Part C: Describe what your inequality looks like on a number line. Be sure to include whether the
circle is open or closed and the direction the line is shaded.
Answers
Answer:
Step-by-step explanation:
Maximum capacity of the elevator = 2000 pounds
Combined weight of the elevator = 428 pounds
A). Let the possible weights that can be added to the elevator = w pounds
B). Therefore, inequality representing this situation will be,
428 + w < 2000
C). By solving the given inequality,
(428 + w) - 428 < 2000 - 428
w < 1572 pounds
Now we draw this inequality on a number line.
helppp helping my sister
Answers
PLZ HELP!! I RLY NEED IT!! Josie selected 6 books from thr library. However, he can only check out 4 books at a time. How many possible selections can he make?
Answers
Answer:
4 selections
Step-by-step explanation:
We are told in the question that:
Josie selected 6 books from the library. However, he can only check out 4 books at a time.
The number of possible selections can he make is 4 selections. This is because, He can only take 4 books out of the library at a time. This is the standard.
Please help math experts thank you
Answers
Answer:
.33333 or rounded .33
Step-by-step explanation:
There are 4 months that end in an r
This means that 1 third of the months end in r or .33
Tom has a 15 pounds bag of cat food. If he feeds his cat 1/4 pound
of food each day. How many days will the 15 pound bag of
cat food last? Show your thinking.
Answers
Answer:
it will take his cat 60 days to finish the entire bag
Step-by-step explanation:
Find the slope of a line parallel to each given line.
Answers
y = mx +c
y = y coordinate
m = gradient / slope
x = x coordinate
c = y intercept
question is asking to find slope so it will be “m”
Therefore answer
13) 2/3
14) 9/5
In a quiz , team A scored 2 ,4 , -2 , 0 , -2 team B scored -4 ,2 , 2 ,-2 ,4 in successive5 rounds
.Which team scored more and by how much?
Please help
Answers
Answer:
a. 2 b. 2
Step-by-step explanation:
I'll give you brainiest if you help me.
Answers
Answer:
88 degrees.
Step-by-step explanation:
Since AB is equal to BC, ABC is an isosceles triangle. Therefore, the angle of B will be 180-39-39=102 degrees. As the angle of a straight line is 180 degrees, take 180-102-32=46 degrees. This 46 degrees is angle B. Since DEB is an isosceles triangle, 180-46-46=88 degrees. 88 degrees is angle E which is your answer. Edit: (Just added on the explanation.)
need help no bots those guys r so annoying
Answers
Answer:
AC = 16
KL = 5.625
Source(s):
Dude trust me
brainliest tho??
Step-by-step explanation:
5/KL = 12/13.5
12KL = 67.5
KL = 5.625
AC/18 = 12/13.5
13.5AC = 216
AC = 16
The hot tub is shaped like a rectangular prism. It is 7 feet long, 3 1/4 feet deep, and has a volume of 159 1/4 cubic feet. What is the width of the hot tub?
Answers
Answer:
w = 7 feet
Step-by-step explanation:
Volume of a rectangle prism = length × width × height
Length = 7 feet
Width = ?
Height = 3 1/4 feet
Volume = 159 1/4 cubic feet
Volume of a rectangle prism = length × width × height
159 1/4 = 7 × w × 3 1/4
637/4 = 7 × w × 13/4
637/4 = 7 × 13/4 × w
637/4 = 91/4w
w = 637/4 ÷ 91/4
= 637/4 × 4/91
= 637*4 / 4*91
= 2548 / 364
w = 7 feet
If you can help me I would be very thankful!
Answers
Answer:
4x + 2.5y = 184
x = y - 6
Step-by-step explanation:
Let the number of smoothies sold by stand = x
And number of cones sold = y
If the selling price of each cone = $2.5
Selling price of the 'y' cones = $2.5y
Selling price of each smoothies = $4
Then sales of smoothies = $4x
If the total sales of one day = $184
Equation for this situation will be,
4x + 2.5y = 184 -------(1)
If the stand sold 6 less smoothies than the cones,
x = y - 6 -----(2)
Therefore, system of equations contains two equations (1) and (2).
It would take 150 minutes to fill a swimming pool using the water from 5 taps.
A) how many minutes will it take to fill the pool if only 3 of the taps are used? ______ minutes
B) an assumption being made in my working is that all the taps are flowing the same__ ___
Answers
Answer: points for points
Step-by-step explanation:
Hi t sure what to do?
HeLp Me !!!!!!!!!!!!!!!!!!!
