An expression which contains polynomials in both the numerator and denominator.

If f(x)=x-6 and g(x)=x1/2(x+3), find g(x) times f(x)

Elden [556K]

To solve this problem you must apply the proccedure shown below:
1. You have the following functions given in the problem above:
$f(x)=x-6 
$ and $g(x)=x1/2(x+3)=x(x+3)/2$ 
2. You have that g(x) times f(x) can be written as g(x)*f(x). Therefore, you must multiply f(x) * g(x), as following:
 $g(x)*f(x)=(x-6)*x(x+3)/2$ 
3. Applying the distributive property, you have:
 $g(x)*f(x)=( x^{3} + 3x^2 - 6x^{2} -18x)/2$
$g(x)*f(x)=(x^{3} - 3x^{2} -18x)/2$
The answer is: $g(x)*f(x)=(x^{3} - 3x^{2} -18x)/2$

5 0

4 years ago

Jay works as a waiter at a restaurant.

ryzh [129]

Answer:

67.33.

Step-by-step explanation:

To figure out the tip, you need to find 20% of $52.60.

0.2×52.6=10.52

You should leave $10.52 for the waiter if you want to leave him exactly 20%.

To figure the tax, you need to find 8% of $52.60.

0.08×52.6=4.208

Next, add them up:

52.6+10.52+4.208=67.328

The total bill, including tax and tip, will be $67.33.

7 0

2 years ago

A 50-gallon tank is filled with a 40% ethanol solution. How much solution should be drained but and replaced with an 80% ethanol

DIA [1.3K]

How do you create your equations when working on a mixture word problem?

Let's try to think about the general form of a word problem involving mixtures.

In general, we have the following scenario:

a merchant sells two kinds of products (coffee, sweets, etc).

we know the unit prices for both kinds of products and for the final mixture

p

1

US dollars per pound for the first kind of product,

p

2

US dollars per pound for the second kind of product

p

m

US dollars per pound for the mixture

we know the total quantity formed by the mixture of the two products (

q

pounds)

we have to find out the quantities of each product needed to form the mixture

(here we have the variables:

x

denoting the quantity of the first kind of product and

y

denoting the quantity of the second kind of product)

Now, we have sufficient information to work out the equations.

First, we know that the sum of the two quantities is

q

pounds, which gives us the first equation:

x

+

y

=

q

Second, we know that the sale price is the product of quantity and unit price, which gives us the second equation:

p

1

x

+

p

2

y

=

p

m

⋅

q

Now, we have a system of two linear equations that can be easily solved by substitution.

3 0

3 years ago

Determine the intercepts of the line The x and y intercepts please help

Anna007 [38]

Answer:

See below in bold.

Step-by-step explanation:

As we see from the diagram the x -intercept ( where the line intercepts the horizontal x-axis) is (3, 0) and the y-intercept is (0, -10).

5 0

4 years ago

How would I solve this problem in steps pls

gregori [183]

In order to solve for a, we must isolate it. To do this, we should add c to both sides, making a the only term on the left.

Final answer: a=c+d-r

3 0

3 years ago