An if-then statement must hold under any condition. Let's take it case by case:
A. This one makes sense, and is perfect! If two angles are vertical, then they must be congruent. This holds no matter what. This is your answer.
B. This doesn't hold because Alternate Interior Angles can also be congruent (along with many others). Two angles don't <em>have </em>to be vertical to be congruent.
C. This one is also true because this is the contrapositive of Option A. (Read my reasoning on D to know what a contrapositive is). Therefore, this is correct.
D. This one is the contrapositive of B, which makes it the exact same as B. Thus, this is not the answer. Contrapositive, by the way, just means that it's the inverse and opposite of a given statement. Let's say P is the contrapositive of Q. If this is the case, then if Q is true, P must be true. In our case, Option D is the contrapositive of Option B and since Option B is not true, neither is D.
9.) 1 / [3]
When you set the denominators of 2 / 5 and 1 / 3, equal to each other, you receive a denominator of 15, the only denominator the two have in common
Answer:
3x plus 5 is definetely greater than -16 cause of the negative and 8 is bigger also then a negative
Step-by-step explanation:
Answer:
The question is incomplete, here is the complete question.
Year Real GDP per Capita
1985 6,000
1986 6,300
1987 6,700
1988 7,200
1989 7,850
1990 8,250
1991 8,450
1992 8,550
1993 8,575
1994 8,510
1995 8,370
1996 8,100
1997 7,950
1998 7,925
1999 7,960
2000 8,035
2001 8,155
The information above describes the real GDP per capita for a country for the period from 1985 through to 2001. If a new business cycle began in 1985, how long was this cycle? In which year did the peak occur? The trough occurred in which year? How long was the expansion? How long was the recession?
Step-by-step explanation:
a.If a new business cycle began in 1985, how long was this cycle?
The business cycle describes the rise and fall in production output of goods and services in an economy. In the data given above, a business cycle is complete in the year 1998. If the cycle started in 1985 then it was 14 years long.
b. In which year did the peak occur? The trough occurred in which year?
In the data given above, the peak occured in year 1993 (GDP per capita of 8,575) and trough occurred in the year 1998 (GDP per capita of 7,925).
c. How long was the expansion? How long was the recession?
Expansion was 9 years long (1985-1993) and recession was of 5 years (1994-1998).
Answer:
2x^2t + 7xy
Step-by-step explanation:
I'm guessing you want this simplified, since you have not specified what to do,
5xy + 2xy = 7xy
-x^2t + 3x^2t = 2x^2t
= 2x^2t + 7xy
