Answer:
The equations that represent the reflected function are
Step-by-step explanation:
The correct question in the attached figure
we have the function
we know that
A reflection across the y-axis interchanges positive x-values with negative x-values, swapping x and −x.
therefore
The reflection of the given function across the y-axis will be equal to
(Remember interchanges positive x-values with negative x-values)
An equivalent form will be
![f(x)=5(\frac{1}{5})^{(-1)(x)}=5[(\frac{1}{5})^{-1})]^{x}=5(5)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D5%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7B%28-1%29%28x%29%7D%3D5%5B%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7B-1%7D%29%5D%5E%7Bx%7D%3D5%285%29%5E%7Bx%7D)
therefore
The equations that represent the reflected function are
Answer:
Step-by-step explanation:
In a geometric sequence, the next term is a constant times the previous term. This constant is determined by dividing the second term by the first, here giving 5. The remaining terms are checked to see that each is 5 times the previous. 75 is 15×5, 375 is 75×5.
Alternately, the nth term is first term times k^(n-1).
Here, that's 3×5^(10-1), 3×5^9=5859375
Answer:
4(2e - 3)(3e + 1)
Step-by-step explanation:
Given
24e² - 28e - 12 ← factor out 4 from each term
= 4(6e² - 7e - 3) ← factor the quadratic
Consider the factors of the product of the e² term and the constant term which sum to give the coefficient of the e- term.
product = 6 × - 3 = - 18 and sum = - 7
The factors are - 9 and + 2
Use these factors to split the e- term
6e² - 9e + 2e - 3 ( factor the first/second and third/fourth terms )
= 3e(2e - 3) + 1 (2e - 3) ← factor out (2e - 3) from each term
= (2e - 3)(3e + 1)
Then
24e² - 28e - 12 = 4(2e - 3)(3e + 1) ← in factored form
Answer:
There are 10⁻⁷ hydrogen ions in one-liter water
Step-by-step explanation:
Hi there!
a. If the pH = 7.0, then:
-log(H) = 7.0
multiply both sides of the equation by -1
log(H) = -7.0
Apply 10ˣ to both sides
10^(log (H)) = 10⁻⁷
(H) = 10⁻⁷
There are 10⁻⁷ hydrogen ions in one-liter water.
Why 10^(log (H)) = (H)?
Let´s consider this function:
y = 10^(log x)
(Apply log to both sides)
log y = log 10^(log x)
(Apply logarithmic property: log xᵃ = a · log x)
log y = log x · log 10
(log 10 = 1)
log y = log x
y = x
(since y = 10^(log x) and y = x):
10^(log x) = x
That´s why 10^(log (H)) = (H)
2 1/2 + 2 3/5 =
2 5/10 + 2 6/10=
4 11/10 = 5 1/10
5 1/10 - 5 = 1/10
1/10 lb left over
