Find the equation of a line that passes through (5,-3) and is perpendicular to y = x.

a) y=x+2
b) y=x-8
c) y=-x+2
d) y=-x-8​

Answer:

[tex]x = 5[/tex]

Step-by-step explanation:

Find the side length of the square. The formula is for area is

[tex]a = {s}^{2} [/tex]

So take the square root to find the side length.

[tex] \sqrt{121} = \sqrt{ {s}^{2} } [/tex]

[tex]s = 11[/tex]

Now find the perimeter of the square.

[tex]11 \times 4 = 44[/tex]

setup the equation to solve for x. The left side is the perimeter of the rectangle and the right is the perimeter of the square.

[tex]3x + 3x + x - 2 + x - 2 = 44[/tex]

Collect like terms

[tex]8x - 4 = 44[/tex]

subtract 4 from both side

[tex]8x = 40[/tex]

divide both side by 8

[tex]x = 5[/tex]

Answer:

37/10

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The solution to the system of equations x + 2y = 1  and -3x-2y = 5 is:

x  = -3,  y = 2

The given system of equations:

x  +  2y  =  1............(1)

-3x - 2y  =  5..........(2)

This can be written in matrix form as shown:

[tex]\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right][/tex]

Find the determinant of [tex]\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right][/tex]

[tex]\triangle = 1(-2) - 2(-3)\\\triangle = -2+6\\\triangle = 4[/tex]

[tex]\triangle_x = \left[\begin{array}{ccc}1&2\\5&-2\end{array}\right]\\\triangle_x = 1(-2)-2(5)\\\triangle_x = -2-10\\\triangle_x =-12[/tex]

[tex]\triangle_y = \left[\begin{array}{ccc}1&1\\-3&5\end{array}\right]\\\triangle_y = 1(5)-1(-3)\\\triangle_y = 5 + 3\\\triangle_y =8[/tex]

[tex]x = \frac{\triangle_x}{\triangle} \\x = \frac{-12}{4} \\x = -3[/tex]

[tex]y = \frac{\triangle_y}{\triangle} \\y = \frac{8}{4} \\y = 2[/tex]

The solution to the system of equations x + 2y = 1  and -3x-2y = 5 is:

x  = -3,  y = 2

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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]

Answer:

Mia worked 4/5 of an hour less than Galen.

or

Galen spent 4/5 of an hour more working on the project.

Step-by-step explanation:

First we have to find the LCM (Lowest Common Multiple) of 5 and 3 -

3: 3, 6, 9, 15, 18, 21, 24, 27, 30

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

We can see here, that the lowest common multiple is 15.

Now we need to convert the 2/3 and 4/5 into fractions that are equivalent to something fraction that has the denominator of 15.

2/3x5= 10/15

4/5x3= 12/15

So, now, the hours of work time of both Galen and Mia are having the same denominator, now, we can subtract.

3 10/15 - 2 12/15 = 12/15

Now, we understand that 12/15 was the amount of time Galen worked more than Mai. But, still, there is still more to do.

Suspense......

SIMPLIFY!!!

12/15 both come in 3's multiplication table.

12/15 divided by 3 = 4/5

Now, our final answer simplified is 4/5.

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Answer:Yes

Step-by-step explanation:

The solution provided is complete and includes all the steps needed to solve the problem.

The first step is to calculate the area of the square patio by multiplying the length of one side by itself:

10.5 x 10.5 = 110.25.

The second step is to divide the area of the patio by the area of each individual stone to determine the number of stones needed:

110.25 ÷ 1.5 = 73.5.

Since it is not possible to have a fraction of a stone, the answer should be rounded up to the nearest whole number, which is 74.

Therefore, there are 74 stones on the patio.

To learn more about the square;

https://brainly.com/question/28776767

#SPJ3

Answer:

19,500

Step-by-step explanation:

This is probably a good one.

Answer:

this is a function

Step-by-step explanation:

Answer:

C. 2,730

Step-by-step explanation:

Answer:

thanks for telling me the answer god bless you

Step-by-step explanation:

Answer:

The number of slices of salami and the number of calories are not proportional. Step-by-step explanation: we know that. A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or . In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Step-by-step explanation:

I hope the screenshots help, for future references you can you Desmos graphing calculator.

