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MaRussiya [10]
3 years ago
14

Lily is cutting a piece of yarn into 3 (three) pieces. The 2nd piece is 3 times as long as the 1st piece, while the 3rd piece is

6 centimeters longer than the 1st piece. When the yarn has a total length of 211 centimeters, calculate the length of the first piece.
Mathematics
1 answer:
STatiana [176]3 years ago
6 0

Answer:

The length of the first piece = 41 cm

Step-by-step explanation:

Let the length of the first piece = a

Let the length of the second piece = b

Let the length of the third piece = c

we are given the following:

b = 3a . . . . . (1)     (The 2nd piece is 3 times as long as the 1st piece)

c = 6 + a  . . . . (2)    (the 3rd piece is 6 centimeters longer than the 1st piece)

a + b + c = 211 . . . . . (3)    (  the yarn has a total length of 211 centimeters)

Next, let us eliminate two variables, and this can easily be done by substituting the values of b and c in equations 1 and 2 into equation 3. this is done as follows:

a + b + c = 211

a + (3a) + (6 + a) = 211       ( remember that   b = 3a; c = 6 + a)

a + 3a + 6 + a = 211

5a + 6 = 211

5a = 211 - 6 = 205

5a = 205

∴ a = 205 ÷ 5 = 41 cm

a = 41 cm

Therefore the length of the first piece (a) = 41 cm

now  finding b and c

substituting a into equation 1 and 2

b = 3a

b = 3 × 41 = 123

∴ b = 123 cm

c = 6 + a

c = 6 + 41 = 47

∴ c = 47 cm

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I got the answer as letter C, can someone check me to make sure that is correct? Thank you in advance.
Flura [38]

Answer:

The x's cancel  so definitely is choice C:  1/9

Step-by-step explanation:

We have   root( 1/(x^2) )  *  root ((x^2) / 81)

simplifying this we get as follows:

root( 1/(x^2) )  *  root ((x^2) / 81)

= \sqrt{(1/x^2 )}  * \sqrt{(x^2)/81}

=  ( 1/x )   *  (x/9)

the x's cancel

= 1/9

choice C   1/9

3 0
3 years ago
The function p(x) = −2000x2 + 18000x − 15000 models the monthly profit P of a smoothie company, where x represents the price per
ohaa [14]

Answer:

Step-by-step explanation:

Givem the profit function

p(x) = −2000x2 + 18000x − 15000

We are to generate the price range that will generate a monthly profit of at least $25,000

Substitute into the function we have;

25000 = −2000x2 + 18000x − 15000

Divide through by 1000

25 = -2x²+18x-15

Rearrange

-2x²+18x-15-25 = 0

2x²-18x+40 = 0

Divide through by 2

x²-9x+20 = 0

Factorize

x²-5x-4x+20 = 0

x(x-5)-4(x-5) = 0

x-4 = 0 and x-5 = 0

x = 4 and x = 5

Hence the price range that will generate a monthly profit of at least $25,000 is between $4 and $5 inclusive

8 0
3 years ago
Please help me aspa​
Olegator [25]

Answer:

43 .......................

3 0
3 years ago
PLEASE HELP ASAP!!!! 100% CORRECT ANSWERS ONLY PLEASE!!!!
zmey [24]
Area= 2πr

So, 

If you were to multiply the radius by 2 since 2 is not in the equations, 

4*2= 8

8π ft^2 would be the correct answer.

I hope this helps!
~kaikers
5 0
2 years ago
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The owner of small computer repair business has one employee,who paid an hourly rate of $22. The owner estimate His weekly profi
deff fn [24]
The 'x' represents the number of hours 
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