What is the least integer value in the solution set to 7(3x – 1) ≤ 4x? –1
2
3
7

Answer:

a) Δ ABC is rotated around the origin by angle 180° and then translated 1

unite to the right and 3 units up

b) R (O , 180°) and T (x + 1 , y + 3)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 180° then its image

 is (-x , -y)

- If the point (x , y) translated horizontally to the right by h units

 then its image is  (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then its image is  (x - h , y)

- If the point (x , y) translated vertically up by k units

 then its image is  = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then its image is  (x , y - k)

* Lets solve the problem

∵ Δ ABC change its place from 2nd quadrant to the 4th quadrant

  and reverse its direction Point A up and its image A" down

∵ No change in its size

∴ Triangle ABC rotates 180° clockwise around the origin

# Remember : There is no difference between rotating 180° clockwise

  or  anti-clockwise around the origin

∵ The vertices of Δ ABC are:

# A = (-3 , 5)

# B = (-3 , 2)

# C = (-1 , 2)

∵ If point (x , y) rotated about the origin by angle 180° then its image

 is (-x , -y)

∴ A'' = (3 , -5)

∴ B'' = (3 , -2)

∴ C'' = (1 , -2)

∴ Triangle ABC rotates 180° around the origin to form ΔA"B"C"

∵ The vertices of Δ A'B'C are:

# A' = (4 , -2)

# B' = (4 , 1)

# C' = (2 , 1)

- By comparing the x-coordinates and y-coordinates of points of

 Δ A''B''C'' and Δ A'B'C' we will find that every x-coordinate add by 1

 and every y-coordinate add by 3

∵ 4 - 3 = 1 and 2 - 1 = 1 ⇒ x- coordinates

∵ -2 - (-5) = -2 + 5 = 3 and 1 - (-2) = 1 + 2 = 3 ⇒ y-coordinates

∴ ΔA''B''C'' translates to the right 1 unite and up 3 units to form

  Δ A'B'C'

a) Δ ABC is rotated around the origin by angle 180° and then

   translated 1 unite to the right and 3 units up

b) R (O , 180°) and T (x + 1 , y + 3)

Answer:

0.1414... in a fraction is 14/99

Step-by-step explanation:

Given the number 0.1414...

we have to represent the above in terms of fraction

Let x=0.1414....  →  (1)

Multiplying by 100 on both sides

100x=14.1414....     → (2)

Subtract (1) from (2), we get

99x=14

x=14/99

hence, 0.1414... in a fraction is 14/99

Answer:

y = 12x - 5

Step-by-step explanation:

Answer:

y = (12 - 5)

Brainliest?

Step-by-step explanation:

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