Which algebraic expression is equivalent to the expression below?

(8x + 12) + (9x - 3)
A.
20x - 6
B.
17x + 9
C.
29x - 3
D.
17x + 15

Answer:

[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]

Step-by-step explanation:

We have the function:

[tex]f(x)=x^3-\frac{11}{2}x^2-4x[/tex]

And we want to determine the intervals for which the function is increasing or decreasing.

We will need to first find the critical points of the function. Note that our original function is continuous across the entire x-axis.

To find the critical points, we need to find the first derivative and then solve for the x. So:

[tex]f^\prime(x)=\frac{d}{dx}[x^3-\frac{11}{2}x^2-4x][/tex]

Differentiate:

[tex]f^\prime(x)=(3x^2)-\frac{11}{2}(2x)-(4) \\ f^\prime(x)=3x^2-11x-4[/tex]

Set the derivative equal to 0 and solve for x:

[tex]0=3x^2-11x-4[/tex]

Factor:

[tex]0=3x^2-12x+x-4 \\ 0=3x(x-4)+(x-4) \\ 0=(3x+1)(x-4)[/tex]

Zero Product Property:

[tex]3x+1=0\text{ or } x-4=0 \\ x=-\frac{1}{3}\text{ or } x=4[/tex]

Therefore, our critical points are -1/3 and 4.

We can thus sketch the following number line:

<————-(-1/3)——————————————(4)—————>

Now, let’s test values for the three intervals: less than -1/3, between -1/3 and 4, and greater than 4.

For less then -1/3, we can use -1. So, substitute -1 for x for our first derivative and see which we get:

[tex]f^\prime(-1)=3(-1)^2-11(-1)-4=3+11-4=10>0[/tex]

The result is positive.

Therefore, for all numbers less than -1/3,f(x) is increasing (since its derivative is positive).

For between -1/3 and 4, we can use 0. Substitute 0 for our derivative:

[tex]f^\prime(0)=3(0)^2-11(0)-4=-4<0[/tex]

The result is negative.

Therefore, for all numbers between -1/3 and 4, f(x) is decreasing (since its derivative is negative).

And finally, for greater than 4, we can use 5:

[tex]f^\prime(5)=3(5)^2-11(5)-4=16>0[/tex]

The result is positive.

Therefore, for all numbers greater than 4, f(x) is increasing (since its derivative is positive.

Therefore:

[tex]\text{$f(x)$ is increasing for $x<-\frac{1}{3}$ and $x>4$}\\ \text{ $f(x)$ is decreasing for $-\frac{1}{3}<x<4$}[/tex]

In interval notation:

[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]

Answer:

x=59

Step-by-step explanation:

The sum of the interior angles of a triangle add up to 180 degrees.  That means that (x+12)+(x)+(x-9)=180 degrees in total.  If we combine the like terms (combine the xs and regular constant values), the xs add up to 3x (x+x+x) and the regular constants add up to 3 (12+-9=3).  If we rewrite this in a more simplified form, we get 3x+3=180.  Subtract 3 on both sides to get 3x=177 because we want to isolate x.  3x=177 divide 3 on both sides and we get 59.  x=59

Answer:

-6

Step-by-step explanation:

-10-(-4)=-1+4=-6

Hope this helps plz mark brainliest ;D

Answer:

26123 is the answer have a good day

Answer:

238

Step-by-step explanation:

juans has 10 more than kevin's, so you just subtract 10 from 248, getting 238

Answer:

x=2/3 or x=−1/2

Step-by-step explanation:

6x²−x=2

6x²−x−2=2−2

6x²−x−2=0

(3x−2)(2x+1)=0

3x−2=0 or 2x+1=0

x=2/3 or x=−1/2

5>0-3

Step By Step- 5 is greater than 0-3 because 0-3 would equal a negative number, and all positive numbers are greater than negative numbers

Answer:

5>0-3

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Answer:

to create an equation that is parallel to a line, you keep the slope or rate of change the same, all you do is change the y intercept. so you have to keep

y = 2x, but then you can add any number to the end.

Answer:The expression is 6y - 4x

Step-by-step explanation:

Answer:

-4x+6y

Step-by-step explanation:

4x+6y-8x4

(4x-8x)+6y

−4x+6y

Answer:

x = 33.13 units

Step-by-step explanation:

Let the altitude of the triangle be h units.

