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Murrr4er [49]
3 years ago
7

What two numbers add up to 45 and multiply and get 121

Mathematics
1 answer:
umka2103 [35]3 years ago
4 0
Let the two numbers be x and y.

We have x+y=45
⇒ y= 45-x.

The two numbers multiply and get 121, so we have another equation:
x*y = 121 (1)

Plug y= 45-x in (1), we have:
x* (45-x)=121
⇒ 45x - x^2 = 121 (distributive property)
⇒ x^2 - 45x = -121 (multiply -1 on both sides)
⇒ x^2- 45x + 121= 0
⇒ x= 42.128 or x= 2.872

y= 45- 42.128= 2.872
or y= 45- 2.872= 42.128.

Because it does not matter what number, x or y, is larger, the two numbers are 2.872 and 42.128.

Hope this helps~


 
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If a 24-kg mass stretches a spring 15 cm, what mass will stretch the spring 10 cm
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Answer:

<h2>16kg</h2>

Step-by-step explanation:

 This problem is borers on elasticity of materials.

according to Hooke's law,<em> "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."</em>

F= ke

where F is the applied force in N

          k is the spring constant N/m

          e is the extension in meters

Given data

mass m= 24kg

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we can solve for the spring constant k

we also know that the force F = mg

assuming g=9.81m/s^{2}

therefore

24*9.81=k*0.15\\235.44=k*0.15\\k=\frac{235.44}{0.15} \\k=1569.6N/m\\

We can use this value of k to solve for the mass that will cause an extension of  10cm= 0.1m

x*9.81=1569.6*0.1\\\\x= \frac{156.96}{9.81} \\\x= 16kg

5 0
3 years ago
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Answer:

a. 3, 100 degrees

- I know 6 is 100 degrees and angle 3 is identical to angle 6. Therefore, angle 3 is 100 degrees.

b. 6, 100 degrees

- Angle 3 and 6 are identical. This means angle 6 is 100 degrees.

c. 4, 80

- Knowing a straight line is 180 degrees and all other angles are 100 degrees, I subtracted 180-100 = 80 degrees

Step-by-step explanation:

Everything was explained above, but be sure to know...

       N

W             E

       S

- Hope that helps! Please let me know if you need further explanation.

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