Convert to fractional notation (improper fraction): 6 5/8
1 answer:
You might be interested in
Answer:
see attached
Step-by-step explanation:
That things are the same when they're both the same as something else is the "transitive property." It applies to many things, from interchangeable parts to math expressions to geometrical objects, as here.
When there are 3 given statements, and two of them are shown as such, it isn't hard to determine what the third one is.
The remaining blanks can be filled by the process of elimination.
Answer:
see explanation
Step-by-step explanation:
A
Given
(x² + 3)² + 21 = 10x² + 30 ← factor out 10 from each term on the right side
(x² + 3)² + 21 = 10(x² + 3) ← subtract 10(x² + 3) from both sides
(x² + 3)² - 10(x² + 3) + 21 = 0
Substituting u = x² + 3 into the equation gives
u² - 10u + 21 = 0 → D
---------------------------------------------
B
Using u² - 10u + 21 = 0 to solve the equation
Consider the factors of the constant term (+ 21) which sum to give the coefficient of the u- term (- 10)
The factors are - 3 and - 7, since
- 3 × - 7 = 21 and - 3 - 7 = - 10, thus
(u - 3)(u - 7) = 0
Equate each factor to zero and solve for u
u - 3 = 0 ⇒ u = 3
u - 7 = 0 ⇒ u = 7
We now have to use the substitution to convert the solutions into terms of x, that is
x² + 3 = 3 ( subtract 3 from both sides )
x² = 0 ⇒ x = 0 → D
x² + 3 = 7 ( subtract 3 from both sides )
x² = 4 ( take the square root of both sides )
x = ± = ± 2
Thus x = - 2 → C
x = 2 → E
