Answer:
∠QST = 115°
Step-by-step explanation:
Because all angles on a straight line must add to 180 and so should the total angles in a triangle:
∠UST + 23x = 180
And:
∠UST + 12x + 55 = 180
So knowing this, ∠U + ∠T must add up to 23x because 180 - ∠UST is the same for both above equations:
55 + 12x = 23x
Subtract 12x from both sides to isolate the 55 and 23x:
55 + 12x - 12x = 23x - 12x
55 = 11x
Divide both sides by 11:
x = 5
As ∠QST = 23x, we can substitute in the known x:
23x =
23(5) =
23 * 5 = 115
So ∠QST = 115°
Hope this helps!
Volume of hemisphere = 2πr³/3
Volume of cone = πr²h/3
Where r = 2 and h = 9
Volume = volume of hemisphere + volume of cone
Volume = 2π(2)³/3 + π(2)²(9)/3
Volume = 16π/3 + 36π/3
Volume = 52π/3
Answer:
The two integers are 23 and 12
Step-by-step explanation:
Let the two integers be f and g
Let f be the biggest and g the smallest integer
From the first statement, the sum of the two integers is 35 i.e
f + g = 35. (1)
From second statement, we were told that when the smaller integer is subtracted from twice the larger, the result is 34 i.e
2f — g = 34. (2)
Now we'll solve by elimination method as follows:
Add equation (2) and (1) together:
2f — g = 34
+ f + g = 35
3f = 69
Divide both side by the coefficient of f i.e 3
f = 69/3
f = 23
Substituting the value of f into equation(1)
f + g = 35
23 + g = 35
Collect like terms
g = 35 — 23
g = 12
The two integers are 23 and 12
The answer would be False.
