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1. Sample space:

2. Probabilities of getting each sum

Explanation:

1. Sample space.

Sample space is the set consituted by the total possible outcomes. Since each number cube has 6 possible outcomes, the number of possible outcomes when you toss two number cubes is 6×6 = 36.  Thus, your sample space must have 36 elements.

You can found the sample space using a chart:

123456

1234567

2345678

3456789

45678910

567891011

6789101112

Hence, the sample space is the set of all the numbers inside the square:

2. Probabilities of getting each sum.

The probability of getting each sum is the number of times each sum appear in the sample space divided by the size of the sample space (36):

Probability of getting 2:

Probability of getting 3:

Probability of getting 4:

Probability of getting 5:

Probability of getting 6:

Probability of getting 7:

Probability of getting 8:

Probability of getting 9:

Probability of getting 10:

Probability of getting 11:

Probability of getting 12:

-8

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