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suter [353]
3 years ago
12

Josh has a rectangular garden with an area of 324 square feet that he would like to enclose with a fence. If the garden has a le

ngth of 24 feet, how much fencing would he need?
Mathematics
1 answer:
Firlakuza [10]3 years ago
8 0
13.5



324÷24=13.5


Josh will need 13.5 fencing.
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What is the coefficient of the x^5y^5- term in the biomial expansion of (2x-3y)^10
jasenka [17]

<u>Answer:</u>

 The coefficient of x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552

<u>Solution: </u>

The given expression is (2 x-3 y)^{10}

As per binomial theorem, we know,

(x+y)^{n}=\sum n C_{k} x^{n-k} y^{k}

Now here a = 2x, b = (- 3y) and n = 10 and k = 0,1,2,….10

Now x^{5}\times y^5 will be the 6 term where k =5

Now, \mathrm{T}_{6}=10 \mathrm{C}_{5} \times(2 \mathrm{x})^{(10-5)} \times(-3 \mathrm{y})^{5}=10 \mathrm{C}_{5} 2^{5} \times \mathrm{x}^{5} \times(-3)^{5} \times \mathrm{y}^{5}

So, the coefficient of x^{5} \times y^{5} \text { is }=10\left(5 \times 2^{5} \times(-3)^{5}\right.

10 \mathrm{C}_{5}=\frac{10 !}{5 ! \times(10-5) !}=\frac{10 !}{5 !+5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=\left(\frac{30240}{120}\right)=252

The coefficient of x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552

6 0
3 years ago
What is the variable in this expression?<br> 4b + 2b + 1⁄4
Shtirlitz [24]

Answer:

the variable is "b"

Step-by-step explanation:

7 0
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What is the inverse of the function?<br> f(x) = 1/3x-5
OlgaM077 [116]

Answer:

        -1

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Step-by-step explanation:

1)  in f(x) = 1/3x-5, replace f(x)= with y= as follows:  y = (1/3)x - 5

2) interchange x and y, obtaining:  x = (1/3)y - 5

3) solve this result for y:  (1/3)y = -x - 5, or -(x + 5).  Next, multiply both sides by                        3 to eliminate the fraction (1/3):  y = -3(x + 5)

4)  replace y with the symbol for "inverse of f(x);

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       f   (x) = -3(x + 5)

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3 years ago
When will the sum of two numbers be zero
mash [69]
The sum of two numbers will be zero when you have the same number and one is positive and one is negative. For example 1 + -1= 0
8 0
3 years ago
Read 2 more answers
A<br> 2x + 5<br> 3x - 2<br> B+<br> X = [? ]
WITCHER [35]

Answer:   7

Step-by-step explanation:

They are alternate interior angle

2x + 5 = 3x -2

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-x = -7

x = 7

4 0
3 years ago
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