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frez [133]
3 years ago
11

Find the equivalent ratio for 32:__=12:24

Mathematics
2 answers:
Igoryamba3 years ago
6 0
   
32 : 64 = 12 : 24

or


\displaystyle\\
 \frac{32}{\bf64} = \frac{12}{24}



V125BC [204]3 years ago
5 0

Answer:

32: 64= 12 : 24.

Step-by-step explanation:

Given : 32:__= 12 : 24.

To find : Find the equivalent ratio.

Solution : We have given  32:__= 12 : 24.

Let the number be x .

32 : x = 12 : 24.

\frac{32}{x}=\frac{12}{24}.

On cross multiplication

32 * 24 = 12 *x .

On dividing both sides by 12 .

x = 32 * 2.

x = 64.

Then ratio :  32: 64= 12 : 24.

Therefore, 32: 64= 12 : 24.

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√180 can be expressed in the form p√q. where p and q are integers. Find the smallest value of p + q. ​
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Answer:  

The smallest value of p+q is 11

It happens when p = 6 and q = 5.

=======================================================

Explanation:

Let's factor 180 in such a way that exactly one factor is a perfect square.

I'll ignore the trivial factor of 1.

Here are the possible factorizations we could go with:

180 = 4*45

180 = 9*20

180 = 36*5

Those factorizations then lead to the following

\sqrt{180} = \sqrt{4*45} = \sqrt{4}*\sqrt{45}= 2\sqrt{45}\\\\\sqrt{180} = \sqrt{9*20} = \sqrt{9}*\sqrt{20}= 3\sqrt{20}\\\\\sqrt{180} = \sqrt{36*5} = \sqrt{36}*\sqrt{5}= 6\sqrt{5}\\\\

Then we have

p+q = 2+45 = 47

p+q = 3+20 = 23

p+q = 6+5 = 11

The smallest value of p+q is 11 and it happens when p = 6 and q = 5.

Side note: p+q is smallest when we go with the largest perfect square factor.

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