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3 years ago

How to multiply radical expressions

2 answers:

7 0

Divide and simplify radical expressions that contain a single term. You can do more than just simplify radical expressions. You can multiply and divide them, too. You can use your knowledge of exponents to help you when you have to operate on radical expressions this way.

Dahasolnce [82]3 years ago

5 0

both problems, the Product Raised to a Power Rule is used right away and then the expression is simplified. Notice that both radicals are cube roots, so you can use the rule to multiply the radicands. Look for perfect cubes in the radicand.

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Consider the function f(x) = 8x^3 +1. If f(g(x)) = x and g(f(x)) = x , find g(x) ?

Elena L [17]

$g( \: f(x) \: ) = x$

And

$f( \: g(x) \: ) = x$ _________________________________

So :

$g(x) = {f}^{ - 1}(x)$

And

$f(x) = {g}^{ - 1}(x)$

_________________________________

So to find g(x) , we must find the inverse of f(x) .

Let's do it .....

$f(x) = 8 {x}^{3} + 1$

$y = 8 {x}^{3} + 1$

Subtract the sides of the equation minus 1

$y - 1 = 8 {x}^{3}$

Divided the sides of the equation by 8

$\frac{y - 1}{8} = {x}^{3} \\$

From the sides of the equation, we take the radical with interval 3

$\sqrt[3]{ \frac{y - 1}{8} } = x \\$

$\sqrt[3]{ \frac{1}{8}(y - 1) } = x \\$

$\frac{1}{2} \sqrt[3]{y - 1} = x \\$

$\frac{ \sqrt[3]{y - 1} }{2} = x \\$

So ;

${f}^{ - 1}(x) = \frac{ \sqrt[3]{x - 1} }{2} \\$

Now we find g(x) which is :

$g(x) = \frac{ \sqrt[3]{x - 1} }{2} \\$

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

7 0

3 years ago

The sum of four consecutive intergers is 8 What are the intergers

Semmy [17]

Consecutive integers are 1 apart
so the 4 are
x, x+1,x+2,x+3

they add to 8

x+x+1+x+2+x+3=8
4x+6=8
minus 6 both sides
4x=2
divide both sides by 4
x=1/2
false, 1/2 is not an integer

if it was adding to 18, then the integers would be 3,4,5,6
but we can't find consecutive integers that add to 8

5 0

3 years ago

Read 2 more answers

A service call to repair a washing machine costs $35 plus $20 per hour. Raphael ‘s machine took 2 hour to fix. How much did the

Lady bird [3.3K]

There is a mandatory fixed rate of $ 35 that Raphael will have to pay once the service call has been made. This fixed rate is the constant.

The per hour rate is $20. Suppose the machine took "x" hours to get fixed. Then the variable part of the repair cost will be $20x$ .

Thus, Repair Cost=Fixed Rate Cost+Variable Cost

Or, $y=35+20x$ where $y$ is the total repair cost. Thus, if Raphael ‘s machine took 2 hour to fix, the repair cost is:

$y=35+20\times 2=35+40=75$ dollars.

Therefore, the last option is the correct option.

5 0

3 years ago

Read 2 more answers

10 divided 2-3(5times0)

artcher [175]

Answer:

Step-by-step explanation:

10÷2-3 (5×0)

10÷2-3×0
5-0
5

3 0

3 years ago

Find the missing values of the variables. The diagram is not to scale. (Image attached below)thank you ! :)

aniked [119]

Answer:

$\begin{gathered} x=\text{ 99}\degree \\ y\text{ = 64}\degree \end{gathered}$

Explanation:

Here, we want to get the value of x and y

From the given image, the angle y and 116 lie on a straight line

The sum of the angles on a straight line is 180 degrees

Thus:

$\begin{gathered} 116\text{ + y = 180} \\ y\text{ =180-116} \\ y\text{ = 64}\degree \end{gathered}$

The sum of the internal angles of a polygon can be calculated by the formula:

$180(n-2)$

where n is the number of sides the polygon has

In the case of the given question, n is 4

Substituting the value of n, we have it that:

$180(4-2)\text{ = 360 degrees}$

To get the value of x:

$\begin{gathered} x\text{ + y + 125 + 72 = 360} \\ But\text{ from above , y = 64}\degree \\ Substituting\text{ this:} \\ x\text{ + 64 + 125 + 72 = 360} \\ x\text{ = 360-125-64-72} \\ x\text{ = 99 } \end{gathered}$

4 0

1 year ago