Answer:
Step-by-step explanation:
You want to solve ...
Answer:
B. 2x + 5, with the restriction x ≠ five over 2
Step-by-step explanation:
The given expression is the difference of squares, so factors as ...
the product of the quantity 2x plus 5 and the quantity 2x minus 5 over the quantity 2x minus 5
You will note that the numerator and denominator have a common factor:
the quantity 2x minus 5
Factoring that out gives ...
2x + 5, with the restriction x ≠ five over 2 (x is restricted from being a value that makes the denominator zero.)
_____
<em>Comment on the form of the answer</em>
Since you have written your math expressions using words instead of symbols, we assume you can read them more easily that way. So, we have provided the explanation in the form you can most easily understand. (Personally, I prefer math symbols. They are more compact and tend to be less ambiguous.)
*Given
Money of Phoebe - 3 times as much as Andy
Money of Andy - 2 times as much as Polly
Total money of Phoebe, - <span>£270
</span> Andy and Polly
*Solution
Let
B - Phoebe's money
A - Andy's money
L - Polly's money
1. The money of the Phoebe, Andy, and Polly, when added together would total <span>£270. Thus,
</span>
B + A + L = <span>£270 (EQUATION 1)
2. Phoebe has three times as much money as Andy and this is expressed as
B = 3A
3. Andy has twice as much money as Polly and this is expressed as
A = 2L</span> (EQUATION 2)
<span>
4. This means that Phoebe has ____ as much money as Polly,
B = 3A
B = 3 x (2L)
B = 6L </span>(EQUATION 3)<span>
This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only.
5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes,
6L + 2L + L = </span><span>£270
</span> 9L = <span>£270
</span> L = <span>£30
So, Polly has </span><span>£30.
6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively.
</span>
A = 2L
A = 2(£30)
A = £60
Andy has £60
B = 6L
B = 6(£30)
B = £180
Phoebe has £180
Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.
The ratio is common, so you could write:
a1 * r^4 = a^5 (you do r^4 because there are 4 times you need to multiply by the ratio to get from a1 to a5)
Plug in the values:
3 * r^4 = 48
Divide by 3:
r^4 = 16
Take the fourth root of both sides:
r = 2
The common ratio is 2.
