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user100 [1]
3 years ago
9

Frank the lumberjack has a log that is 291 centimetres long. He cuts it into three pieces. Work out the length of the third piec

e if the first two pieces are 67cm and 181cm long.
Mathematics
1 answer:
Gekata [30.6K]3 years ago
4 0

Answer:

43cm

Step-by-step explanation:

Given

Length of Log = 291cm

First Piece = 67cm

Second Piece = 181cm

Required

Determine the length of the third piece

Given that the log was cut into three;

<em>this implies that;</em>

Length of Log = First Piece + Second Piece + Third Piece

Substitute values for first piece, second piece and length of log;

291 = 67 + 181 + Third\ Piece

291 = 248 + Third\ Piece

Subtract both sides by 248

291 - 248 = 248 - 248 + Third\ Piece

43 = Third\ Piece

Third\ Piece = 43

<em>Hence, the length of the third piece is 43cm</em>

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Triangle ABC is formed by the vertices A(1,2,-1), B(-3,-6,2)and C(3,-2,0).
Vesnalui [34]

Answer:

Point D: (0,-4, 1 )

<em>d</em> = √41

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Pre-Calculus</u>

  • Midpoint Formula [3D]: (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}, \frac{z_1+z_2}{2} )
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Step-by-step explanation:

<u>Step 1: Define</u>

Point A(1, 2, -1)

Point B(-3, -6, 2)

Point C(3, -2, 0)

<u>Step 2: Find Point D</u>

Simply plug in your coordinates B and C into the midpoint formula to find midpoint

  1. Substitute [MF]:                    (\frac{-3+3}{2},\frac{-6-2}{2}, \frac{2+0}{2} )
  2. Add/Subtract:                       (\frac{0}{2},\frac{-8}{2}, \frac{2}{2} )
  3. Divide:                                  (0,-4, 1 )

<u>Step 3: Find distance </u><em><u>d</u></em>

Simply plug in the 2 coordinates A and D into the distance formula to find distance <em>d</em>

  1. Substitute [DF]:                    d = \sqrt{(0-1)^2+(-4-2)^2+(1+1)^2}
  2. Subtract/Add:                       d = \sqrt{(-1)^2+(-6)^2+(2)^2}
  3. Exponents:                           d = \sqrt{1+36+4}
  4. Add:                                      d = \sqrt{41}
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Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked
RUDIKE [14]

<em><u>The system of equations that represents this situation are:</u></em>

q + p = 2

4q + 5p = 8

<em><u>Solution:</u></em>

Let  q be the number of hours it took Courtney to walk from her house to the beach

Let p be the number of hours it took her to walk from the beach to the park

<em><u>The entire walk took 2 hours</u></em>

Therefore,

q + p = 2 ------- eqn 1

<em><u>The  total distance Courtney walked was 8 kilometers</u></em>

Total distance = 8 km

Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour

Then walked  from the beach to the park at a constant speed of 5 kilometers per hour

<em><u>Distance is given as:</u></em>

distance = speed \times time

<em><u>From her house to the beach:</u></em>

distance = 4 \times q = 4q

<em><u>From the beach to the park:</u></em>

distance = 5 \times p = 5p

We know that,

Total distance = 8 km

Therefore,

4q + 5p = 8 ------ eqn 2

<em><u>Thus the system of equations that represents this situation are:</u></em>

q + p = 2

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3 years ago
rice that costs $480 which is for 8 members is used 20 days. What is the cost of rice which is required for 12 members for 15 da
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Answer:

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