x + y = 311 ---> (multiply by 3) ---> 3x + 3y = 933
.5x - 1.5y = 38550 ---> (multiply by 2) ---> x - 3y = 77100
(add down the columns) ---> 4x = 78033
x = 19508.25
x + y = 311 ---> 19508.25 + y = 311 ---> y = -19197.25
1.08^x = 3.076923
If the variable is an exponent, use logs (or lns):
log(1.08^x) = log(3.076923)
An exponent in a log expression, comes out as a multiplier:
x·log(1.08) = log(3.076923)
Divide by log(1.08):
x = log(3.076923) / log(1.08)
x = 14.60388...
(You can use either the log key or the ln key.)
If the problem is: (4√2)/2 = 2√2/1 = 2√2
2x = 0.5 + 75
2x = 75.5
x = 75.5 ÷ 2 = 37.75
They aren't equal!
A common denominator for the denominators 7 and 9 is 63.
422 3/7 = 422 27/63
367 5/9 = 357 35/63
Since you can't subtract 35 from 27, change 422 27/63 to 421 90/63
Now: 421 90/63 - 357 35/63 = 64 55/63
For a die, the possiblilities are: 1, 2, 3, 4, 5, 6. Of these numbers, the odd prime numbers are 3 and 5 (1 isn't called a prime).
So, the probability of getting an odd prime number is 1/3.
One-third of 256 chances is 85.333 times --> 83 times.
There are a few ways.
One way is to move the numeric term to the other side:
36x² - 81 = 0 Add 81 to both sides:
36x² = 81 Divide both sides by 36:
x² = 81/36 Find the square root of both sides; don't forget the ± sign:
x = ± 9/6 = ± 3/2
Since he paid $141.00 for two sets, he paid $70.50 for each one.
Without a discount, he would have paid $75.85 for each one.
The amount that he saved: $75.85 - $70.50 = $5.35 per set.
To calculate the percentage off: divide the amount saved by the original price:
To calculate the percentage off: $5.35 / $75.85 = 0.07 (approximately) = 7% off.
It's the part divided by the whole times 100: 1000 / 35000 x 100 = 2.86%
