Cora said that (5b)^2 = 10b^2. Describe her mistake and state the correct answer.
1 answer:
The easiest answer I know is if you swap the s with
s, then there will be two equations called parabolas. They open upward if the value is positive and open downward if the value is negative. If the exponent is 2, then it's a parabola. If it's 3, then it's a cubic function, because cube is for "3". Square is for "2". If you look at both parabolas, you can see that
is wider than
.
So the best answer I can think of is She made a mistake because the parabola on the 10x² graph is wider than the (5x)² graph. Also, it's because 5x and 10x are not the same thing. When an x value increases, the graph is narrower.
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Answer:
The sum of reciprocals is 2/3.
You don't need complex numbers to solve this, but if you try to find a and b you will need complex numbers.
Step-by-step explanation:
a+b = 2
a*b = 3
1/a + 1/b = x
(a*b)*(1/a + 1/b) = (a*b)x
b + a = (a*b)(x)
2 = 3x
x = 2/3
b = 2 - a
a*(2 - a) = 3
-a^2 + 2a = 3
-a^2 + 2a - 3 = 0
a^2 - 2a + 3 = 0
let's solve the quadratic equation
a^2 - 2a + 3 = a^2 - 2a + 1 + 2 = (a - 1)^2 + 2 = 0
(a - 1)^2 = -2
these options correspond to a and b from the original question.