84/2 = 42
42/2 = 21
21/3 = 7
7/7 = 1
84 = 2^2 * 3 * 7
Answer:
x = -7/40
, y = -11/20
Step-by-step explanation:
Solve the following system:
{12 x - 2 y = -1 | (equation 1)
4 x + 6 y = -4 | (equation 2)
Subtract 1/3 × (equation 1) from equation 2:
{12 x - 2 y = -1 | (equation 1)
0 x+(20 y)/3 = (-11)/3 | (equation 2)
Multiply equation 2 by 3:
{12 x - 2 y = -1 | (equation 1)
0 x+20 y = -11 | (equation 2)
Divide equation 2 by 20:
{12 x - 2 y = -1 | (equation 1)
0 x+y = (-11)/20 | (equation 2)
Add 2 × (equation 2) to equation 1:
{12 x+0 y = (-21)/10 | (equation 1)
0 x+y = -11/20 | (equation 2)
Divide equation 1 by 12:
{x+0 y = (-7)/40 | (equation 1)
0 x+y = -11/20 | (equation 2)
Collect results:
Answer: {x = -7/40
, y = -11/20
Perpendicular means that it has a slope that is the reciprocal of the original, and parallel means that the slopes are the same.
Answer:
<u>P (E1) = 1/2 or 50%</u>
<u>P (E2) = 3/13 or 23%</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Number of playing cards = 52
Number of suits = 4
Number of cards per suit = 13
Number of black suits = 2
Number of red suits = 2
2. Suppose E1 = the outcome is a red card and E2 = the outcome is a face card (K, Q, J). Determine P(E1 or E2).
P (E1) = Number of red cards/Total of playing cards
P (E1) = 26/52 = 1/2 = 50%
P (E2) = Number of face cards/Total of playing cards
P (E2) = 12/52 = 3/13 = 23%
