Answer:
p+q = 38/15
Step-by-step explanation:
2/3+p = 1. p = 1 - 2/3
4/5 + q = 3. q = 3 - 4/5
p + q = 1 - 2/3 + 3 - 4/5
-2/3 - 4/5 (common denominator = 15)
4 - 10/15 - 12/15 = 4 - 22/15
4 - 22/15 = (4*15 - 22)/15
= 38/15
Answer:
Perpendicular
<em />
Step-by-step explanation:
Given
Required
Is AB and CD parallel?
First, we need to calculate the slope (m) of AB and CD
For AB:
So:
For CD:
So:
For Lines to be parallel, the slope must be equal:
i.e. 
This condition is not true because:
For Lines to be perpendicular, the slope must be:
This implies:
<em>Hence, the lines are perpendicular</em>
What they said was correct!!
confirming
Answer:
x = 1/3, x = -1.
Step-by-step explanation:
2x(x + 2) + (x - 1)² = 2
Distribute the 2x into x + 2.
2x² + 4x + (x - 1)² = 2
Square (x - 1).
2x² + 4x + x² - x - x + 1 = 2
Combine terms.
2x² + x² + 4x - 2x + 1 = 2
Combine terms again.
3x² + 2x + 1 = 2
Subtract 2 from both sides.
3x² + 2x - 1 = 0
Factor.
(3x - 1)(x + 1) = 0.
Finding the x-values here is the same thing as finding the 0s, so set both of the expressions to 0.
3x - 1 = 0
Add 1 to both sides.
3x = 1
Divide by 3.
x = 1/3.
x + 1 = 0
Subtract 1 from both sides.
x = -1.
In order to determine the probability that the coin chosen is a dime, determine first the total number of sample coins. In this problem, there are 52 coins all in all. Next, divide the number of dimes in the sample with the total number of coins. This gives us 10/52. Simplifying the fraction further yields to 5/26. Thus, the probability that the coin chosen is dime is 5/26. The answer is letter c.