Answers
Answer:45.1%
Step-by-step explanation:
which shows the solution in the inequality? -2x > 18
A. x >9
B. x<-9
C. x>-9
D.x<9
HELP PLEASE
Answers
Answer: x<-9
Step-by-step explanation:
-2x>18
-2x/(-2)<18/(-2)
x< -9
The value of the solution in the inequality is,
⇒ x < - 9
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ - 2x > 18
Now, We can simplify as;
⇒ - 2x > 18
⇒ - x > 18/2
⇒ - x > 9
⇒ x < - 9
Thus, The value of the solution in the inequality is,
⇒ x < - 9
Learn more about the inequality visit:
https://brainly.com/question/25944814
#SPJ2
What is 57.9709 divided by 3.456072
Answers
Answer: 16.77363782
Step-by-step explanation:
helpppppppppppppp pleaseeeeeee
Answers
Answer:
C
Step-by-step explanation:
hope this helps
Answer:
Step-by-step explanation:
FYI
Find the measurement of the angle indicated for each trapezoid
Answers
Answer:
45
Step-by-step explanation:
Guys pls help
4) If f(-x)=-f(x) for all x, f is an
function.
Odd Function
Even Function
Neither
Answers
Answer:
Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f. A function f is odd if the graph of f is symmetric with respect to the origin. Algebraically, f is odd if and only if f(-x) = -f(x) for all x in the domain of f brainliest ?
Solve for x ax-bx/x+c = d, if a =/b+d
Answers
Answer:
dc/a-b-d
Step-by-step explanation:
ax – bx = d
x + c
Multiply both sides by x + c
ax – bx
(x + c) = d(x + c)
x + c
Simplify
ax – bx
(x+c): ax – bx
x + c
ax – bx = d(x+c)
Expand d(x+c): dx + cd
ax — bx = dx + cd
Subtract dx from both sides
ax – bx – dx = dx + cd – dx
Simplify
ax – bx – dx = cd
Factor ax – bx – dx: x(a – b – d)
x(a - b- d) = cd
Divide both sides by a – b – d; a + b + d
x(a – b - d) cd
a + b + d
a - b - d
a – b-d
Simplify
X =dc/a-b-d
The value of 'x' in the algebraic equation is [tex]\rm x= \frac{dc}{a-b-d} \\[/tex] where [tex]\rm a\neq b+d[/tex]
It is given that the algebraic equation [tex]\rm \frac{ax-bx}{x+c}= d[/tex]
It is required to solve the algebraic (polynomial) equation if [tex]\rm a\neq b+d[/tex]
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have an algebraic equation:
[tex]\rm \frac{ax-bx}{x+c}= d[/tex]
[tex]\rm \frac{ax-bx}{x+c}= d\\\\\rm ax-bx=d(x+c)\\\rm ax-bx=dx+dc\\\rm ax-bx-dx=dc\\\rm (a-b-d)x=dc\\\\\rm x= \frac{dc}{a-b-d} \\[/tex]
Thus, the value of 'x' in the algebraic equation is [tex]\rm x= \frac{dc}{a-b-d} \\[/tex] where [tex]\rm a\neq b+d[/tex]
Learn more about Polynomial here:
brainly.com/question/17822016
Can somebody plz help me out:)))
Answers
Answer:28 possibly? I know that you connect it with the angles use across from the angle I hope I helped a little
Step-by-step explanation:
Answer:
Sin 30°
= 0.5 appromaxit
Rebecca is sharing a pizza with some friends. Below is an Image of how she cuts the pizza.
AE is a diameter of the 20 in pizza!
a) If rebecca wants the biggest piece which one would she choose ( name it by its arc)? Be careful the image may not be drawn to scale
b) Rebecca loves stuffed crust!! She decides to figure out the length of cheese in her piece of the crust ( hint find the arc length
Answers
Answer:
a) The piece of pizza she should choose is BE
b) The length of the cheese in her piece of the crust is approximately 20.07 inches
Step-by-step explanation:
The given diameter of the pizza, AE = 20 in.
The measure of the arc AB, [tex]m\widehat{AB}[/tex] = ∠ACB = 65°
The measure of the arc DE, [tex]m\widehat{DE}[/tex] = ∠DCE = 110°
Given that AE is the diameter of the circular pizza, we have;
[tex]m\widehat{BE}[/tex] = ∠BCE = 180° - ∠ACB = 180° - 65° = 115°
Similarly;
∠ACD = 180° - ∠DCE = 180° - 110° = 70°
a) The biggest piece of pizza is the piece with the largest angle which is the piece formed by arc BE, [tex]m\widehat{BE}[/tex] = 115°
The piece of pizza she should choose is the piece, BE
b) Arc length = (Arc angle)/360 × (Circumference of the circle)
The circumference of the circular pizza, C = π × Diameter = π × length [tex]\overline {AE}[/tex]
∴ C = π × 20 in.
The arc length of the arc BE = 115/360 × π × 20 = 115·π/18 ≈ 20.07
The length of the cheese in her piece of the crust, l = The arc length of the arc BE ≈ 20.07 inches.
Out of 100 employees at a company, 92 employees either work part time or work 5 days each week. There are 14 employees who work part time and 80 employees who work 5 days each week. What is the probability that a randomly selected employee works both part time and 5 days each week?
