Answer:
x = -5.39
Step-by-step explanation:
x + (−2.4) = −7.79
x = −7.79 + 2.4
x = -5.39
Answer:
see explanation
Step-by-step explanation:
(43)
3
- 75x³ ← factor out 3x³ from each term
= 3x³(x² - 25) ← this is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , thus
x² - 25 = x² - 5² = (x - 5)(x + 5)
Thus
3
- 75x³ = 3x³(x - 5)(x + 5)
(44)
81c² + 72c + 16 ← is a perfect square of the form
(ac + b)² = a²c² + 2abc + b²
Compare coefficients of like terms
a² = 81 ⇒ a =
= 9
b² = 16 ⇒ b =
= 4
and 2ab = 2 × 9 × 4 = 72
Thus
81c² + 72c + 16 = (9c + 4)²
Answer:
y= -1x+1
Step-by-step explanation:
Answer: 648
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Explanation:
We have this set of digits: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
From that set, we can only pick three items. We cannot select the same digit twice.
Consider a blank three digit number such that it is composed of slot A, slot B, slot C.
Since the number must be larger than 100, this means that we cannot select 0 as the first digit. We go from a pool of 10 digits to 10-1 = 9 digits for our first selection.
In other words, we have this subset to select from
{1, 2, 3, 4, 5, 6, 7, 8, 9}
So we have 9 choices for slot A.
For slot B, we also have 9 choices since 0 is now included. For instance, if we selected the digit '4' then we have this subset of choices left over: {0, 1, 2, 3, 5, 6, 7, 8, 9} which is exactly 9 items.
For slot C, we have 9-1 = 8 items left to choose from. For example: If we choose '4' for slot A, and '2' for slot B, then we have this subset to choose from: {0, 1, 3, 5, 6, 7, 8, 9} exactly 8 items
In summary so far, we have...
9 choices for slot A
9 choices for slot B
8 choices for slot C
Giving a total of 9*9*8=81*8=648 different three digit numbers. You'll notice that I'm using the counting principle which allows for the multiplication to happen. Think of a probability tree.
<span>2t + 8 - 8 - t = -3
t = -3 (combine like terms)</span>