Is the graph of the linear inequality y > -x - 3?

Second Graph

Step-by-step explanation:

Given the linear inequality, y > -x - 3, an easier way of determining its graph is through a test point.

A test point is an ordered pair that is not on the actual line of the graph. The point of origin, (0, 0) is often used for this purpose.

Substitute the values of (0, 0) into the linear inequality to find out whether it satisfies the given inequality statement:

y > -x - 3

0 > - (0) - 3

0 > - 0 - 3

0 > -3 (True statement). Therefore, the shaded region must contain the test point since it is one of the solutions to the given linear inequality.

Hence, the correct answer is the second graph.

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

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