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3 years ago

Kamal wrote the augmented matrix below to represent a system of equations.

Mathematics

2 answers:

atroni [7]3 years ago

8 0

Answer:

Step-by-step explanation:

edge

Sergio039 [100]3 years ago

7 0

Answer:

$\left[\begin{array}{cccc}1&0&1&|-1\\-3&-9&3&|27\\3&2&0&|-2\end{array}\right]$

Step-by-step explanation:

Given [Missing from the question]

$\left[\begin{array}{cccc}1&0&1&|-1\\1&3&-1&|-9\\3&2&0&|-2\end{array}\right]$

Required

$R_2 \to -3R_2$

This implies that, we form a new matrix where the second row of the new matrix is a product of -3 and the second row of the previous matrix.

So, we have:

$Initial =\left[\begin{array}{cccc}1&0&1&|-1\\1&3&-1&|-9\\3&2&0&|-2\end{array}\right]$

$New =\left[\begin{array}{cccc}1&0&1&|-1\\-3*1&-3*3&-3*-1&|-3*-9\\3&2&0&|-2\end{array}\right]$

$New =\left[\begin{array}{cccc}1&0&1&|-1\\-3&-9&3&|27\\3&2&0&|-2\end{array}\right]$

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PLEASE HELP!!! Trapezoid ABCD was dilated to create trapezoid A'B'C'D'. Which statements are true about the trapezoids? Check al

hichkok12 [17]

Answer:

Option A , B and D are true.

The statement which are true:

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

Step-by-step explanation:

Given in figure trapezoid ABCD;

The coordinates of ABCD are:

A= (-4, 0)

B = (-2, 4)

C = (2,4)

D = (4, 0)

Since, trapezoid ABCD was dilated to create trapezoid A'B'C'D' as shown in figure;

The coordinates of A'B'C'D' are;

A' =(-2, 0)

B'=(-1, 2)

C' = (1, 2)

D' = (2, 0)

First calculate the length of AD

Using Distance formula for any two points i.e,

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Since, A = (-4, 0) and D = (4, 0)

then;

Length of AD = $\sqrt{(4-(-4))^2+(0-0)^2} = \sqrt{(4+4)^2} =\sqrt{64}=8$ units

Therefore, the length of side AD is, 8 units.

Similarly find the length of A'D'.

Where A' = (-2, 0) and D' =(2,0)

Using distance formula:

Length of A'D' = $\sqrt{(2-(-2))^2+(0-0)^2} =\sqrt{(2+2)^2}= \sqrt{4^2} = 4$

Therefore, the length of side A'D' is, 4 units.

Now, find the slope of CD and C'D'

where C =(2, 4) , D = (4, 0) , C' = (1, 2) and D' =(2,0)

using slope formula for any two points is given by:

$Slope = \frac{y_2-y_1}{x_2-x_1}$

$Slope of CD = \frac{0-4}{4-2} = \frac{-4}{2} = -2$

Similarly,

$Slope of C'D' = \frac{0-2}{2-1} = \frac{-4}{2} = -2$

Since, Sides CD and C'D' have same slope i.e, -2

Scale factor(k) states that every coordinate of the original figure has been multiplied by the scale factor.

If k > 1, then the image is an enlargement.

if 0<k< 1, then the image is a reduction.

If k = 1, then the figure and the image are congruent.

The rule for dilation with scale factor(k) is;

$(x, y) \rightarrow (kx , ky)$

To find the scale factor:

A = (-4, 0) and A' = (-2, 0)

$(-2, 0) \rightarrow (-4k , 0)$

On comparing we ghet;

-4k = -2

Divide -4 both sides we get;

$k = \frac{1}{2}$

∴ The Scale factor is, $k = \frac{1}{2}$

Since, k < 1 which implies the image is a reduction.

Therefore, the statements which are true regarding about trapezoids are;

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, $\frac{1}{2}$

6 0

3 years ago

For what value of mc009-1 is the function one-to-one?

exis [7]

Using the concept of an one-to-one function, it will be one-to-one for c = 13.

<h3>What is an one-to-one function?</h3>

A function is said to be one-to-one if each output is mapped to only one input.

In this problem, outputs 2, 5 and 11 have already been matched to inputs 1, 3 and 5, respectively, hence the output for input 6 has to be c = 13 for a one-to-one function.

More can be learned about one-to-one functions at brainly.com/question/10853542

#SPJ1

4 0

2 years ago

Find the value of x.

Alik [6]

Answer:

$x =15$

Step-by-step explanation:

In $\odot D,$ AB and AC are chords which are equidistant from the center of the circle.

$\therefore Chord \: AB \cong Chord\: AC$

$\therefore m \widehat {AB} = m\widehat {AC}$

(Equal chords intercept equal arcs)

$\because m \widehat {AB} = (10x-23)\degree$

$\therefore m \widehat {AC} = (10x-23)\degree$

$m \widehat {AB} +m \widehat {AC} +106\degree = 360\degree$

(Arc sum postulate of a circle)

$(10x-23)\degree + (10x-23)\degree= 360\degree- 106\degree$

$2(10x-23)\degree = 254\degree$

$(10x-23)\degree = 127\degree$

$10x-23 = 127$

$10x = 127+23$

$10x = 150$

$x = \frac {150}{10}$

$x =15$

5 0

3 years ago

2.2a+3.4b=1.2a+2.6 solve for a

Ilia_Sergeevich [38]

Answer:

A = 2.6-3.4b

Step-by-step explanation:

4 0

3 years ago

Please answer these questions and have the work shown:

ahrayia [7]

Answer:

number one 50 I think and 3 is 75 not positive but I hope it helps

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers