Answer:
Step-by-step explanation:
Question (1).
OQ and RT are the parallel lines and UN is a transversal intersecting these lines at two different points P and S.
A). ∠OPS ≅ ∠RSU [corresponding angles]
B). m∠OPS + m∠RSP = 180° [Consecutive interior angles]
C). m∠OPS + m∠OPN = 180° [Linear pair of angles]
D). Since, ∠OPS ≅ ∠TSP [Alternate interior angles]
And m∠TSP + m∠TSU = 180° [Linear pair of angles]
Therefore, Option (A) is the correct option.
Question (2).
A). m∠RSP + m∠RSU = 180° [Linear pair of angles]
B). m∠RSP + m∠PST = 180° [Linear pair of angles]
C). ∠RSP ≅ ∠TSU [Vertically opposite angles]
D). m∠RSP + m∠OPS = 180° [Consecutive interior angles]
Therefore, Option (C) will be the answer.
The correct answer is: A. 150 more students tickets sold than adult tickets.
Answer:
c.) y=2x+3
Step-by-step explanation:
the slope is 2 and the y-intercept is 3
Answer:
for the perimeter to be made into a equation it would take the equation
2(3x - 5) + 2(2x + 1)
And for the perimeter to equal 42 x would have to equal 5
Step-by-step explanation:
so first of all we have to find our equation to equal 42:
2(3x - 5) + 2(2x + 1) = 42
you then multiply 2 for both parentheses:
(3x * 2) + (-5 * 2) + (2x * 2) + (1 * 2) = 42
so its now:
6x -10 + 4x + 2 = 42
now your going to add variables to variables and numbers to numbers:
(6x + 4x) + ( -10 + 2) = 42
to get:
10x + (-8) = 42
Now your going to add 8 to both sides:
10x + (-8) = 42
+8 +8
Giving the equation:
10x = 50
now you divide both sides by 10 to get:
10x/ 10 = 50/10
x = 5
to solve you put 5 in place of the variable x:
2(3*5 - 5) + 2(2*5 + 1)
2(15 - 5) + 2(10 + 1)
20 + 22 = 42
So x equals 5 if the perimeter equaled 42
Triangle is attached below
The triangle is 12 by 10 by 8
Perimeter:
To find perimeter we add all the sides of the triangle
Perimeter P = 12 + 10 + 8 = 30 units
Semi perimeter:
Semi perimeter is half of its perimeter
We know P = 30
Semi perimeter s= 
= 
= 15 units
Area:
If we know the sides of the triangle then we use Heron's formula to find the area of the triangle
Where s= semi perimeter
a,b,c are the sides of the triangle
s= 15 units
a= 12 units
b= 10 units
c= 8 units
A= 39.7 square units
