The factors for given equation f(x)=
.
- (x-1) - No
- (x-3) - No
- (x+3) - Yes
- (x-5) - Yes
- (x+5) - Yes
<u>Step-by-step explanation:</u>
The given equation is f(x)= .
Add 0 at the end of the equation.
= 0.
Let us group the given equation,
=0.
⇒ Group 1: 
.
Group 2: 
.
Pull out factor from each group,
⇒ Group 1: 
.
Group 2: (x+3) (-25).
Join the two group since both (x+3) is common in both groups.
=0.
One of the factor is (x+3).
Other factors are solved by the formula, 
.
= (x+5) (x-5) .
The other factors are (x+5) and (x-5).
the answer is d (i think) because anything aboveboard .90, whether it is positive or negative
Answer:
The functions are inverses; f(g(x)) = x ⇒ answer D
⇒ answer D
Step-by-step explanation:
* <em>Lets explain how to find the inverse of a function</em>
- Let f(x) = y
- Exchange x and y
- Solve to find the new y
- The new y = 
* <em>Lets use these steps to solve the problems</em>
∵ 
∵ f(x) = y
∴ 
- Exchange x and y
∴ 
- Square the two sides
∴ x² = y - 3
- Add 3 to both sides
∴ x² + 3 = y
- Change y by
∴ 
∵ g(x) = x² + 3
∴ 
∴ <u><em>The functions are inverses to each other</em></u>
* <em>Now lets find f(g(x))</em>
- To find f(g(x)) substitute x in f(x) by g(x)
∵
∵ g(x) = x² + 3
∴ 
∴ <u><em>f(g(x)) = x</em></u>
∴ The functions are inverses; f(g(x)) = x
* <em>Lets find the inverse of h(x)</em>
∵ h(x) = 3x² - 1 where x ≥ 0
- Let h(x) = y
∴ y = 3x² - 1
- Exchange x and y
∴ x = 3y² - 1
- Add 1 to both sides
∴ x + 1 = 3y²
- Divide both sides by 3
∴ 
- Take √ for both sides
∴ ± 
∵ x ≥ 0
∴ We will chose the positive value of the square root
∴
- replace y by 
∴
Answer: He bought 8 quarts
Step-by-step explanation:
There are 4 quarts in a gallon so if you multiply 4 by 2 then you get 8,
Answer:
A. 1/32
Step-by-step explanation:
Ok, the probability for one of the coins to land on heads is 1/2 cause a coin have to sides and chance is 50% that it will land on either of its sides.
If you have 2 coins the probability will be 1/2 for the first coin to land on heads and 1/2 for the second one. The overall probability for 2 coins would be (1/2)*(1/2)=1/4. You could also see it is 1/4 because all of the possible combinations of 2 coins are 4 (HH, HT, TH, TT) and HH is one of four.
It's the same if you have 5 coins. The probability will be (1/2)*(1/2)*(1/2)*(1/2)*(1/2)=1/32 in other words HHHHH is one of 32 possible combinations of 5 coins.
