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Sati [7]
2 years ago
10

Tina is planning to fence in an area for her dog. She wants to create a rectangular area of 1,600 square feet for her pet and ca

n afford to purchase 160 feet of fence. In two or more complete sentences, explain the algebraic model, calculations and reasoning necessary to determine the dimensions of the rectangular area.
Mathematics
1 answer:
castortr0y [4]2 years ago
4 0

The dimensions of the rectangular area of Tina's fence is 40 ft by 40 ft

<h3 />

<h3>Area of a rectangle:</h3>
  • area = lw

where

l = length

w = width

She wants to create a rectangular area of 1,600 square feet for her pet . Therefore,

  • area = 1600 ft²

lw = 1600

Therefore,

perimeter = 160 ft

Then,

perimeter of rectangle = 2(l + w)

160 = 2(l + w)

l + w = 80

Let's combine the equations

lw = 1600

l + w = 80

l = 80 - w

Therefore,

w(80 - w) = 1600

80w - w² = 1600

Therefore,

w² - 80w + 1600 = 0

w² - 40w - 40w + 1600 = 0

w(w - 40) - 40(w - 40) = 0

(w - 40)(w - 40) = 0

w = 40 or 40

Therefore, the dimensions can be calculated as follows:

lw = 1600

40l = 1600

l = 1600 / 40

l = 40 ft

Therefore, the dimensions are 40ft by 40 ft

learn more on algebraic model here: brainly.com/question/4151078

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Answer:

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Step-by-step explanation:

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2000

7 0
2 years ago
How is Pascal's triangle used in binomial theorem?.
Scorpion4ik [409]

To simplify the process of expanding a binomial of the type (a+b) n (a + b) n, use Pascal's triangle. The same numbered row in Pascal's triangle will match the power of n that the binomial is being raised to.

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7 0
1 year ago
Sole the system by elimination -4x+9y=9 x-3y=-6
Natalka [10]

Answer:

A) -4x + 9y = 9

B) x -3y = -6

We multiply B) by 3

B) 3x -9y = -18 Then add it to A)

A) -4x + 9y = 9

-x = -9

x = 9

9 -3y = -6

3y = 15

y = 5


Step-by-step explanation:


5 0
3 years ago
Hiking up a mountain, you notice that the air temperature drops 10 degrees every 1000 meters increase in elevation. Write a mult
Elina [12.6K]

 decrease in temperature if you hike up the mountain 3000 meters is  -30° .

<u>Step-by-step explanation:</u>

Here we have , Hiking up a mountain, you notice that the air temperature drops 10 degrees every 1000 meters increase in elevation . We need to find Write a multiplication expression to represent the decrease in temperature if you hike up the mountain 3000 meters. Let's find out:

For every 1000 meters rise in elevation , there is decrease in 10° of temperature . So , For rise in n meters in  elevation , there is decrease in n×10° of temperature i.e

Decrease in temperature = (n/1000)×(-10) i.e.

⇒  (n/1000)×(-10)

⇒ \frac{n}{1000}(-10)

At n = 3000 meters:

⇒ \frac{3000}{1000}(-10)

⇒ 3}(-10)

⇒ -30°  

Therefore ,  decrease in temperature if you hike up the mountain 3000 meters is  -30° .

8 0
3 years ago
Karl makes 7 1/2 batches of cookies using 1 1/2 dozen eggs. Suppose Karl only
vredina [299]

Answer:

5\ batches\ of\ cookies

Step-by-step explanation:

we know that

Karl makes 7 1/2 batches of cookies using 1 1/2 dozen eggs

so using proportion

Find out how many batches of cookies could he make with a dozen eggs

step 1

Convert mixed numbers to an improper fraction

7\frac{1}{2}=\frac{7*2+1}{2}=\frac{15}{2}

1\frac{1}{2}=\frac{1*2+1}{2}=\frac{3}{2}

step 2

Applying proportion

Let

x ----> the amount of batches of cookies

\frac{(15/2)}{(3/2)}\frac{batches}{dozen\ eggs}=\frac{x}{1}\frac{batches}{dozen\ eggs}\\\\x=\frac{15}{3}\\\\x=5\ batches\ of\ cookies

5 0
3 years ago
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