Round 4.93 to 1 decimal place

A farmer wants to fence a rectangular garden next to his house which forms the northern boundary. The fencingfor the southern bo

Ivahew [28]

Answer:

10 ft x 10 ft

Area = 100 ft^2

Step-by-step explanation:

Let 'S' be the length of the southern boundary fence and 'W' the length of the eastern and western sides of the fence.

The total area is given by:

$A=S*W$

The cost function is given by:

$\$ 120 = \$3*2W+\$6*S\\20 = W+S\\W = 20-S$

Replacing that relationship into the Area function and finding its derivate, we can find the value of 'S' for which the area is maximized when the derivate equals zero:

$A=S*(20-S)\\A=20S-S^2\\\frac{dA}{dS} = \frac{d(20S-S^2)}{dS}\\0= 20-2S\\S=10$

If S=10 then W =20 -10 = 10

Therefore, the largest area enclosed by the fence is:

$A=S*W\\A=10*10 = 100\ ft^2$

5 0

3 years ago

Solve x: (On the attachment). Please help! Homework due in for tomorrow! Xx

emmasim [6.3K]

Hello!

Explanation:

Distributive property: → $a(b+c)=ab+ac$

First do expand.

$4(x+1)=4x+4$

Then you subtract by 4 from both sides of an equation.

$4x+4-4=2x+4-4$

Simplify by equation.

$4x=2x$

Next, subtract by 2x from both sides of an equation.

$4x-2x=2x-2x$

Simplify.

$2x=0$

You can also divide by 2 from both sides of an equation.

$\frac{2x}{2}= \frac{0}{2}$

Finally, simplify by equation and dividing into the groups.

$0/2=0$

Answer: → $\boxed{x=0}$

Hope this helps!

6 0

4 years ago

In Lesson 3.05 we discussed comparing the key features of two functions given in different forms. Given the functions below:

vladimir1956 [14]

Answer:

Step-by-step explanation:

a) Compare the y-intercepts of f(x) and g(x). Use complete sentences.

The functions f(x) and g(x) are different, the y-intercepts for each function is y-intercepts (0,-1/3) for f(x)= 1/x-3 and y-intercepts (0,0) for g(x) as shown on the graph.

b) Compare the vertical asymptotes of f(x) and g(x). Use complete sentences.

The functions f(x) and g(x) have different Vertical Asymptotes, f(x)= 1/x-3 Vertical Asymptotes is x = 3 while g(x) as shown on the graph Vertical Asymptotes is x = 4. Both functions do have Horizontal Asymptotes that are the same y = 0

8 0

3 years ago

Earl is ordering supplies. Yellow paper costs $4.00 per ream while white paper costs $7.50 per ream. He would like to order 100

Eddi Din [679]

Answer:

Earl should order 76 yellow paper reams and 24 white paper reams.

Step-by-step explanation:

This problem can be computed as system of equations.

I will say that x is the number of yellow paper reams and that y is the number of white paper reams.

Earl will order 100 reams in total, so

x + y = 100

He has a budget of $484, so this is what he is going to spend. Each yellow paper ream(x) costs $4.00 and each white paper ream costs $7.50, so we know that

4x + 7.5y = 484

To know how many reams of each color should he order, we need to solve the following system of equations

1) x + y = 100

2) 4x + 7.5y = 484

I am going to write x as a function of y in equation 1), and then replace it in equation 2).

x = 100-y

Now replacing in equation 2)

4(100-y) + 7.5y = 484

400 - 4y + 7.5y = 484

3.5y = 84

y = 24.

Returning to equation 1)

x = 100-y = 100-24 = 76

So, Earl should order 76 yellow paper reams and 24 white paper reams.

5 0

3 years ago

Help show work 42,44,46,48,50 assig 9

Sedbober [7]

Answer: see below

Step-by-step explanation:

42) 11 < 3y + 2 < 20

-2 -2 -2

9 < 3y < 18

÷3 ÷3 ÷3

3 < y < 6

Graph: o----------o

3 6

44) 36 ≥ 1 - 5z > -21

-1 -1 -1

35 ≥ -5z > -22

÷ -5 ↓ ÷ -5 ↓ ÷ -5

7 ≤ z < 4.4

Graph: o------------ ·

4.4 7

46) 6b + 3 < 15 or 4b - 2 > 18

-3 -3 +2 +2

6b < 12 4b > 20

÷6 ÷6 ÷4 ÷4

b < 2 or b > 5

Graph: ←--------o o---------→

2 5

48) 8d < -64 and 5d > 25

÷8 ÷8 ÷5 ÷5

d < -8 and d > 5

there is no number that is both less than - 8 and greater than 5

No Solution

Graph: (empty)

50) 15x > 30 and 18x < -36

÷15 ÷15 ÷18 ÷18

x > 2 and x < -2

there is no number that is both less than - 2 and greater than 2

No Solution

Graph: (empty)

7 0

3 years ago