F(x) = x2 - 4x

) Find the coordinates of the point A' which is the symmetric point

soldier1979 [14.2K]

Let, coordinate of point A' is (x,y).

Since, A' is the symmetric point A(3, 2) with respect to the line 2x + y - 12 = 0.

So, slope of line containing A and A' will be perpendicular to the line 2x + y - 12 = 0 and also their center lies in the line too.

Now, their center is given by :

$C( \dfrac{x+3}{2}, \dfrac{y+2}{2})$

Also, product of slope will be -1 .( Since, they are parallel )

$\dfrac{y-2}{x-3} \times -2 = -1\\\\2y - 4 = x - 3\\\\2y - x = 1$

x = 2y - 1

So, $C( \dfrac{2y -1 +3}{2}, \dfrac{y+2}{2})\\\\C( \dfrac{2y + 2}{2}, \dfrac{y+2}{2})$

Also, C satisfy given line :

$2\times ( \dfrac{2y + 2}{2}) + \dfrac{y+2}{2} = 12\\\\4y + 4 + y + 2 = 24\\\\5y = 18\\\\y = \dfrac{18}{5}$

Also,

$x = 2\times \dfrac{18}{5 } - 1\\\\x = \dfrac{31}{5}$

Therefore, the symmetric points is $A'(\dfrac{31}{5}, \dfrac{18}{5})$ .

7 0

2 years ago

On a farm in iowa lived grandpa bill in a big yellow house on the top of the hill. His 70th birthday was this very day. All of h

DENIUS [597]

Let g be the number of grandchildren, and d be the number of dogs. They both have only one head, so the number of heads is

$g+d=33$

Grandchildren have 2 legs, while dogs have 4. So, the total number of legs is

$2g+4d=84$

From the first equation (the one for the heads) we can derive

$g=33-d$

Substitute this into the second to get

$2g+4d=84 \implies 2(33-d)+4d=84 \iff 2d=18 \iff d=9$

So, there are 9 dogs and (from the first equation

$g=33-9=24$

8 0

2 years ago

Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus

Nuetrik [128]

The equation of a line that is passing through the points (0, 4) and (1, 6) will be y = 2x + 4.

<h3>What is the linear system?</h3>

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A coordinate plane. The x-axis and y-axis are each scaled by one.

A graph of a line goes through the points (0, 4) and (1, 6) will be

The equation of a line that is passing through the points (0, 4) and (1, 6) will be

y - 4 = [6 - 4 / 1 - 0] (x - 0)

y - 4 = 2x

y = 2x + 4

The graph is given below.

More about the linear system link is given below.

brainly.com/question/20379472

#SPJ1

6 0

2 years ago

HELP ASAP 10 POINTSSS

kiruha [24]

Answer:

Complementary angles, adjacent angles

Step-by-step explanation:

Which relationships describe angles 1 and 2?

Options: Complementary angles, vertical angles, supplementary angles, adjacent angles

Angles 1 and 2 are opposite to the 90° angle. So, the angles' relationship to that angles is a vertical angle, meaning that the two add up to 90°.

Complementary angles add up to 90°, so this option is correct.

Vertical angles are the pairs of opposite angles formed by two intersecting lines. Because the two angles do not follow this definition, this option is incorrect.

Supplementary angles add up to 180°. However, we know that the two add up to 90°, so this option is incorrect.

Adjacent angles are angles that are next to each other, so this option is correct.

I hope this helps! Feel free to ask any questions!

6 0

2 years ago

Jenny has nine marbles, but her best friend Susie gives her ten more! However, the neighborhood bully, Danny, steals four marble

wlad13 [49]

Answer:

50

Step-by-step explanation:

she starts with 9 plus the 10. so she has 19. Danny takes 4 so she has 15. then she trades so she gets 3 per marble she trades so it's like 15 times 3 which is 45. plus the 7 her parents gave her which is 52 and she gives 2 to her sister. so it's 50

5 0

2 years ago

F(x) = x2 - 4x - 21.