Answer:
The product of any two rational numbers is therefore a rational number, because it too may be expressed as a fraction. For example, 5/7 and 13/120 are both rational numbers, and their product, 65/840, is also a rational number.
Step-by-step explanation:
Here's a little known but very useful factoid:
If they're inversely proportional,
then their product is constant.
Here's how to use it:
-- We're told that Y = 8 when X = 7.
So when y=8 and x=7, their product is 56 .
-- If Y REALLY varies inversely as X, then
their product is ALWAYS going to be 56.
-- So when Y=4, X= (56/4) = 14 .
Answer:
(a - b)^2 = 49 - 4b^2 +2ab
Step-by-step explanation:
Given: a^2 + b^2 = 7b (assuming A is really “a”)
b^2 + (2b - a)^2 = 7^2
Find; (a - b)^2
Plan: Use Algebraic Manipulation
Start with b^2 + (2b - a)^2 = 7^2 =>
b^2 + 4b^2 - 4ab + a^2 = 49 by expanding the binomial.
a^2 + b^2 + 4b^2 - 4ab = 49 rearranging terms
a^2 + b^2 -2ab - 2ab + 4b^2 = 49 =>
a^2 - 2ab + b^2 = 49 - 4b^2 +2ab rearranging and subtracting 4b^2 and adding 2ab to both sides of the equation and by factoring a^2 - 2ab + b^2
(a - b)^2 = 49 - 4b^2 +2ab
Double Check: recalculated ✅ ✅
(a - b)^2 = 49 - 4b^2 +2ab
The answer is 192 y^8.
(4y^2)^3 = 64y^6
64y^6 • 3y^2= 192y^8
When “multiplying” a number with an exponent, you add the 2 exponents.