Do you need to regroup 56+3 when adding to a two digit number

You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

$P=2x+2y$

On the other hand, since the available money to buy fence is D dollars,

$\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}$

Furthermore, the area of the enclosed land is given by

$A=xy$

Solving the second equation for x,

$\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}$

Substituting into the equation for the area,

$\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}$

To find the maximum possible area, solve A'(y)=0, as shown below

$\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}$

Therefore, the corresponding value of x is

$\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}$ <h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2> $\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}$ <h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

7 0

10 months ago

On a timed session please help I have one more question after this.....

olya-2409 [2.1K]

The coffee shop used 52 pounds of Type A coffee.

Step-by-step explanation:

Cost of Type A coffee per pound = 5.25

Cost of Type B coffee per pound = 4.10

Total pounds used in blend = 142

Total cost = 642.00

Let,

x be the pounds of Type A coffee used

y be the pounds of Type B coffee used

According to given statement;

x+y=142 Eqn 1

5.25x+4.10y=642.00 Eqn 2

Multiplying Eqn 1 by 4.10

$4.10(x+y=142)\\4.10x+4.10y=582.20\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(5.25x+4.10y)-(4.10x+4.10y)=642.00-582.20\\5.25x+4.10y-4.10x-4.10y=59.80\\1.15x=59.80\\$

Dividing both sides by 1.15

$\frac{1.15x}{1.15}=\frac{59.80}{1.15}\\x=52\\$

The coffee shop used 52 pounds of Type A coffee.

Keywords: linear equation, elimination method

Learn more about elimination method at:

#LearnwithBrainly

5 0

3 years ago

Based on the number line, about how many ounces are there in 8 pounds?

Reika [66]

Answer: 128 ounces

Step-by-step explanation:

16 ounces are in each pound. so if you take that number and times it with the number 8 you would get 128 ounces.

8 0

2 years ago

Assume X and Y are independent random variables with the following distributions:

allsm [11]

Answer:

Step-by-step explanation:

Given that X and Y are independent random variables with the following distributions:

x -1 10 1 2 Total

p 0.3 0.1 0.5 0.1 1

xp -0.3 1 0.5 0.2 1.4

x^2p 0.3 10 0.5 0.4 11.2

Mean of X = 1.4

Var(x) = 11.2-1.4^2 = 9.24

y 2 3 5

p 0.6 0.3 0.1 1

yp 1.2 0.9 0.5 0 2.6

y^2p 2.4 2.7 2.5 0 7.6

Mean of Y = 2.6

Var(Y) = 11.2-1.4^2 = 0.84

3) W=3+2x

Mean of w =3+2*Mean of x = 7.2

Var (w) = 0+2^2 Var(x)= 36.96

8 0

3 years ago

5 Ethan scored x points in a game. His younger sister scored 8 points when she

Nuetrik [128]

The remaining values will be<u> 19, 20, 21, 22 and 23</u>

<h3 /><h3>System of equations</h3>

Given the following parameters

Ethan's score = x points

His younger sister's score = 8 points

If their total score is y points, hence the equation relating x and y is expressed as:

x + 8 = y

x = 8 - y

If x = 10

y = x + 8

y = 18

The ramining values will be<u> 19, 20, 21, 22 and 23</u>

Learn more on tables and values here: brainly.com/question/9265203

7 0

2 years ago