They're not equivalent.
(vertical bars) represents the absolute value of x. How it works is that it turns negative numbers positive but leaves 0 and positive numbers alone (hence it gets a number's distance from 0 on the number line).
(square brackets) usually represents the floor function, which returns the largest integer that is less than or equal to x. (The floor of x can also be written as
--- it depends on what your textbook/source says).
To solve
, you first transform it into the equivalent equation
. Then by definition of absolute value, there are only two solutions for the first equation: x = 10 or x = -10.
[x] = 10 has infinitely many solutions. For example, the floor of 10 is 10, so
, thus a solution for the second equation is x = 10
The floor of 10.1 is 10, so
, thus another solution for the second equation is x = 10.1.
The two equations do not have the same solution set (as x = 10.1 does not solve |x| - 3 = 7 but solves [x] = 10), so they're not equivalent.
Answer:
(b)
Step-by-step explanation:
Under a reflection in the y-axis
a point (x, y ) → (- x, y ), hence
P(4, 1 ) → P'(- 4, 1 )
Q(2, - 8 ) → Q'(- 2, - 8 )
R(- 8, 1 ) → R'(8, 1 )
<u><em /></u><em />The correct answer to the question above is 4/13. Below it shows how it's achieved...<u><em>
EQUATION:</em></u>
P(A|B) = <u>P(A ∩ B)
</u> P(B)
<u>
</u>Step 1: Identify
P(B) = 5/14
P(A ∩ B) = 10/91
<u>
</u>Step 2: Insert into the equation and Solve
10/91 ÷ 5/14
Use reciprocal to divide
10/91 × 14/5
Simplify the answer
140/455
Simplified (Final Answer)
4/13
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</u>
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</u>
Answer:
Step-by-step explanation:So to me I would trust the medical journal published in 1982. Back then they were more people that studied those kind of things. And back then there was like people finding out different types of plants and medical resources. (hope this helps you)..:)