Equations that are equivalent to the equation y-4=5(x+2)

a farmer is planning a rectangular area for her chickens. the area of the rectangle will be 200 square feet. three sides of the

Vladimir79 [104]

Let

x---------> the length side of the rectangular area

y---------> the width side of the rectangular area

we know that

the area of the rectangle is equal to

$A=x*y\\ A= 200\ ft^{2} \\ x*y=200$

$y=\frac{200}{x}$ -----> equation $1$

The perimeter of the rectangle is equal to

$P=2x+2y$

but remember that the fourth side of the rectangle will be formed by a portion of the barn wall

so

$P=x+2y$ -----> equation $2$

To minimize the cost we must minimize the perimeter

Substitute the equation $1$ in the equation $2$

$P=x+2*[\frac{200}{x} ]$

Using a graph tool

see the attached figure

The minimum of the graph is the point $(20,40)$

that means for $x=20\ ft$

the perimeter is a minimum and equal to $40\ ft$

Find the value of y

$y=\frac{200}{x}$

$y=\frac{200}{20}$

$y=10\ ft$

The cost of fencing is equal to

$5*40= \$200$

therefore

the answer is

the length side of the the fourth wall will be $20\ ft$

7 0

4 years ago

A 4-foot tall child walks directly away from a 12-foot tall lamppost at 2 mph. How quickly is the length of her shadow increasin

xz_007 [3.2K]

Answer:

The length of the shadow is increasing with the rate of 1.5 feet per sec

Step-by-step explanation:

Let AB and CD represents the height of the lamppost and child respectively ( shown below )

Also, let E be a point represents the position of child.

In triangles ABE and CDE,

$\angle ABE\cong \angle CDE$ ( right angles )

$\angle AEB\cong \angle CED$ ( common angles )

By AA similarity postulate,

$\triangle ABE\sim \triangle CDE$

∵ Corresponding sides of similar triangles are in same proportion,

$\implies \frac{AB}{CD}=\frac{BE}{DE}$

We have, AB = 12 ft, CD = 4 ft, BE = BD + DE = 6 + DE,

$\implies \frac{12}{4}=\frac{6+DE}{DE}$

$12DE = 24 + 4DE$

$8DE = 24$

$DE=3$

Now, the speed of walking = 2 mph = $\frac{2\times 5280}{3600}\approx 2.933\text{ ft per sec}$

Note: 1 mile = 5280 ft, 1 hour = 3600 sec

Thus, the time taken by child to reach at E

$= \frac{\text{Walked distance}}{\text{Walking speed}}$

$=\frac{6}{2.933}$

= 2.045 hours

Hence, the change rate in the length of shadow

$= \frac{\text{Length of shadow}}{\text{Time taken}}$

$=\frac{3}{2.045}$

= 1.5 ft per sec.

3 0

3 years ago

Which of the four tables below represents a function? *

nadezda [96]

The answer is 4.

A function shouldn’t have repeated Xs which is all 3 other tables do.

4 0

4 years ago

For what values of the variable are the following expressions defined?

Rom4ik [11]

Answer:

The Expression will be defined if the denominator is not equal to 0 since any number divided by 0 is undefined.
Therfore our main priority here is to check the denominator only because it's the only part that can make the expression undefined
the expression will be defined for all real numbers (a) BUT 3+a must not equal to 0 therfore (a) can be all real numbers but must never be equal to -3

Step-by-step explanation:

$a \: is \: an \: element \: of \: all \: real \: numbers \: but \: not \: not \: equal \: to \: -3$
HOPE THIS HELPS!

3 0

2 years ago

8. Shelley and Jim sold tickets to the basketball game. Good seats were $3 each and not so good seats cost

OverLord2011 [107]

Answer:

100 not so good seats

50 good seats

Step-by-step explanation:

Let x represent good seats and y represent not so good seats

[i] 3x + 2y = 350

[ii] x+y = 150

[iii] y = 150 - x

substitute this to equation [i]

3x + 2y = .350

3x + 2 (150-x ) = 350

3x + 300 - 2x = 350

3x-2x = 350 - 300

x = 50 good seats

now substitute what you got to equation [iii]

y = 150 - 50 = 100 not so good seats

when we check the answer by using equation [i] we find that it is correct:

3x + 2y = 350

3(50) + 2(100) = 350

150 + 200 = 350

350 = 350

3 0

3 years ago