Answer:
The smallest value of p+q is 11
It happens when p = 6 and q = 5.
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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}\\\\](https://tex.z-dn.net/?f=%5Csqrt%7B180%7D%20%3D%20%5Csqrt%7B4%2A45%7D%20%3D%20%5Csqrt%7B4%7D%2A%5Csqrt%7B45%7D%3D%202%5Csqrt%7B45%7D%5C%5C%5C%5C%5Csqrt%7B180%7D%20%3D%20%5Csqrt%7B9%2A20%7D%20%3D%20%5Csqrt%7B9%7D%2A%5Csqrt%7B20%7D%3D%203%5Csqrt%7B20%7D%5C%5C%5C%5C%5Csqrt%7B180%7D%20%3D%20%5Csqrt%7B36%2A5%7D%20%3D%20%5Csqrt%7B36%7D%2A%5Csqrt%7B5%7D%3D%206%5Csqrt%7B5%7D%5C%5C%5C%5C)
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.
Answer:
c
Step-by-step explanation:
75 is supplementary to angle b. then angle a = 180-75=105
She could use the following methods:
8 dimes
16 nickles
2 quarter and 3 dimes
2 quarters and 6 nickles
so, 4 combos
The answer I’m pretty sure is 14.4