Select all tables that represent a proportional relationship between X and Y

The 'constant of proportionality k' DOES NOT remain constant for all the points in the table.

Therefore, the table DOES NOT represent a proportional relationship between X and Y.

Step-by-step explanation:

We know that when y varies directly with x, we get

y ∝ x

y = kx

k = y/x

where k is called the 'constant of proportionality'.

Given the table

x         0          5           10             15

y         2         17           32             47

Let us calculate the k value for all the points

FOR (0, 2)

k = y/x

substitute x = 0, and y = 2

k = 2 / 0 = ∞

FOR (5, 17)

k = y/x

substitute x = 5, and y = 17

k = 17/5

k = 3.4

FOR (10, 32)

k = y/x

substitute x = 10, and y = 32

k = 32/10

k = 16/5

k = 3.2

FOR (15, 47)

k = y/x

substitute x = 15, and y = 47

k = 47/15

k = 3.1

It is clear that the 'constant of proportionality k' DOES NOT remain constant for all the points in the table.

Therefore, the table DOES NOT represent a proportional relationship between X and Y.

1e+27

step-by-step explanation:

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