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2 years ago

Simplify. -2(y+3)+4y

Mathematics

2 answers:

stiks02 [169]2 years ago

6 0

The correct answer is 2y-6 let me know if you want to know how I got that

Pavel [41]2 years ago

3 0

Answer:

-6+2y

Step-by-step explanation:

-2(y+3)+4y

Use distributive property for -2 and (y+3)

-2y-6+4y

Then simplify=

-6+2y or 2y-6

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Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 6x(1/3) + 3x(4/3). You must justi

stealth61 [152]

Applying our power rule gets us our first derivative,

$\rm f'(x)=6\frac13x^{-2/3}+3\cdot\frac43x^{1/3}$

simplifying a little bit,

$\rm f'(x)=2x^{-2/3}+4x^{1/3}$

looking for critical points,

$\rm 0=2x^{-2/3}+4x^{1/3}$

We can apply more factoring.
I hope this next step isn't too confusing.
We want to factor out the smallest power of x from both terms,
and also the 2 from each.

$0=2x^{-2/3}\left(1+2x\right)$

When you divide x^(-2/3) out of x^(1/3),
it leaves you with x^(3/3) or simply x.

Then apply your Zero-Factor Property,

$\rm 0=2x^{-2/3}\qquad\qquad\qquad 0=(1+2x)$

and solve for x in each case to find your critical points.

Apply your First Derivative Test to further classify these points. You should end up finding that x=-1/2 is an relative extreme value, while x=0 is not.

Let's come back to this,

$\rm f'(x)=2x^{-2/3}+4x^{1/3}$

and take our second derivative.

$\rm f''(x)=-\frac43x^{-5/3}+\frac43x^{-2/3}$

Looking for inflection points,

$\rm 0=-\frac43x^{-5/3}+\frac43x^{-2/3}$

Again, pulling out the smaller power of x, and fractional part,

$\rm 0=-\frac43x^{-5/3}\left(1-x\right)$

And again, apply your Zero-Factor Property, setting each factor to zero and solving for x in each case. You should find that x=0 and x=1 are possible inflection points.

Applying your Second Derivative Test should verify that both points are in fact inflection points, locations where the function changes concavity.

8 0

3 years ago

Please please use explanation with answer

KIM [24]

Answer:

$\large\boxed{\theta=-\dfrac{\pi}{4}+k\pi\ or\ \theta=k\pi}\ for\ k\in\mathbb{Z}$

Step-by-step explanation:

$\tan^2\theta+\tan\theta=0\\\\\tan\theta(\tan\theta+1)=0\iff\tan\theta=0\ \vee\ \tan\theta+1=0\\\\\tan\theta=0\Rightarrow \theta=k\pi\ \text{for}\ k\in\mathbb{Z}\\\\\tan\theta+1=0\qquad\text{subtract 1 from both sides}\\\\\tan\theta=-1\Rightarrow\theta=-\dfrac{\pi}{4}+k\pi\ \text{for}\ k\in\mathbb{Z}$

5 0

2 years ago

Woody and Jen were paid $60 to paint the garage. Jim started at 8 a.M. And Woody didn't arrive until 10 a.M. The work was comple

Dennis_Churaev [7]

Answer:

$36

Step-by-step explanation:

Jim worked from 8am - 2 pm , which is 6 hours

Woody worked form 10am - 2pm, which is 4 hours

If we take the total time (4+6 = 10) and divide the amount they got, we have:

$60/10 = $6 per hour worked

Since Jim worked 6 hours, he will be paid 6 * 6 = $36

The rest, 60 - 36 = $24 would be paid to Woody (he worked less).

Jim's fair share of earning is $36

8 0

3 years ago

How much more is 4/6 Than 5/6

Sveta_85 [38]

5/6 is 1/6 more than 4/6. All you had to do is subtract 4/6 from 5/6 to get 1/6.

6 0

3 years ago

Read 2 more answers

The graph of a line is shown below. What is the equation of the line, in slope-intercept form, that is parallel to this line and

Alex_Xolod [135]

Earlier in this chapter we have expressed linear equations using the standard form Ax + By = C. Now we're going to show another way of expressing linear equations by using the slope-intercept form y = mx + b.

In the slope-intercept form you use the slope of the line and the y-intercept to express the linear function.

y=mx+by=mx+b

Where m is the slope and b is the y-intercept.

Example

Graph the equation

y−2x=1y−2x=1

rewrite in slope-intercept form

y=2x+1y=2x+1

Identify the slope and the y-intercept

m = 2 and b = 1

Plot the point corresponding to the y-intercept, (0,1)

The m-value, the slope, tells us that for each step to the right on the x-axis we move 2 steps upwards on the y-axis (since m = 2)

And once you have your second point you can just draw a line through the two points and extend it in both directions.

You can check to see that the line you've drawn is the correct one by substituting the coordinates of the second point into the original equation. If the equation holds true than the second point is correct.

Our second point = (1, 3)

y−2x=1y−2x=1

3−2⋅1=3−2=13−2⋅1=3−2=1

Our second point is a solution to the equation i.e. the line we drew is correct.

A line that passes through the origin has a y-intersect of zero, b = 0, and represents a direct variation.

y=mxy=mx

In a direct variation the nonzero number m is called the constant of variation.

You can name a function, f by using the function notion

f(x)=mx+bf(x)=mx+b

f(x) is another name for y and is read as "the value of f at x" or "f of x". You can use other letters than f to name functions.

A group of functions that have similar characteristics are called a family of functions. All functions that can be written on the form f(x) = mx + b belong to the family of linear functions.

The most basic function in a family of functions is called the parent function. The parent function of all linear functions is

f(x)=x

4 0

3 years ago