Independent variables, which can be controlled or manipulated; dependent variables, which (we hope) are affected by our changes to the independent variables
The answers should be about 9 minutes and 2.4 seconds.
Answer:
2x+50 and 5x-55 both are congruent or have same measure.
Step-by-step explanation:
Since we want to prove that both lines are parallel, this means no theorems that involve with parallel lines apply here.
First of, we know that AC is a straight line and has a measure as 180° via straight angle.
x+25 and 2x+50 are supplementary which means they both add up to 180°.
Sum of two measures form a straight line which has 180°.
Therefore:-
x+25+2x+50=180
Combine like terms:-
3x+75=180
Subtract 75 both sides:-
3x+75-75=180-75
3x=105
Divide both sides by 3.
x=35°
Thus, x = 35°
Then we substitute x = 35 in every angles/measures.
x+25 = 35°+25° = 60°
2x+50 = 2(35°)+50° = 70°+50° = 120°
5x-55 = 5(35°)-55 = 175°-55° = 120°
Since 2x+50 and 5x-55 have same measure or are congruent, this proves that both lines are parallel.
Answer: 11113200
Step-by-step explanation:
We know that , the number of combination of choosing r things from n things is given by :-

Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-
Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-
Then , the number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors :-


∴ The number of ways to choose a dancing committee if it is to consist of 4 freshmen, 5 sophomores, 2 juniors, and 3 seniors = 11113200
Answer:
no
Step-by-step explanation:
A trapezoid is shown, not a bag. If we assume that this shape is supposed to be the front of the bag, Mariam does NOT have enough pink fabric to make the front of the bag from pink fabric.
The area of the trapezoid shown is ...
A = (1/2)(b1 +b2)h
A = (1/2)(9 in + 8 in)(15 in) = 127.5 in^2
This area is larger than the amount of fabric Mariam has, so she does not have enough.