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Scorpion4ik [409]
3 years ago
13

Determine the LCM of 12 and 48.​

Mathematics
1 answer:
Pavel [41]3 years ago
7 0

Answer:

48

Step-by-step explanation:

If you factor both, you get:

12 = 2*2*3

48 = 2*2*2*2*3

Now take all the prime factors and find how many times they occur at most.

Then you get 2*2*2*2*3 = 48.

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Problem page the longer leg of a right triangle is 1ft longer than the shorter leg. the hypotenuse is 9ft longer than the shorte
LenKa [72]
Hello,

To solve this problem we want to use the Pythagorean Theorem. 
The pythagorean theorem states that for a 90° triangle, 

a^{2} +  b^{2}  =  c^{2}

where a and b represent the two legs of the triangle, and c represents the hypotenuse. 

Let a = the longer leg and b = the shorter leg.
If the longer leg of the triangle is 1 foot longer than the shorter leg, then
a = b +1. 

If the hypotenuse is 9 feet longer than the shorter leg, then c = b + 9.
Using the equations we created, we can plug them into the Pythagorean Theorem to solve for a, b, and c. 

Doing this, we have:
a^{2} +  b^{2} =  c^{2}
(b+1)^{2}  + b =  (b+9)^{2}

Expanding this, we get b^{2} + 2b + 1 +  b^{2}  =  b^{2} + 18b + 81

 2b^{2} + 2b + 1 =  b^{2} + 18b + 81

 b^{2}  + 1 = 16b + 81

 b^{2} = 16b + 80
 
b^{2} - 16b - 80 = 0



Solving for b, we get b = 20, and b = -4.
The length of the side of a triangle cannot be negative, so we know that b = 20. 

However, we should check this with the original question to make sure it checks out.

a = b + 1
a = 20 + 1 = 21

c = b + 9
c = 20 + 9 = 29

So, we have a = 21, b = 20, and c = 29. (Also, 20-21-29 is a well known Pythagorean triple)
Using the Pythagorean Theorem, we have:

21^{2} +  20^{2} =  29^{2}
441 + 400 = 841
841 = 841, checks out.

So, the shorter leg is 20 feet, the longer leg is 21 feet, and the hypotenuse is 29 feet. 

Hope this helps!

7 0
3 years ago
Explain why 7*8 is not a number sentence
Naily [24]
Because it is really simple if it was an equation then it would be a number sentence since it only has 2 numbers and 1 thing that u are doing it is not a number sentence
4 0
2 years ago
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your d
Naily [24]

Answer:

With a correlation coefficient of 0.109 you can not be confident at all; this is about as close to a random guess you could get.  

Step-by-step explanation:

Lines of best fit are used to try to make a correlation (relationship) about data that will either be positive (uphill), negative (downhill) or no correlation (points are scattered).  Correlation coefficients based off of a line of best fit will fall between -1 and +1 where -1 would represent a perfect negative relationship and +1 would represent a perfect positive relationship.  A correlation coefficient of 0 would indicate that there is no relationship.  So, if your data shows a correlation coefficient of 0.109, which is closest to 0 on a number line, then you can't be sure that your data has a very close relationship.


7 0
3 years ago
The area of a rectangle that is 15 feet long and 10 feet wide is
butalik [34]

Answer:

use photo math plz mark me brainlisist

Step-by-step explanation:

6 0
3 years ago
Solve for g.<br> 9 - g = 2g
svp [43]

Answer:

g=3

Step-by-step explanation:

9 - g = 2g

+g       +g

9=3g

divide both sides by 3

g=9

8 0
3 years ago
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