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iragen [17]
3 years ago
5

One number is 4 more than another. the difference between their squares is 64. what are the numbers

Mathematics
1 answer:
lora16 [44]3 years ago
5 0
We have to set up 2 different equations if we are to solve for 2 unknowns.  The first equation is x = y + 4.  One number (x) is (=) 4 more than another (y + 4).  Since we have determined that x is larger (cuz it's 4 more than y), when we set up their difference, we are going to subtract y from x cuz x is bigger.  The second equation then is x^{2} - y^{2} =64.  In our first equation we said that x = y + 4, so let's sub that value in for x in the second equation: (y+4) ^{2} - y^{2} =64.  Expand that binomial to get y^{2} +8y+16- y^{2} =64.  Of course the y squared terms cancel each other out leaving us with 8y + 16 = 64.  Solving for y we get that y = 6.  Subbing 6 in for y in our first equation, x = 6 + 4 tells us that x = 10. Yay!

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B. -1/8

Step-by-step explanation:

Using the terms given in the sequence:

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3 years ago
If log(base4)x=2.5 and log(base Y)125=-3/2, find the numerical value of x/y, in simplest form.
Naya [18.7K]
X = (2^2)^(2.5) 
<span>x = 2^(2 * 2.5) </span>
<span>x = 2^5 </span>
<span>x = 32 
</span>y^(-3/2) = 125 
<span>y^(-3) = 125^2 </span>
<span>y^(-3) = (5^3)^2 </span>
<span>y^(-3) = (5^2)^3 </span>
<span>y^(-3) = 25^3 </span>
<span>y = 25^(-1) </span>
<span>y = 1/25 </span>


<span>x/y => </span>
<span>32 / (1/25) => </span>
<span>32 * 25 => </span>
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