What is the prime factorization of 144?
2
O 2x62
O 22 x 34
x
O 23 x 32
х
0 24 x 32
Х
Help pls thx

The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.

In this question we shall use the first and second derivative tests to determine the optimal dimensions of a rectangular plot of land. The perimeter ([tex]p[/tex]), in feet, and the area of the rectangular plot ([tex]A[/tex]), in square feet, of land are described below:

[tex]p = 2\cdot (w+l)[/tex] (1)

[tex]A = w\cdot l[/tex] (2)

Where:

In addition, the cost of fencing of the rectangular plot ([tex]C[/tex]), in monetary units, is:

[tex]C = c\cdot p[/tex] (3)

Where [tex]c[/tex] is the fencing unit cost, in monetary units per foot.

Now we apply (2) and (3) in (1):

[tex]p = 2\cdot \left(\frac{A}{l}+l \right)[/tex]

[tex]\frac{C}{c} = 2\cdot (\frac{A}{l}+l )[/tex]

[tex]\frac{C\cdot l}{c} = 2\cdot (A+l^{2})[/tex]

[tex]\frac{C\cdot l}{c}-2\cdot l^{2} = 2\cdot A[/tex]

[tex]\frac{C\cdot l}{2\cdot c} - l^{2} = A[/tex] (4)

We notice that fencing costs are directly proportional to the area to be fenced. Let suppose that cost is the maximum allowable and we proceed to perform the first and second derivative tests:

FDT

[tex]\frac{C}{2\cdot c}-2\cdot l = 0[/tex]

[tex]l = \frac{C}{4\cdot c}[/tex]

SDT

[tex]A'' = -2[/tex]

Which means that length leads to a maximum area.

If we know that [tex]c = 8[/tex] and [tex]C = 4000[/tex], then the dimensions of the rectangular plot of land are, respectively:

[tex]l = \frac{4000}{4\cdot (8)}[/tex]

[tex]l = 125\,ft[/tex]

[tex]A = \frac{(4000)\cdot (125)}{2\cdot (8)} -125^{2}[/tex]

[tex]A = 15625\,ft^{2}[/tex]

[tex]w = \frac{15625\,ft^{2}}{125\,ft}[/tex]

[tex]w = 125\,ft[/tex]

The dimensions for the plot that would enclose the most area are a length and a width of 125 feet.

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Answer:

well tutors are very cool they help you with your subjects so i dont see any probelm with them.

Step-by-step explanation:

Answer:

simple look at y intercept then look at slope or you can solve two points by using the formula y2-y1/x2-x1

but your formula is

y =1/2 +5 so b would be your answer

Answer:

Step-by-step explanation:

Given is an absolute value function f(x) = |x|

Its vertex is at origin, the function is decreasing at negative values of x and increasing at positive values of x:

Correct answer choice is A

The sum of all positive integers that satisfy the condition as described is; 100

The number set of n is therefore;

n = {1, 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}.

According to the question;

The data set therefore includes all odd numbers; This is so because the question says; if n is odd; then n is a multiple of 5.

The sum of all positive integers that satisfy the condition is therefore;

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Step-by-step explanation: To solve for x in this literal equation, I would first distribute the C through the parentheses to get y = cx + cb.

Now subtract cb from both sides to get y - cb = cx.

Finally, divide both sides by c to get y - cb / c = x.

9514 1404 393

Explanation:

The correct order of the steps is ...

A proof always starts with "given". It always ends with a statement of what you have proved.

To fill in the sequence between these, it helps to think about what the relationships are and why you can conclude that the theorem is correct.

Answer:

12

Step-by-step explanation:

335 + 13.75x = 500

Subtract 335 from each side

13.75x = 165

Divide each side by 13.75

x = 12

You can attend 12 dance classes with $500.

9514 1404 393

Answer:

  12 classes

Step-by-step explanation:

The total cost for c classes will be ...

  335 + 13.75c = 500

  13.75c = 165 . . . . . . . . . .subtract 335

  c = 12 . . . . . . . . . . . divide by 13.75

You will take 12 classes.

Answer:

181.3

Step-by-step explanation:

I hope this helps!

Answer:

y=2/3x-4

Step-by-step explanation:

we can see that x goes up 1 for every 1.5y and if we start y at 0 x starts at -4 so if y is one than x has to be 2/3-4 becuase it is -4 + 2/3 for every 1 y goes up or one for every 1.5 y goes up. hope this answer was helpful.

