Thanks for the new rank appreciate it.

Sam needs a web designer. Designer A is offering her services for an initial $500 in addition to $100 per hour. Designer B is of

gavmur [86]

Answer:

2 hours

Step-by-step explanation:

Let's denote the amount of time we need to find out, t.

=> 600 + 50t < 500 + 100t

or 600 - 500 < 100t - 50t

or 100 < 50t

or 100/50 < t

or t > 2

=> After 2 hours, company B will be cheaper option than company A

3 0

3 years ago

Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four

shutvik [7]

Answer:

Largest possible total area of the four pens is $22562.5\:ft^{2}$

Step-by-step explanation:

Assume width as x and length as y. Given that length of fencing is 950 feet which encloses rectangular area which is divided into four pens as shown in diagram ( Refer to attachment),

So perimeter of the rectangular area as per diagram is given as,

Perimeter = width + width + width + width + width + length+ length

Substituting the value,

$950=x+x+x+x+x+y+y$ ….1

Now area of rectangular diagram is given as follows,

$A=xy$ ….2

Solving equation 1 for y, subtracting 2x from both sides,

$\dfrac{950-5x}{2}= y$

$475-\dfrac{5x}{2}= y$

Substituting the value in equation 2,

$A=x\left(475-\dfrac{5x}{2}\right)$

Simplifying

$A=475x-\dfrac{5x^{2}}{2}$

To find the largest possible area, differentiate A with respect to x,

$\dfrac{dA}{dx}=\dfrac{d}{dx}\left(475x-\dfrac{5x^{2}}{2}\right)$

Applying sum rule of derivative,

$\dfrac{dA}{dx}=\dfrac{d}{dx}\left(475x\right)-\dfrac{d}{dx}\left(\dfrac{5x^{2}}{2}\right)$

Applying constant multiple rule of derivative,

$\dfrac{dA}{dx}=475\dfrac{d}{dx}\left(x\right)-\dfrac{5}{2}\dfrac{d}{dx}\left(x^{2}\right)$

Applying power rule of derivative,

$\dfrac{dA}{dx}=475\left(1x^{1-1}\right)-\dfrac{5}{2}\left(2x^{2-1}\right)$

$\dfrac{dA}{dx}=475\left(x\right)-\dfrac{5}{2}\left(2x\right)$

$\dfrac{dA}{dx}=475-5x$

Now find the critical number by solving as follows,

$\dfrac{dA}{dx}=0$

$475-5x =0$

$475=5x$

$95=x$

Since there is only one critical point, directly substitute the value of x into equation of A,

$A=475\left(95\right)-\dfrac{5\left(95\right)^{2}}{2}$

Simplifying,

$A=45125-\dfrac{45125}{2}$

$A=\dfrac{45125}{2}$

So, the largest possible area is $22562.5\:ft^{2}$

3 0

4 years ago

What is the solution to log Subscript 3 Baseline (x + 12) = log Subscript 3 Baseline (5 x)

Charra [1.4K]

Answer:

x = 3

Step-by-step explanation:

brainly.com/question/14265179?utm_source=

log3(x + 12)=log3(5x)

since the bases are the same

since they both have log3

log3 cancels out

(x + 12)=(5x)

x + 12=5x

12 = 4x

3 = x

5 0

2 years ago

Complete the square to transfer into vertex form and find the vertex: f(x)= x^2+6x-22

ioda

Answer:

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of

b

.

(

b

2

)

2

=

(

−

3

)

2

Add the term to each side of the equation.

x

2

−

6

x

+

(

−

3

)

2

=

22

+

(

−

3

)

2

Simplify the equation.

Tap for more steps...

x

2

−

6

x

+

9

=

31

Factor the perfect trinomial square into

(

x

−

3

)

2

.

(

x

−

3

)

2

=

31

Solve the equation for

x

.

Tap for more steps...

x

=

±

√

31

+

3

The result can be shown in multiple forms.

Exact Form:

x

=

±

√

31

+

3

Decimal Form:

x

=

8.56776436

…

,

−

2.56776436

…

Step-by-step explanation:

thats took a while lol

5 0

4 years ago

Read 2 more answers

Alan has 6 water bottles in her desk. In how many different ways can he choose 2 water bottles?

elena55 [62]

Answer:

15 ways

Step-by-step explanation:

The answer would be 6 choose 2, which is:

$\frac{6!}{2!4!} = \frac{6\cdot5\cdot4!}{4!2!}=\frac{6\cdot5}{2}=15$

Therefore, there are 15 ways to choose 2 of the 6 water bottles Alan has.

By the way, if this helps, could you please give me brainliest? :)

5 0

3 years ago