Answer:
Step-by-step explanation:
1. multiply both sides by 2
<em>3b-4=2c</em>
2. add 4 to both sides
3b=2c+4
3. divide both sides by 3
b= ![\frac{2b+4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2b%2B4%7D%7B3%7D)
Answer:
44
Step-by-step explanation:
Answer:
<em> Anna's wand can cast 70 spells</em>
<em></em>
Step-by-step explanation:
Elsa's wand can cast 53 spells
her wand casts 17 fewer cells than her sister Anna's
Amount of spells cast by Anna's wand = ?
We write the question down in the form of an equation
![x - 17 = 53](https://tex.z-dn.net/?f=x%20-%2017%20%3D%2053)
where
is the amount of spells Anna's wand can cast.
we then proceed to solve by collecting like terms to different sides of the equation. We'll have
![x = 53 + 17](https://tex.z-dn.net/?f=x%20%3D%2053%20%2B%2017)
which leaves us with
![x = 70](https://tex.z-dn.net/?f=x%20%3D%2070)
This means that<em> Anna's wand can cast 70 spells.</em>
Given:
The table of values for the function f(x).
To find:
The values
and
.
Solution:
From the given table, it is clear that the function f(x) is defined as:
![f(x)=\{(-14,11),(-7,-12),(-12,-5),(9,1),(10,-2),(-2,13)\}](https://tex.z-dn.net/?f=f%28x%29%3D%5C%7B%28-14%2C11%29%2C%28-7%2C-12%29%2C%28-12%2C-5%29%2C%289%2C1%29%2C%2810%2C-2%29%2C%28-2%2C13%29%5C%7D)
We know that if (a,b) is in the function f(x), then (b,a) must be in the function
. So, the inverse function is defined as:
![f^{-1}(x)=\{(11,-14),(-12,-7),(-5,-12),(1,9),(-2,10),(13,-2)\}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5C%7B%2811%2C-14%29%2C%28-12%2C-7%29%2C%28-5%2C-12%29%2C%281%2C9%29%2C%28-2%2C10%29%2C%2813%2C-2%29%5C%7D)
And,
![f^{-1}(f(a))=f^{1}(b)](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28f%28a%29%29%3Df%5E%7B1%7D%28b%29)
...(i)
Using (i), we get
![f^{-1}(f(3.14))=3.14](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28f%283.14%29%29%3D3.14)
Now,
![f(f(-7))=f(-12)](https://tex.z-dn.net/?f=f%28f%28-7%29%29%3Df%28-12%29)
![f(f(-7))=5](https://tex.z-dn.net/?f=f%28f%28-7%29%29%3D5)
Therefore, the required values are
and
.
The answer in the problem will be B I believe