The point A has coordinates (1, 1) and the point B has coordinates (5, k).
The line AB has equation 3x+4y=7.
a. (i) show that k=2
(ii) hence find the coordinates of the mid-point of AB
b. (i) find the gradient of AB
c. The line AC is perpendicular to the line AB.
(i) Find the gradient of AC.
(ii) Hence find an equation of the line AC.
(iii)Given that the point C lies on the x-axis, find its x-coordinate.
Part II
The line L has equation y+2x=12 and the curve C has equation y=x^{2} -4x +9.
(i) Show that the x-coordinates of the points of intersection of L and C satisfy the equation x^{2} - 2x - 3 = 0
(ii) Hence find the coordinates of the points of intersection of L and C

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

~

c: y > - 1/6x + 1

step-by-step explanation:

dashed line - meaning this < or > also not equal

solid line - meaning this < or > also equal

your answer is c because y > means up & it's shaded up, but y < means down

hope this ! : )

a is 8.b is 10.c is 10.5. d is -.5

step-by-step explanation:

just minus the smallest number from the biggest.

c) the median for town a 30" is greater than the median for town b 25"

step-by-step explanation:

town a, median = q2 = 30

town b, median - q2 = 25

so the median for town a 30" is greater than the median for town b 25"