X + (x + 1) + (x + 2) = 126
3x = 123
x = 41
So the sides are 41, 42 and 43
Answer:
E. 300
Step-by-step explanation:
A rectangle split in half diagonally yields 2 right triangles.
((For this problem, you are probably supposed to use the pythagorean theorem to find the diagonal length, and then calculate perimeter (length of fence around triangular field). In other words:
(sqrt( (50m)^2 + (120m)^2 )) + 50m + 120m)
))
By definition, the hypotenuse (diagonal) is the longest side.
This means that it must be longer than 120m.
If you add the 2 sides (50m + 120m), you get 170m.
Since the third side has to be longer than 120m, the answer _must_ be over 290m (170m + 120m).
300m is the only answer that fits.
The error is in the second step they subtracted 3 from both sides but it was a 3x, which you can not do.
Correction.
9x+18+3x=1
12x+18=1
12x=-17
x=-17/12
9514 1404 393
Answer:
$3400
Step-by-step explanation:
The way these tax tables are structured, you pay 3% on the first $10,000, 5% on the next $40,000, and 5.5% on the remaining $20,000 above $50,000.
tax = 0.03·10,000 +0.05·(50,000 -10,000) +0.055·(70,000 -50000)
= 300 + 2000 +1100
= 3400 . . . dollars
The tax owed on $70,000 is $3,400.
_____
<em>Additional comment</em>
I like to rewrite this sort of table to a different format:
- 3% of income . . . . . . . . . . . . . . . applies for income ≤ 10,000
- (5% of income) -$200 . . . . . . . . applies for 10,000 < income ≤ 50,000
- (5.5% of income) -$450 . . . . . . .applies for 50,000 < income ≤ 100,000
For an income of $70,000, the tax computation using this form is one multiplication and one addition, rather than 3 multiplications and 4 additions as used when navigating the given table.
Use the the double angle formula:
sin(2A)=2sin(A)cos(A)
substitute 2x for A, then
20sin(2x)cos(2x)=10(sin(2(2x))cos(2(2x))=10sin(4x)
