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Oliga [24]
3 years ago
11

Miguel buys 100 feet of fence to enclose a rectangular area of his backyard so his dog can run freely. What is the maximum area,

in square feet, he can enclose?
Mathematics
1 answer:
sdas [7]3 years ago
5 0
Suppose the length of the triangle is x, if the perimeter of the rectangle is 100 ft, the width of the rectangle will be (50-x) ft.
Area of rectangle will be:
A=length*width
A=x(50-x)
A=50x-x^2
at maximum area, dA/dx=0
thus
dA/dx=50-2x=0
solving for x we get
2x=50
x=25
thus for maximum area length=25 ft
the size of the width will be
50-x=50-25=25 ft
thus the maximum area will be:
25*25=625 sq. feet
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Complete the table of values
Agata [3.3K]
Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify! 

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example, 3^{-2} =
\frac{1}{3^{2} }.
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example, (\frac{3}{4}) ^{3}  =  \frac{ 3^{3} }{4^{3} }.
3) The zero exponent rule<span> says that any number raised to zero is 1. For example, 3^{0} = 1.
</span>

Back to the Problem:
Problem 1 
The x-values are in the left column. The title of the right column tells you that the function is y =  4^{-x}. The x-values are:
<span>1) x = 0
</span>Plug this into y = 4^{-x} to find letter a:
y = 4^{-x}\\&#10;y = 4^{-0}\\&#10;y = 4^{0}\\&#10;y = 1
<span>
2) x = 2
</span>Plug this into y = 4^{-x} to find letter b:
y = 4^{-x}\\ &#10;y = 4^{-2}\\ &#10;y =  \frac{1}{4^{2}} \\  &#10;y= \frac{1}{16}
<span>
3) x = 4
</span>Plug this into y = 4^{-x} to find letter c:
y = 4^{-x}\\ &#10;y = 4^{-4}\\ &#10;y =  \frac{1}{4^{4}} \\  &#10;y= \frac{1}{256}
<span>

Problem 2
</span>The x-values are in the left column. The title of the right column tells you that the function is y =  (\frac{2}{3})^x. The x-values are:
<span>1) x = 0
</span>Plug this into y = (\frac{2}{3})^x to find letter d:
y = (\frac{2}{3})^x\\&#10;y = (\frac{2}{3})^0\\&#10;y = 1
<span>
2) x = 2
</span>Plug this into y = (\frac{2}{3})^x to find letter e:
y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^2\\ y = \frac{2^2}{3^2}\\&#10;y =  \frac{4}{9}
<span>
3) x = 4
</span>Plug this into y = (\frac{2}{3})^x to find letter f:
y = (\frac{2}{3})^x\\ y = (\frac{2}{3})^4\\ y = \frac{2^4}{3^4}\\ y = \frac{16}{81}
<span>
-------

Answers: 
a = 1
b = </span>\frac{1}{16}<span>
c = </span>\frac{1}{256}
d = 1
e = \frac{4}{9}
f = \frac{16}{81}
5 0
3 years ago
Please help how to solve
tatiyna

Answer:

=  > in \: the \: bigger \: triangle \\ height = 14 \: ft \\ base = 22.5 \: ft \\  =  > in \: smaller \: triangle \\ height = x \: ft \\ base = 9 \: ft \\ using \: ratios \\  \frac{bigger \: height}{smaller \: height}  =  \frac{bigger \: base}{smaller \: base}  \\  \frac{14}{x}  =  \frac{22.5}{9}  \\  \frac{14}{x}  = 2.5 \\ x =  \frac{14}{2.5}  \\ x = 5.6 \: ft

7 0
3 years ago
What is this problem -12=4(x-7)-8x
Fofino [41]

-12=4(x-7)-8x

One solution was found :

                  x = -4

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :


                    -12-(4*(x-7)-8*x)=0


Step by step solution :

Step  1  :

Equation at the end of step  1  :

 -12 -  (4 • (x - 7) -  8x)  = 0

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :


  4x + 16  =   4 • (x + 4)


Equation at the end of step  3  :

 4 • (x + 4)  = 0

Step  4  :

Equations which are never true :

4.1      Solve :    4   =  0

Hope this helps you, Have a nice day.

4 0
3 years ago
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Strike441 [17]

The function based on the information will be S = -0.005D + 95.

<h3>How to illustrate the function?</h3>

It should be noted that d is the distance from the starting point while S is the speed.

The points given are (0 95)( 4000, 75).

Slope = (75 - 95)(4000 - 0)

= 0.005

The equation will be:

S = -0.005D + 95

Learn more about functions on:

brainly.com/question/25638609

#SPJ1

6 0
1 year ago
Which are solutions of the equation x2 – 16 = 0? Check all that apply.
san4es73 [151]

Answer:

x=-4

x=4

Step-by-step explanation:

4 0
3 years ago
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