In a triangle, the three interior angles always add to 180°
5x + 7x + 8x = 180
20x = 180
x = 180/20
x = 9
m∠1 = 5x = 5*9 = 45°
m∠2 = 7x = 7*9 = 63°
m∠3 = 8x = 8*9 = 72°
Answer:
45°, 63° and 72°
(a) Answer: One solution.
Explanation: two lines that have same slope with opposite sign will necessarily cross each other at a single point, as one is "pointing uphill" and the other "downhill."
(b) Answer: Infinitely many solutions.
Explanation:
2x + 3y = 5.5
4x + 6y = 11 | divide by 2
-->
2x + 3y = 5.5
2x + 3y = 5.5
--> equations are identical.
2x + 3y = 2x + 3y
so any (x,y) will satisfy this equation. This means infinitely many solutions.
(c) Answer: One solution
Explanation:
Continuing the two lines it becomes obvious they will cross at one point (the solution)
(d) Answer: No solution
Explanation: If the two lines are parallel, they will never cross (by definition of "parallel"). Therefore there will be no solution to the corresponding linear system.
First place: Liz
Faster: Amanda
Longest time: Steve
Answer:
5/12
Step-by-step explanation:
Since 1/2 is the same distance from zero and one, we can use it to judge whether a fraction is closer to 0 or 1.
Since 5/8 is greater than 4/8 which is 1/2, it is closer to 1.
Since 8/10 is greater than 5/10 which is 1/2, it is closer to 1.
Since 5/12 is less than 6/12 which is 1/2, it is closer to 0.
So our answer is C. 5/12
