Simplify -9 + (-1/3 y ) + 6 -4/3y.

Maggie graphed the image of a 90 counterclockwise rotation about vertex A of . Coordinates B and C of are (2, 6) and (4, 3) and

Lemur [1.5K]

Answer:

A(2,2)

Step-by-step explanation:

Let the vertex A has coordinates $(x_A,y_A)$

Vectors AB and AB' are perpendicular, then

$\overrightarrow {AB}=(2-x_A,6-y_A)\\ \\\overrightarrow {AB'}=(-2-x_A,2-y_A)\\ \\\overrightarrow {AB}\perp\overrightarrow {AB'}\Rightarrow \overrightarrow {AB}\cdot \overrightarrow {AB'}=0\Rightarrow (2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0$

Vectors AC and AC' are perpendicular, then

$\overrightarrow {AC}=(4-x_A,3-y_A)\\ \\\overrightarrow {AC'}=(1-x_A,4-y_A)\\ \\\overrightarrow {AC}\perp\overrightarrow {AC'}\Rightarrow \overrightarrow {AC}\cdot \overrightarrow {AC'}=0\Rightarrow (4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0$

Now, solve the system of two equations:

$\left\{\begin{array}{l}(2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0\\ \\(4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0\end{array}\right.\\ \\\left\{\begin{array}{l}-4-2x_A+2x_A+x_A^2+12-6y_A-2y_A+y^2_A=0\\ \\4-4x_A-x_A+x_A^2+12-3y_A-4y_A+y_A^2=0\end{array}\right.\\ \\\left\{\begin{array}{l}x_A^2+y_A^2-8y_A+8=0\\ \\x_A^2+y_A^2-5x_A-7y_A+16=0\end{array}\right.$

Subtract these two equations:

$5x_A-y_A-8=0\Rightarrow y_A=5x_A-8$

Substitute it into the first equation:

$x_A^2+(5x_A-8)^2-8(5x_A-8)+8=0\\ \\x_A^2+25x_A^2-80x_A+64-40x_A+64+8=0\\ \\26x_A^2-120x_A+136=0\\ \\13x_A^2-60x_A+68=0\\ \\D=(-60)^2-4\cdot 13\cdot 68=3600-3536=64\\ \\x_{A_{1,2}}=\dfrac{60\pm8}{2\cdot 13}=\dfrac{34}{13},2$

Then

$y_{A_{1,2}}=5\cdot \dfrac{34}{13}-8 \text{ or } 5\cdot 2-8\\ \\=\dfrac{66}{13}\text{ or } 2$

Rotation by 90° counterclockwise about A(2,2) gives image points B' and C' (see attached diagram)

8 0

3 years ago

Dane started running at half past three in the afternoon. He stopped running at ten minutes after four. How long did Dane run?

Tatiana [17]

He ran for 40 minutes!

4 0

3 years ago

Read 2 more answers

Solve over the set of real numbers for the equation below x-2=√2x-1

Anon25 [30]

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

<h3>What is the solution of the equation?</h3>

The solution of the equation means the value of the unknown or variable.

The equation is given below.

x – 2 = √(2x – 1)

Square on both side, then we have

(x – 2)² = 2x – 1

x² – 4x + 4 = 2x – 1

x² – 6x + 5 = 0

x² – 5x – x + 5 = 0

x(x – 5) – 1(x – 5) = 0

(x – 5)(x – 1) = 0

x = 1, 5

The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.

More about the solution of the equation link is given below.

brainly.com/question/545403

#SPJ1

6 0

1 year ago

A cross-shaped pattern is made by arranging four identical rectangles around the side of a square, as shown in the diagram.

const2013 [10]

Answer:

88 cm

Step-by-step explanation:

The side of the square = 6 cm, so the shorter side of each rectangle = 6 cms.

The area of each rectangle = 36 * 1 1/3

= 36 * 4/3 = 48 cm^2

So the longer side of each rectangle = 48 / 6 = 8 cms

Therefore, the perimeter of the whole figure

= 4( shorter sides ) + 8(longer sides)

= 4*6 + 8*8

= 24 + 64

= 88 cm (answer)

7 0

3 years ago

9. (12 pts) daniel is paying $600 for his auto insurance, and he is wondering if he is overpaying compared to his friends. he se

Karolina [17]

Answer:

Step-by-step explanation:

1) The sample and the population of this study is the friends who replied his email which includes in his contact list. then, the number of the replied to his email are 9 friends.

population: the whole friends include in his contact list.

3) Type I error occurs when one incorrectly rejects the null hypothesis

Here there is possibility of type I error

7 0

3 years ago