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GalinKa [24]
3 years ago
12

If it takes 5 elves 5 minutes to make 5 dolls, how long would it take 100 elves to make 100 dolls?

Mathematics
2 answers:
klasskru [66]3 years ago
8 0

Answer: 5 minutes

Step-by-step explanation: If 5 elves can make 5 dolls in 5 minutes then an elf can make 5 dolls in twice the time it would take 5 elves to do it which is 25 minutes.

This means it takes an elf 25/5 = 5 minutes to make one doll

One elf can make 100 dolls in 100 x 5 = 500 minutes

Then it will take 100 elves 500/100 = 5 minutes to make 100 dolls.

NOTE: This method of solving is known as the unitary method. Be careful to note that it won't take 100 elves a hundred minutes to make 100 dolls because it's a concerted effort (each of the 100 elves is making 1 doll in the same time duration (5 minutes))

Natalka [10]3 years ago
7 0
5 elves*5 minutes=5 dolls
1 elf *5 minutes=1 doll

so it takes 5 minutes for an elf to make doll

100 elves*100 minutes/5=100*20=2000 dolls in 100 minutes by 100 elves
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Molodets [167]

Answer:

198.00

Step-by-step explanation:

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8 0
2 years ago
Solve for x.<br> 2x² +21x-61 = (x+7)²<br><br> Please
Ymorist [56]

Answer:

x = \frac{-7 +\sqrt{489} }{2}

x = \frac{-7 - \sqrt{489} }{2}

Step-by-step explanation:

2x² +21x-61 = (x+7)²

expand

2x² + 21x - 61 = x² + 14x +49

move everything to one side

x² + 7x - 12 = 0

use quadratic formula

x = \frac{-b +- \sqrt{b^{2}-4ac } }{2a}

plug in the values

x = \frac{-7 +- \sqrt{7^{2}-4(1)(-110) } }{2(1)}

solve

x = \frac{-7 +- \sqrt{49-4(1)(-110) } }{2}

x = \frac{-7 +- \sqrt{49 + 440 } }{2}

x = \frac{-7 +- \sqrt{489} }{2}

7 0
2 years ago
Read 2 more answers
Circle A has center (0, 0) and radius 3. Circle B has center (-5, 0) and radius 1. What sequence of transformations could be use
Dmitrij [34]

A translation of T(x, y) = (- 5, 2) and a dilation with center (- 5, 2) with a scale factor of 1 / 3 are necessary to transform circle A into circle B. (Correct choice: D)

<h3>What sequence of rigid transformations can be done on a circle</h3>

In this problem we must determine the sequence of transformations require to transform circle A into circle B. From analytical geometry we know that the equation of the circle in standard form is:

(x - h)² + (y - k)² = r²

Where:

  • (h, k) - Coordinates of the center.
  • r - Radius of the circle.

Then, we need to apply the following rigid transformations:

Translation

f(x, y) → f(x - h, y - k), where (h, k) is the translation vector.

Dilation with center at the center of the circle

r → k · r, where k is the scale factor.

The circle A is represented by x² + y² = 3, then we derive the expression for the circle B:

f(x, y) → f(x + 5, y - 2)

(x + 5)² + (y - 2)² = 9

r → k · r

(x + 5)² + (y - 2)² = (1 / 3)² · 9

(x + 5)² + (y - 2)² = 1

Then, a translation of T(x, y) = (- 5, 2) and a dilation with center (- 5, 2) are necessary to transform circle A into circle B.

To learn more on rigid transformations: brainly.com/question/28004150

#SPJ1

8 0
1 year ago
Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last
Virty [35]

I believe dividing is always the last step.


5 0
3 years ago
Read 2 more answers
Solve the following:<br> A) 4x-1/2=x+7<br> B) 3x+2=2x+13/3<br> C) 2x-7/4=3+x/3
s2008m [1.1K]

Answer:

a. 2.5  

b. 2.333

c. 2.85

Step-by-step explanation:

A) 1. subtract -x on both sides              2. to get 3x-1/2=7  

3. Add 1/2 on both sides                    4. to get 3x=7.5    

5. divide 3 on both sides                   6. To get... x=2.5

B)1. Same process.                               2. x+2=13/3        

3. x=13/3-2                                         4. x= 2.33(repeating)

C) 1. same process.                           2. 2x-x/3=3+7/4

3. 2x-x/3=4.75                                  4. Isolate -x/3  

5.-x/3=4.75-2x                                    6. multiply both sides by 3          

7. -x=14.25-6x                                      8. 5x=14.25

9. x= 2.85

* remember to distribute the 3 to each variable.

4 0
3 years ago
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