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3 years ago

If f(x)=x+4 and g(x)=x^3 what is (g*f)(-3)

Mathematics

1 answer:

Molodets [167]3 years ago

4 0

Step-by-step explanation:

g*f(x)=g(x+4)=(x+4)³

g*f(-3)=(-3+4)³

= 1³=1

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A sequence of transformations maps abc onto a'b'c'. the type of transformation that maps abc onto a'b'c' is a _____.

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Answer: idk I need it to

Step-by-step explanation: for my test

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4 years ago

Read 2 more answers

Consider the system of equations:

AVprozaik [17]

$\large{\underline{\underline{\pmb{\sf {\color {blue}{Solution:}}}}}}$

Since, we know that in Elimination method we have to first the value of "x" or either "y". For that we have to multiply a number which makes the both equation's "x" or "y" equal so that we cut cancel it and find the solution.

Here's an example:

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Equation 1: - 2x + 3y = 9

Equation 2: - 8x - 7y = 10

We can see that in "Equation 1" the first number is "- 2x" and in "Equation 2" the first number is "-8x". So, what we do in Elimination method is that we have to make the first number of both the equations equal or same.

Eg:

- 2x + 3y = 9.

- 8x + 7y = 10--(ii)

Now,we can see that in "Equation 2" the first number is "8x" whereas in "Equation 1" the first number is "-2x". We have to multiply with any number that makes the both the first number of equation is same.

So, I'm taking the number "4" to multiply it with equation 1, which gives us the result,

$4( - 2x + 3y) = 9 \times 4 \\ \\ \leadsto - 8x + 12y = 36$

Now, we've subtract both the equation to get the results.

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2 years ago

There are 3/4 pound of hamburger me there are three hamburger patties that was made each patti weighs the same how much does eac

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4 years ago

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3 years ago

Let a and b be two positive numbers. If 2a + 3b=6 then the maximum product of these a and b is:

VikaD [51]

Answer:

a= 3/2

b= 1

a*b= 3/2

Step-by-step explanation:

For getting this problem we need to think in terms of only one unknown. Lets start by looking at our equation:

2a + 3b=6

No, we need to see what happens to a*b. Lets get the value of one of these unknowns in terms of the other, this is, a in terms of b or b in terms of a. Here, I will get a in terms of b (if you like, do the other way and compare):

2a + 3b=6

Subtract 3b in both sides:

2a = 6 - 3b

Now divide both sides by 2 to get a alone:

a = (6 - 3b)/2

a = 3 - 3/2 b

Now lets try to multiply a by b, using this a we found above:

a*b = (3 - 3/2 b)*b

Using distributive:

a*b = 3b - 3/2 b^2

So, we have an expression for a*b that depends only on b. Notice that this expression is a parabola with negative coefficient on the square term, what makes it a negative parabola that MUST have a maximum value. So, we have an expression for a*b that can be maximized, so we can find the maximum of a*b by the derivative of the expression. Lets derive in b:

(3b - 3/2 b^2)' = (3b)' - (3/2 b^2)' = 3 - 3b

So, the derivative equal to 0 gives us the maximum:

3 - 3b = 0

Suming 3b in both sides:

3 = 3b

Dividing by 3:

1 = b

So, we maximize our expression a*b when b is equal to 1. Now, we can replace it on a = 3 - 3/2 b to find b:

a = 3 - 3/2(1) = 3 - 3/2 = 3/2

Thus, a is equal to 3/2 and the product a*b is maximized when:

a = 3/2

b = 1

And the product is a*b= (3/2) * 1 = 3/2

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3 years ago