The total cost of rice and beans bought by Gabriel is 6b + 4r.
The simplified expression of the final cost is 4b + 3r.
<h3>What is simplification?</h3>
Simplification can be defined as a process of replacing a mathematical expression by the cancellation of common factors, regrouping of terms in the same variable to get the more simple form of the given expression.
Given that
6b + 4r represents the total cost of the rice and beans Gabriel bought.
He returns 2 bags of beans and 1 bag of rice.
This can be written as,
Then, the total number of bags of rice and beans is given as,
When we simplify the above equation, we get,
Hence we can conclude that the expression for rice and beans after the return is (4b+3r).
To know more about simplification, follow the link given below.
brainly.com/question/12616840.
D=2r=2·4=8 cm
A = L² (L=d)
A = 8² = 64 cm²
Answer:
The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.
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Hope it help you
Answer:
Step-by-step explanation:
<u>Optimizing With Derivatives
</u>
The procedure to optimize a function (find its maximum or minimum) consists in
:
- Produce a function which depends on only one variable
- Compute the first derivative and set it equal to 0
- Find the values for the variable, called critical points
- Compute the second derivative
- Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum
We know a cylinder has a volume of 4 
. The volume of a cylinder is given by
Equating it to 4
Let's solve for h
A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is
Replacing the formula of h
Simplifying
We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero
Rearranging
Solving for r
![\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%7D%7B%5Cpi%20%7D%7D%5Capprox%201.084%5C%20feet)
Computing h
We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative
We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.
The minimum area is
For some number to be divisible by 12 it has to be divisible by 6 and by 2.
we can write number n as:
n = 6 + 12*k where k is positive integer.
If we divide n by 12 we will get remainder 6 because 12*k part is divisible by 12.
The part 12*k is as said divisible by 12 which means it is divisible by 6 (as first stated) and it has remainder 0. That leaves us with 6/6 which again has 0 as remainder. That means that number n is divisible by 6
The answer is 0