[tex] \sin 65 \degree = \frac{h}{31} \\ \\ 0.906307787 = \frac{h}{31} \\ \\ h = 0.906307787 \times 31 \\ \\ h = 28.0955414 \\ \\ \cos \: 32 \degree = \frac{h}{x} \\ \\ 0.8480480962 = \frac{28.0955414}{x} \\ \\ x = \frac{28.0955414}{0.8480480962} \\ \\ x = 33.1296556 \\ \\ x \approx 33.13 \: units[/tex]

Answer:

Step-by-step explanation:

Step 1

Find the length of vertical line segment, lets call it h. Use function cos

Step 2

Find x using another function, sin

Answer:

hello your question is incomplete attached below is the complete question and solution

answer :  general solution ( X ) = [tex]C_{1} e^{3t} \left \{ {{1} \atop {-1}} \right. + C_{2} e^{3t} \left \{ {{1} \atop {-1}} \right.[/tex]

Step-by-step explanation:

attached below is the detailed solution to determine the general solution of the given system

general solution ( X ) = [tex]C_{1} e^{3t} \left \{ {{1} \atop {-1}} \right. + C_{2} e^{3t} \left \{ {{1} \atop {-1}} \right.[/tex]

Answer: x= -56/9

Step-by-step explanation:

34+12x=3x-22

Subtract 12x from both sides

34=-9x-22

Add 22 to both sides

56=-9x

Divide -9 by both sides to get x alone

56/-9=x

So

x=-56/9

Answer:

x = 3

Step-by-step explanation:

10x−3x+5=26 (Given)

7x + 5 = 26 (Combine like terms)

7x = 21 (subtraction Property of equaity)

x = 3 (division Property of equaity)

Answer:

-2= y=-13, (x,y)= (-2,-13)

0= y= -3, (x,y)= (0,-3)

1= y= 2, (x,y)= (1,2).

Step-by-step explanation:

Please mark as brainliest. :)

Answer:

Yes, my partner is correct because as the fat increases the calories increase. And when the points are rising from the left to the right, this indicates a positive correlation.

Step-by-step explanation:

Answer:

3 - 3 = 0 units There is no distance, the points are in the same place.

Step-by-step explanation:

Answer:

x <(with a line underneath the carrot) -11

Step-by-step explanation:

Hope this helps! Could not find the symbol.

The inequality for x which is less than or equal to -11 is written as x ≤ -11 or  x + 11 ≤ 0.

Inequality shows relation between two expression which are not equal to each others.

Let the required number is x.

In the given question,

Number x is less than or equal to -11.

The inequality for x which is less than or equal to -11 can be written as,

x ≤ -11

The inequality can be further simplified as,

⇒x + 11 ≤ 0

The inequality for x is x + 11 ≤ 0.

To know more about Inequality on:

https://brainly.com/question/20383699

#SPJ2

Answer:

[tex]\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }[/tex]

Step-by-step explanation:

Recall that using the chain rule we can state:

[tex]\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}[/tex]

and therefore solve for dy/dx as long as dx/dt is different from zero.

Then we find dy/dt  and dx/dt,

Given that

[tex]x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)[/tex]

And similarly:

[tex]y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)[/tex]

Therefore, dy/dx can be determined by the quotient of the expressions we just found:

[tex]\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}[/tex]

now notice that we can find   [tex]cos(t) = \sqrt[3]{y}[/tex]  from the expression for y,

and   [tex]sin(t) = \sqrt[3]{x}[/tex]  from its expression for x.

Therefore dy/dx can be written in terms of x and y as:

[tex]\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }[/tex]

Answer: 11 hours

Step-by-step explanation:

22/2 = 11

Not sure what you mean but will be explaining about y = 0 and x =0 anyway.

So for x = 0, that means the value of x is 0.

y = -2(0)+8

y=0+8

y=8

So when x = 0, the value of y is 8 (y = 8) or we can write (0,8)

For y = 0, that means the value of y is 0.

0=-2x+8

-8=-2x

-2x=-8

x=4

So when y = 0, x = 4. We can write as (4,0)

Answer:

15.20

Step-by-step explanation:

Answer:y = -0.6x + 5

Step-by-step explanation:

Answer:

yessir the one on top is right btw

Step-by-step explanation:

hope this helped