An equation has infinitely many solutions if it can be manipulated all the way to an identity (i.e. an equality where the right and left hand side are the same). We have:
A) 
which is impossible
B) 
which is an equality
C) 
which has a unique solution
D) 
which has a unique solution
Answer:
1000 in
Step-by-step explanation:
Given
The dimension of the small cube is 1\ in.1 in.
No of the cubes is 10^6106
If the small cubes are arranged on the floor
The area of the cubes is
\Rightarrow 10^6\times 1^2\ in.^2⇒106×12 in.2
Answer:
(x - 5)² = 41
Step-by-step explanation:
* Lets revise the completing square form
- the form x² ± bx + c is a completing square if it can be put in the form
(x ± h)² , where b = 2h and c = h²
# The completing square is x² ± bx + c = (x ± h)²
# Remember c must be positive because it is = h²
* Lets use this form to solve the problem
∵ x² - 10x = 16
- Lets equate 2h by -10
∵ 2h = -10 ⇒ divide both sides by 2
∴ h = -5
∴ h² = (-5)² = 25
∵ c = h²
∴ c = 25
- The completing square is x² - 10x + 25
∵ The equation is x² - 10x = 16
- We will add 25 and subtract 25 to the equation to make the
completing square without change the terms of the equation
∴ x² - 10x + 25 - 25 = 16
∴ (x² - 10x + 25) - 25 = 16 ⇒ add 25 to both sides
∴ (x² - 10x + 25) = 41
* Use the rule of the completing square above
- Let (x² - 10x + 25) = (x - 5)²
∴ (x - 5)² = 41
Answer:
<h3>A. </h3>
- log
= log 3 - x³ log x = log 3
- 3x³ log x = 3 log 3
- x³ log x³ = log 3³
= 3³- x³ = 3
- x =
<h3>B.</h3>
- 4ˣ + 6ˣ = 9ˣ
- 2²ˣ + 2ˣ3ˣ = 3²ˣ
<u>Divide both sides by 2²ˣ</u>
<u>Substitute (3/2)ˣ = t</u>
<u>Solve for t:</u>
<u>Positive root is considered as (3/2)ˣ can't be negative.</u>
- (3/2)ˣ = (1 + √5)/2
- x = log [(1 + √5)/2] / log (3/2)
- x = 1.18681439028
