Answer:
x = 16
Step-by-step explanation:
The diagram can be misleading because angle A does not correspond to angle F. Rather angle F corresponds to angle C.
In congruent triangles, corresponding angles have the same measure. The sum of angles is always 180°, so we have ...
... m∠A +m∠B +m∠C = 180°
... (3x+6)° +50° +(9x -68)° = 180°
... 12x -12 = 180 . . . . . divide by °, collect terms
... x -1 = 15 . . . . . . . . . .divide by the coefficient of x
... x = 16 . . . . . . . . . . . add 1
_____
<em>Check</em>
m∠A = (3x+6)° = 54°
m∠C = (9x -68)° = 76°
The total of angles is 54° +50° +76° = 180°. . . . . as it should be
Answer:
192π
Step-by-step explanation:
cylinder volume is base times height
2πr^2 = base = 64π
height = 3
64π*3 = 192π
Answer:
Two times at (-1,0) and (2.5,0)
Step-by-step explanation:
When the graph intersects or touches x-axis, y is equal to 0
so y = -2x^2 + 3x + 5
=> 0 = -2x^2 + 3x + 5
The formula to solve a quadratic equation of the form ax^2 + bx + c = 0 is equal to x = [-b +/-√(b^2 - 4ac)]/2a
so a = -2
b = 3
c = 5
substitute in the formula
x = [-3 +/- √(3^2 - 4x-2x5)]/2(-2)
x = [-3 +/- √(9 + 40)]/(-4)
x = [-3 +/- 7]/(-4)
x1 = (-3 + 7)/(-4) = 4/-4 = -1
x2 = (-3 - 7)/(-4) = -10/-4 = 5/2 = 2.5
so the graph has two x-intercepts (-1,0) and (2.5,0), therefore it intersects x-axis two times
Answer:
$870
Step-by-step explanation:
To figure out how much the final value here is, use the formula A = P(1 + rt). (A = total accured amount, P = principal, r = rate (%), t = time (years))
A = 600 * (1 + (10 * 9/200)) (multiply 10 by 9 and put that over 200)
A = 600 * (1 + (90/200)) (90/200 simplifies to 9/20)
A = 600 * (1 + (9/20)) (add 1 (20/20) to 9/20 to get 29/20)
A = 600 * 29/20 (Multiply 600 by 29 and put that over 20)
A = 17400/20 (Divide 17400 by 20 to get 870)
A = 870
$870 is the final value.
