find the coordinates of the point which divides the line segment joining the points (4, -3) and (8.5) in the ratio 3:1 internally

The coordinates of the division point are (7, 3)

Step-by-step explanation:

The coordinates of the point (x, y) which divides a segment with endpoints (x1, y1) and (x2, y2) at a ratio m1: m2 internally is ( , ).

∵ The line segment joining the points (4, -3) and (8, 5)

∴ x1 = 4 and x2 = 8

∴ y1 = -3 and y2 = 5

∵ The point divides the segment at ratio 3: 1

∴ m1 = 3 and m2 = 1

→ By using the rule above

∵ x = = =

∴ x = 7

∵ y = = =

∴ y = 3

∴ The coordinates of the division point are (7, 3)

c. (3,2,6) is the answer.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15