Answer:

7x

Step-by-step explanation:

(5.2 + 6.8)x - (25 ÷ 5)x

12x-(25divied by 5)x

12x-5x

7x

Answer:

20.5

Step-by-step explanation:

Use Pythagorean theorem,

[tex]x^2 = 14^2 +15^2 \\\\\implies x^2 =421\\\\\implies x =\sqrt{421}\\\\\implies x =20.5[/tex]

Answer:

Range is 7 to 42

Step-by-step explanation:

The answer is D, the last one

Answer: 10

Step-by-step explanation:

Answer:

Both of the angles will add up to 180 degrees so let’s make an equation.

5x-5+2x+10=180

First we collect like terms

5x+2x-5+10=180

Add them up

7x+5=180

Move the constant to the right

7x=180-5

7x=175

7x/7=175/7

x=25

So yes it’s true x=25.

Now we find the respective angles,

5x-5

5(25)-5

125-5

120

So angle one is 120 degrees.

2x+10

2(25)+10

50+10

60

So angle two is 60 degrees.

Now to check,

120+60=180

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Negative discriminant means that the fucntion has no real roots

so in the quadratic function b^2-4ac if this section is negative there are no real roots, so yes a would be the answer

Bonus: if u want to know.

However, in linear algebra which ofc i know ur not taking there would be something called imangiary roots, or complex roots.

Answer:

for me the picture is blurry sorry

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

Answer:

[tex]\frac{19}{5}= 3\frac{4}{5}[/tex]

Step-by-step explanation:

5 can go into 19 three times. This will leave a remainder of 4. Therefore, 19/5 as a mixed number is 3 4/5.

Answer:

5.235 (Simplifies as $5.24)

Step-by-step explanation:

1 gal = 20 miles

1.5 gal = 30 miles

1 gal = $3.49

1.5 gal = $5.235

Answer:

[tex]4x \times {10}^{3} [/tex]

Step-by-step explanation:

[tex] \frac{1.2}{3} \times \frac{ {10}^{9} }{ {10}^{5} } [/tex]

[tex]0.4 \times {10}^{9 - 5} [/tex]

[tex]0.4 \times {10}^{4} [/tex]

[tex] = 4 \times {10}^{3} [/tex]

Answer: I'll give you formula

Step-by-step explanation: circumference = 2 x π x radius

radius = diameter÷2      area = π × radius²

9514 1404 393

Answer:

Step-by-step explanation:

Let x and y represent the hotel charges in the two cities. The relations we are given are ...

  x - y = -1500 . . . . . . second city hotel charge was 1500 more

  0.03x +0.095y = 580 . . . . . total tax paid was 580

Using the first equation, we can write an expression for x:

  x = y -1500

Substituting that into the second equation gives ...

  0.03(y -1500) +0.095y = 580

  0.125y = 625 . . . . . . . add 45 to both sides and simplify

  y = 5000 . . . . . . . . . . multiply by 8

  x = 5000 -1500 = 3500

The hotel charges were ...

  First city: $3500

  Second city: $5000

Answer:

The probability that a costumer will be seated at a round table are 44/60 and the probability that he will be seated by the window is 13/60

The probability that a customer will be seated at a round table is  [tex]\frac{19}{30}[/tex]  and  by the window is [tex]\frac{13}{60}[/tex].

Probability is a ratio of the number of favorable outcomes to the number of possible outcomes of the experiment.

Probability [tex]=\frac{Number \ of\ outcomes}{Number\ of\ possible\ outcome}[/tex]

We have,

Total number of tables [tex]=60[/tex]

Number of round tables [tex]=38[/tex]

Number of tables located by the window [tex]=13[/tex]

Number of round tables located by the window [tex]=6[/tex]

Now,

Number of possible outcomes customer will be seated at a round table [tex]=38[/tex]

So,

Probability of seated at a round table [tex]=\frac{Number \ of\ outcomes}{Number\ of\ possible\ outcome}[/tex]

                                                                [tex]=\frac{38}{60}=\frac{19}{30}[/tex]

Now,

Number of possible outcomes customer will be seated by the window [tex]=13[/tex]

Probability  of seated by the window[tex]=\frac{Number \ of\ outcomes}{Number\ of\ possible\ outcome}[/tex]

                                                               [tex]=\frac{13}{60}[/tex]

So, probability that a customer will be seated at a round table is  [tex]\frac{19}{30}[/tex]  and  by the window is [tex]\frac{13}{60}[/tex].

Hence, we can say that the probability that a customer will be seated at a round table is  [tex]\frac{19}{30}[/tex]  and  by the window is [tex]\frac{13}{60}[/tex].

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Answer:

C. 1

Step-by-step explanation:

We have to convert   4/15  into decimal.

Divide 4 by 15

When we divide 4 by 15, we get 0.26666666666.....

As we can see that, the number 6 is repeating

Only one digit is repeating

Hence, the correct answer is one 6

-13.30

that might be the answer