Answers
Answer: 0.02
Step-by-step explanation:
OpenStudy (judygreeneyes):
Hi - If you are working on this kind of problem, you probably know the formula for the probability of a union of two events. Let's call working part time Event A, and let's call working 5 days a week Event B. Let's look at the information we are given. We are told that 14 people work part time, so that is P(A) = 14/100 - 0.14 . We are told that 80 employees work 5 days a week, so P(B) = 80/100 = .80 . We are given the union (there are 92 employees who work either one or the other), which is the union, P(A U B) = 92/100 = .92 .. The question is asking for the probability of someone working both part time and fll time, which is the intersection of events A and B, or P(A and B). If you recall the formula for the probability of the union, it is
P(A U B) = P(A) +P(B) - P(A and B).
The problem has given us each of these pieces except the intersection, so we can solve for it,
If you plug in P(A U B) = 0.92 and P(A) = 0.14, and P(B) = 0.80, you can solve for P(A and B), which will give you the answer.
I hope this helps you.
Credit: https://questioncove.com/updates/5734d282e4b06d54e1496ac8
Answer:
The probability that a randomly selected employee works both part time and 5 days each week is 0.02
Step-by-step explanation:
What is probability?
Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event.
The total employees =100
Let A= Employees who work part time = 14
and B = Employees who work 5 days each week = 80
Then, A∪B= 92
We have to find, P(A∩B)
P(A∪B)=P(A)+P(B)-P(A∩B)
[tex]\frac{92}{100}=\frac{14}{100}+\frac{80}{100}-[/tex]P(A∩B)
0.92=0.14+0.8-P(A∩B)
0.92=0.94-P(A∩B)
P(A∩B)=0.02
Hence, the probability that a randomly selected employee works both part time and 5 days each week is 0.02.
To know more about probability here
https://brainly.com/question/23044118
# SPJ2
A 68 kg deer has a momentum of 952 kg-m/s. What is its velocity?
Answers
Answer:
14 m/s
Step-by-step explanation:
Determine the discriminant and then state how many solutions there are and the nature of the solutions. Do not solve. 6x^2-x-2=0
Answers
Given:
The quadratic equation is:
[tex]6x^2-x-2=0[/tex]
To find:
The nature of the solutions by using the discriminant.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then its discriminant is:
[tex]D=b^2-4ac[/tex]
If D<0, then both roots are complex.
If D=0, then both roots are real and equal.
If D>0, then both roots are real and distinct.
We have,
[tex]6x^2-x-2=0[/tex]
Here, [tex]a=6,b=-1,c=-2[/tex]. So, the value of the discriminant is:
[tex]D=(-1)^2-4(6)(-2)[/tex]
[tex]D=1+48[/tex]
[tex]D=49[/tex]
Since [tex]D>0[/tex], then both roots are real and distinct.
Hence, the discriminant of the given quadratic equation is 49 and both roots are real and distinct.
which equation represents that relationship ??
Answers
Answer:
A
Step-by-step explanation:
A proportional relationship either increases or decreases its points at the same rate. In the first set of ordered pairs, the x values all increase by 3 while the y values all increase by 6, which is twice the value of the x values' increasing. The second set of ordered pairs is not proportional because all pairs' x values increase by 2 while the y values increase by 8 until ordered pair (5, 20), so this set therefore is non-proportional. y = x + 3 is the correct equation because it represents that the y value is always 3 greater than the x value. All the shown ordered pairs for set 1 supports this (3 - 0 = 3, 6 - 3 = 3, 9 - 6 = 3, 12 - 9 = 3).
(PLEASE HELP)
Which of the following would NOT work to make a triangle with the two slide lengths of 2 and 6
A.6
B.5
C.7
D.4
Answers
Given:
The two sides of a triangle are 2 and 6.
To find:
The side length that would NOT work to make a triangle with the two slide lengths of 2 and 6.
Solution:
For a triangle, the sum of two smaller sides must be greater than the largest side.
Let x be the third side.
Case 1: x is the largest side, then
[tex]2+6>x[/tex]
[tex]8>x[/tex] ...(i)
Case 2: x is not the largest side, then
[tex]2+x>6[/tex]
[tex]x>6-2[/tex]
[tex]x>4[/tex] ...(ii)
From (i) and (ii), we get
[tex]4<x<8[/tex]
Here, 4 and 8 are not included.
6, 5, 7 are included in the above interval, but 4 is not included in the above interval. It means 4 would NOT work to make a triangle with the two slide lengths of 2 and 6.
Therefore, the correct option is D.
What is the length, in centimeters, of the hypotenuse of a right triangle with legs measuring V2 cm and 3 cm?
Answers
Answer:
[tex] \sqrt{13} [/tex]
Step-by-step explanation:
A is the hyp. And b/c are the sides
A²=b²+c²=3²+2²=9+4=13
Now take the square root of 13 as the answer
B. Find the perimeter of the garden when the width is
8 feet.
Answers
Answer:
10 - 16
Step-by-step explanation: