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scoundrel [369]
3 years ago
15

Judi is making a frame for a square painting. The square painting is 11 3/8 inches on each side. To make sure that she has enoug

h wood Judi wants to buy two extra inches of wood for each corner. How much wood shoul Judi buy?
Mathematics
1 answer:
dimulka [17.4K]3 years ago
5 0

Answer:

53\frac{1}{2}\ in

Step-by-step explanation:

we know that

The perimeter of a square is equal to

P=4a

where

a is the length side of the square

in this problem we have

a=11\frac{3}{8}\ in

convert to an improper fraction

11\frac{3}{8}\ in=\frac{11*8+3}{8}=\frac{91}{8}\ in

Find the perimeter of the square

P=4\frac{91}{8}=45.5\ in

Remember to adds two extra inches for each corner

so

The wood needed is  

45.5\ in+2*4\ in= 53.5\ in

convert to mixed number

53.5\ in=53\frac{1}{2}\ in

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What are the real and complex solutions of the polynomial equation? x^3-8=0. with imaginary numbers
seraphim [82]

Answer:

Solutions are 2,  -1 +  0.5 sqrt10 i  and -1 - 0.5 sqrt10 i

or 2,  -1 +  1.58 i  and -1 - 1.58i

(where the last 2 are equal to nearest hundredth).


Step-by-step explanation:

The real solution is x = 2:-

x^3 - 8 = 0

x^3 = 8

x = cube root of 8 = 2

Note that a cubic equation must have  a total of 3 roots ( real and complex in this case).  We can find the 2 complex roots by using the following identity:-

a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Here  a = x and b = 2 so we have

(x - 2)(x^2 + 2x + 4) = 0

To find the complex roots we solve x^2 + 2x + 4 = 0:-

Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2

= -1 +/- (sqrt( -10)) / 2

= -1 +  0.5 sqrt10 i  and -1 - 0.5 sqrt10 i

4 0
2 years ago
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Combine the like terms to create an equivalent expression: 2s+(-4s)
Ira Lisetskai [31]

Answer:

-2s

Step-by-step explanation:

2s+(-4s)

2s-4s

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5 0
3 years ago
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Solve for x. x3 =−125
mafiozo [28]

Answer:

x = -5 or x = 5 (-1)^(1/3) or x = -5 (-1)^(2/3)

Step-by-step explanation:

Solve for x:

x^3 = -125

Taking cube roots gives 5 (-1)^(1/3) times the third roots of unity:

Answer:  x = -5 or x = 5 (-1)^(1/3) or x = -5 (-1)^(2/3)

6 0
3 years ago
Three consecutive integers have a sum of 87. Find the integers.
elena-s [515]

Answer:

28, 29, and 30

Step-by-step explanation:

There's probably better ways but you can estimate by knowing 30*3=90 so it should be somewhere pretty close to 30. Guess and check with basic calculations to get 28, 29, and 30.

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2 years ago
In the balcony of an auditorium, there are 20 seats in the first row, 22 seats in the second row and 24 seats in the third row.
JulsSmile [24]

Answer:

is two more than the row before

Step-by-step explanation:

i hope i help\

7 0
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