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vagabundo [1.1K]
3 years ago
11

Describe the effect of the transformation (x,y) --> (x,y+4)

Mathematics
1 answer:
muminat3 years ago
8 0

Answer:

D. Vertical translation of 4 units.

Step-by-step explanation:

This transformation keeps x the same but shifts y up 4 units (adding 4 to it). This is a vertical shift up 4, which we can also call a vertical "translation."

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Convert the following systems of equations to an augmented matrix and use Gauss-Jordan reduction to convert to an equilivalent m
Rasek [7]

Answer:

System of equations:

x_1+2x_2+2x_3=6\\2x_1+x_2+x_3=6\\x_1+x_2+3x_3=6

Augmented matrix:

\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right]

Reduced Row Echelon matrix:

\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right]

Step-by-step explanation:

Convert the system into an augmented matrix:

\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right]

For notation, R_n is the new nth row and r_n the unchanged one.

1. Operations:

R_2=-2r_1+r_2\\R_3=-r_1+r_3

Resulting matrix:

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

2. Operations:

R_2=-\frac{1}{3}r_2

Resulting matrix:

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

3. Operations:

R_3=r_2+r_3

Resulting matrix:

\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&2&2\end{array}\right]

4. Operations:

R_3=\frac{1}{2}r_3

Resulting matrix:

\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right]

4 0
3 years ago
WHOEVER GETS RIGHT GETS BRAINLIEST!!
ozzi

Answer:

Answer B:  min. value at -6

Step-by-step explanation:

Complete the square of f(x) = x^2 - 2x - 5.

Note:  Please use " ^ " to denote exponentiation, as shown.

Start with f(x) = x^2 - 2x - 5.

Identify the coefficient of the x term:  it is 2.

Take half of that and square your result:  (1/2)(2) = 1, and then 1^2 = 1.

Add and subtract this 1 between the 2x term and the constant term:

f(x) = x^2 - 2x    + 1   - 1  - 5

Rewrite x^2 - 2x + 1 as a perfect square:

f(x) = (x - 1)^2 - 1 - 5, or    f(x) = (x - 1)^2 - 6

Compare this to the standard form

                                        f(x) = (x - h)^2 + k

We see that h = 1 and k = -6.

The vertex is located at (h, k); here, it's located at (1, -6).

Thus, the minimum value of this function is at the vertex (1, -6).

This agrees with Answer B:  min. value at -6.

3 0
3 years ago
If the sum of a number and eight is tripled the result is four less than twice the number. Find the number
DiKsa [7]

Answer:

-28

Step-by-step explanation:

Let the number be x

Given that,

3( x+ 8) = 2x - 4

3x + 24 = 2x -4

3x-2x = -4-24

x= -28

Hope it helps....

8 0
2 years ago
Which perfect squares does the number 69 falls in between?
riadik2000 [5.3K]

Answer:

64 and 81

Step-by-step explanation:

4 0
3 years ago
3b 2a=5a−6 solve the equation for a in terms of <br> b.
oee [108]
Is it 3b-2a=5a-6
or
3b+2a=5a-6

you are missing the sign of 2a
4 0
3 years ago
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