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1 year ago

BRAINLIEST ANSWERS ONLY.

Mathematics

1 answer:

mars1129 [50]1 year ago

4 0

Answer:

Heyy

Step-by-step explanation:

△ABC is a right angled triangle and right angle at B

sinA=

, cosA=

⟹sinA+cosA=

BC+AB

[We know that sum of two sides of a triangle is greater than the third side]

⟹sinA+cosA>

Hence, sinA+cosA>1

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A sequence of transformations which moves ΔFGH onto ΔIJK shows that ΔFGH ≅ ΔIJK. Which part of the triangles are congruent by CP

JulijaS [17]

Answer: could you make the question a little clearer

Step-by-step explanation:

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2 years ago

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Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 3y 6212 3x + (x, y. z)

Gekata [30.6K]

Answer:

The solution of the system of linear equations is $x=3, y=4, z=1$

Step-by-step explanation:

We have the system of linear equations:

$2x+3y-6z=12\\x-2y+3z=-2\\3x+y=13$

Gauss-Jordan elimination method is the process of performing row operations to transform any matrix into reduced row-echelon form.

The first step is to transform the system of linear equations into the matrix form. A system of linear equations can be represented in matrix form (Ax=b) using a coefficient matrix (A), a variable matrix (x), and a constant matrix(b).

From the system of linear equations that we have, the coefficient matrix is

$\left[\begin{array}{ccc}2&3&-6\\1&-2&3\\3&1&0\end{array}\right]$

the variable matrix is

$\left[\begin{array}{c}x&y&z\end{array}\right]$

and the constant matrix is

$\left[\begin{array}{c}12&-2&13\end{array}\right]$

We also need the augmented matrix, this matrix is the result of joining the columns of the coefficient matrix and the constant matrix divided by a vertical bar, so

$\left[\begin{array}{ccc|c}2&3&-6&12\\1&-2&3&-2\\3&1&0&13\end{array}\right]$

To transform the augmented matrix to reduced row-echelon form we need to follow these row operations:

multiply the 1st row by 1/2

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\1&-2&3&-2\\3&1&0&13\end{array}\right]$

add -1 times the 1st row to the 2nd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\3&1&0&13\end{array}\right]$

add -3 times the 1st row to the 3rd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\0&-7/2&9&-5\end{array}\right]$

multiply the 2nd row by -2/7

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&-7/2&9&-5\end{array}\right]$

add 7/2 times the 2nd row to the 3rd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&3&3\end{array}\right]$

multiply the 3rd row by 1/3

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&1&1\end{array}\right]$

add 12/7 times the 3rd row to the 2nd row

$\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&0&4\\0&0&1&1\end{array}\right]$

add 3 times the 3rd row to the 1st row

$\left[\begin{array}{ccc|c}1&3/2&0&9\\0&1&0&4\\0&0&1&1\end{array}\right]$

add -3/2 times the 2nd row to the 1st row

$\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&4\\0&0&1&1\end{array}\right]$

From the reduced row echelon form we have that

$x=3\\y=4\\z=1$

Since every column in the coefficient part of the matrix has a leading entry that means our system has a unique solution.

7 0

3 years ago

Which products result in a difference of squares? Check all that apply. (x – y)(y – x) (6 – y)(6 – y) (3 + xz)(–3 + xz) (y2 – xy

kondaur [170]

difference of squares formula:
a^2 – b^2 = (a + b)(a – b)

so answers are

(3 + xz)(–3 + xz)
(y2 – xy)(y2 + xy)
(64y2 + x2)(–x2 + 64y2)


cause
(3 + xz)(–3 + xz)
= (xz + 3 )(xz - 3)
= x^2z^2 - 9

--------------
(y^2 – xy)(y^2 + xy)
= y^4 -x^2y^2

----------

(64y^2 + x^2)(–x2 + 64y^2)
=(64y^2 + x2)(64 - x^2)
= 64^2 y^4 - x^4

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3 years ago

An ostrich can run 25 miles in 40 minutes. How many minutes will it take the ostrich to run 40 miles if it runs at the same spee

fenix001 [56]

The Ostrich will take 64 minutes to cover 40 miles.

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