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o-na [289]
3 years ago
12

9. Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2(

x+6)feet and a width of 3.5x feet. How many feet of fencing will he need to buy? Write and simplify an expression to represent this situation? What properties did you use?
Mathematics
1 answer:
fomenos3 years ago
8 0

Length: 2(x + 6); Width: 3.5x

A rectangle has 4 sides. 2 sides are lengths and 2 sides are widths.

The perimeter is the sum of the measures of all 4 sides.

perimeter = length + length + width + width

perimeter = 2(x + 6) + 2(x + 6) + 3.5x + 3.5x

Use the distributive property on 2(x + 6).

perimeter = 2x + 12 + 2x + 12 + 3.5x + 3.5x

Now let's group all terms with x first, then all the numbers.

perimeter = 2x + 2x + 3.5x + 3.5x + 12 + 12

Now we add like terms. Like terms have exactly the same variables and the same exponents. All terms with x are like terms and can be added together. All terms with no variable are like terms and can be added together.

perimeter = 11x + 24

11x and 24 are not like terms since 11x contains the variable x and 24 has no variable. Since 11x and 24 are not like terms, they cannot be added together. No more simplification can be done, and 11x + 24 is the answer.

Answer: 11x + 24

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Answer:

11

Step-by-step explanation:

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7 0
3 years ago
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Leviafan [203]

Answer:

1) 2x - y = 26.

Step-by-step explanation:

Solution =  (18, 10)

2x - y = 26 fits the bill

as   2(18) - 10

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2 years ago
Find all the zeros of the function <br> g(x)=x^3-4x^2-x+22
vagabundo [1.1K]

Answer:

x = -2, x = 3 − i√8, and x = 3 + i√8

Step-by-step explanation:

g(x) = x³ − 4x² − x + 22

This is a cubic equation, so it must have either 1 or 3 real roots.

Using rational root theorem, we can check if any of those real roots are rational.  Possible rational roots are ±1, ±2, ±11, and ±22.

g(-1) = 18

g(1) = 18

g(-2) = 0

g(2) = 12

g(-11) = 1782

g(11) = 858

g(-22) = -12540

g(22) = 8712

We know -2 is a root.  The other two roots are irrational.  To find them, we must find the other factor of g(x).  We can do this using long division, or we can factor using grouping.

g(x) = x³ − 4x² − 12x + 11x + 22

g(x) = x (x² − 4x − 12) + 11 (x + 2)

g(x) = x (x − 6) (x + 2) + 11 (x + 2)

g(x) = (x (x − 6) + 11) (x + 2)

g(x) = (x² − 6x + 11) (x + 2)

x² − 6x + 11 = 0

Quadratic formula:

x = [ 6 ± √(36 − 4(1)(11)) ] / 2

x = (6 ± 2i√8) / 2

x = 3 ± i√8

The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.

5 0
3 years ago
An experiment started with 100 bacteria. They double in number every hour. Find the number of bacteria after 8 hours.
zzz [600]
There will be 25,6000
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3 years ago
I need the the unknown angle measures
Valentin [98]

Answer: Mark brainliest if satisfied

m<B=72 degrees

m<C= 36 degrees

Step-by-step explanation:

m<B is congruent to m<A

72 times 2 equals 144

180 minus 144 equals 36

6 0
3 years ago
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