Answer:

y = 2/3x -6

Step-by-step explanation:

slope intercept form is y = mx + b ( m is slope)

Answer:

y = -1/7x + 4

Step-by-step explanation:

(3-5)/(7-(-7)) = -2/14 = -1/7

3 = -1/7(7) + b

3 = -1 + b

b = 4

Answer:

17. first box- 88

second box- 176

18. first box- 9

second box- 5 5/8

Step-by-step explanation:

See photo.

Answer:

9.

[tex]x \geqslant - 14[/tex]

10. x<7

Answer:

D.) 256

Step-by-step explanation:

The first week she made 4 hats, the next week she made 4 times as much which is 16( 4x4=16). The third week she made 64 (16x4=64). The fourth week she made 256 (64x4)

Answer:

256 hats.

Step-by-step explanation:

You can see that every week, the number of hats knitted increases times 4;

1st week: 4 hats knitted.

1st week: 4 hats knitted in total.

2nd week: 4 times as many hats knitted the first week; (4 x 4 = 16).

2nd week: 16 hats knitted in total.

3rd week: 4 times as many hats knitted the second week; (16 x 4 = 64).

3rd week: 64 hats knitted in total.

4th week: 4 times as many hats knitted the third week; (64 x 4 = 256).

4th week: 256 hats knitted in total.

Sorry I'm late but I hope this helps :)

Answer:

$10.54

Step-by-step explanation:

42.24 divided by 4

Answer:

if x= 3, so it's 32  if x= 2, so it's 7

Step-by-step explanation:

Answer:

[tex]h=6[/tex]

[tex]k=2.5[/tex]

[tex]m=\sqrt{21}[/tex]

[tex]n=3\sqrt{10}[/tex]

[tex]p=\sqrt{17}[/tex]

Step-by-step explanation:

We can use the Pythagorean Theorem in each case.

Pythagorean Theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

Where [tex]a[/tex] and [tex]b[/tex] are two sides of a right-angle triangle and [tex]c[/tex] is Hypotenuse (the longest side opposite to the right angle)

For [tex]h[/tex]:

[tex]h^{2} +8^{2} =10^{2}[/tex]

[tex]h^{2} +64=100[/tex]

Subtract 64 from both sides:

[tex]h^{2} =100-64[/tex]

[tex]h^{2} =36\\[/tex]

[tex]h=\sqrt{36}[/tex]

[tex]h=6[/tex]

We follow the same process to find  [tex]k,m,n[/tex] and [tex]p[/tex].

Answer:

7x

Step-by-step explanation:

Answer:

7x

Step-by-step explanation:

4x+3x

4+3=7

add x, same answer of 7x

Answer:

x=-58/15

Step-by-step explanation:

distribute first 10-2.5x+12=21-10x-28

Simplify(add the numbers) 22-2.5x=-7-10x

move the variable to the left side 22-2.5x+10x=-7

move the constant to the right side -2.5x+10x=-7-22

simplify like terms 7.5x=-29

divide by 7.5                       x=-58/15

alternate forms are x=-3 13/15                or  x=-3.86

Answer:

m<v= 60 degrees

m<x= 100 degrees

Step-by-step explanation:

1) First let's find the measure of angle v. Most of the time if none of the angles are known then it is impossible to find others. However, this specific triangle is an equilateral, which has special rules. We know this is an equilateral because all the sides have the same length. Equilaterals will always have angles with measures of 60 degrees. This is due to the fact that sides and angles are proportionate. Therefore, if all the sides are the same, then the angles must be as well and 180 divided by 3 is 60.

2) Then, we can find the next measurement. This triangle is isosceles. Isosceles triangles have 2 equal sides and angles. The triangle represented above has 2 congruent sides; therefore, the base triangles must also be congruent. So we know that angles Y and W are 40. To find angle X make the expression 180-(40+40). This means that angle x must be 100 degrees.  

Step-by-step explanation:

-9/13 + -6/13

(-9 - 6)/ 13

= -15/13

hope it helps ya

Answer:

3.00x10^8

Step-by-step explanation:

So you want to make sure the number before the x10^ is beween 10 and 0 not including 10 and 0. So 1.00-9.99.

Move the demcil place up in 300,000,000 till your first number is between 1 and 9.99.

Then count how many places you moved it up, in this case 8

Add the amount of times you moved up to the x10^(in this space).

you answer is now 3.00 plus the x10^8

3.00x10^8

Answer:

(-914)×(0.1)×(-28)=2559.2

Answer: 2

Step-by-step explanation: Thank you

Answer:

The answer is 2

Answer:

both questions are same i think

look at the photo i have sent