Answer:
the corresponding point is (5,-4)
Step-by-step explanation:
x+3=8 <=> x =8-3=5
so f(5+3)=f(8)=-4
so the corresponding point is (5,-4)
Answer:
x=2/5
Step-by-step explanation:
Divide:
2 divided by 5 equals 0.4, which is equivalent to 4/10, which simplifies to 2/5.
Multiply to check:
2/5 times 5 equals 2
So x=2/5
Having obtained:

the next thing to do is collect the first three terms and write them as the square of a binomial, and also collect the last two terms, writing each of them with a denominator equal to 4a^2
We have:

.
Then, we take

to the right side and write these two terms as one:

.
Next, we take the square root of both sides, which has been shown in the solution.
Next, we have to take b/2a to the right hand side as -(b/2a), and removing the square in the denominator of the right hand side expression:

.
Answer: the steps to complete in the boxes are :

.

.

.
Complete Question:
The complete question is shown on the first uploaded image
Answer:
The probability that the random you randomly select species that are greater than 200 kg is = 7/62
Step-by-step explanation:
Step One: Load the data set in to the R work space
data(mammals,package="MASS")
attach(mammals)
Step 2 : Obtain the list of the species that are greater than 200 and store it on y variable.
y <- subset(mammals,body>200)
Step Three : Obtain the total size
nrow(mammals)
Step Four : Obtain the sum of species greater than 200
sum(body > 200)
total size = 62
size with body > 200 = 7
hence
required probability = 7/62
<h2>Writing the Inverse of a Function</h2><h3>
Answer:</h3>
![f^{-1}(x) = \sqrt[3]{\frac{x +5}{3}}\\](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%20%2B5%7D%7B3%7D%7D%5C%5C)
<h3>
Step-by-step explanation:</h3>
<em>Please refer to my Answer from this Questions to know more about Inverse Functions: <u>brainly.com/question/24619467</u></em>
Let
so that the inverse of
is equal to
.
Solving for
:
![f(x) = 3x^3 -5 \\ y = 3x^3 -5 \\ x = 3y^3 -5 \\ 3y^3 -5 = x \\ 3y^3 = x +5 \\ y^3 = \frac{x +5}{3} \\ y = \sqrt[3]{\frac{x +5}{3}}](https://tex.z-dn.net/?f=f%28x%29%20%3D%203x%5E3%20-5%20%5C%5C%20y%20%3D%203x%5E3%20-5%20%5C%5C%20x%20%3D%203y%5E3%20-5%20%5C%5C%203y%5E3%20-5%20%3D%20x%20%5C%5C%203y%5E3%20%3D%20x%20%2B5%20%5C%5C%20y%5E3%20%3D%20%5Cfrac%7Bx%20%2B5%7D%7B3%7D%20%5C%5C%20y%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7Bx%20%2B5%7D%7B3%7D%7D)
Since the inverse of
is equal to
,
.