n - a number
a number squared → n²
six lesss than → ... - 6
six less than a number w squared: n² - 6
Convert all the numbers to real numbers:
6√3 = 10.3923
(3.5)^2 = 12.25
√75 = 8.660
9.8 = 9.8
57/5 = 11.4
A) Now order from largest to smallest:
(3.5)^2, 57/5, 6√3, 9.8, √75
B) We found the order by solving the equations to get real numbers.
C)
Since the numbers are multiplied by a negative number, the greatest number would be the smallest number because it would be closer to zero.
The order would be the reverse of part A:
x√75, 9.8x, 6x√3, 57x/5, x(3.5)^2
D) I replaced x with -1 and calculated for real numbers. All the values were the same as A except they were the negative value.
8-9 8-19 ................................
13/15 of her allowance was spent in total.
To solve this, you'd need to find the least common denominator (LCD) so that both fractions have the same number on the bottom. In this case, the first number that you could get with 5 and 3 was 15.
Next, you'd have to multiply the numerator by the same amount as the denominator, so that the fractions are proportionate. So, for 1/5, since we had to multiply 5 by 3 to get 15, we'd multiply 1 by 3 as well, giving us 3/15. Doing the same with 2/3, we'd get 10/15.
Then, you add the two fractions together (10/15 + 3/15 = 13/15).
Now, in any other case, you could probably simplify the fraction after you've solved the problem. If we got 12/15 instead of 13/15, then we could simplify that to 4/5, since both 12 and 15 are divisible by 3. But in this case, this is the simplest form of that fraction.
Hope this helped!!!
3x² - 21
Factor 3 from both terms:
3 (x² - 7)
To me, that's as far as you should need to go. But if you want to get
completely carried away, you could go one step further, since you have
the difference of two squares:
3 (x + √7) (x - √7)
Of course, there's no end now, because the last binomial could be
considered another difference of two squares, so you'd have to
factor that too:
3 (x + √7) (√x + ⁴√7) (√x - ⁴√7)
but to me, this would be nonsense.
