The two numbers are 35 and 65.
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
For example, 2x – 5 = 13.
Given that, two numbers, their sum is 100 and the difference between them is 30. We need to find the number,
Let the 2 numbers be x and y.
y = x + 30
Sum of the two numbers = 100
x + y = 100
x + (x + 30) = 100
2x = 70
x = 35
y = x + 30 = 65
Hence, the two numbers are 35 and 65.
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Answer:
, , and
Step-by-step explanation:
1.
Let's find a common denominator:
=
2/(x-1)x(x+1)
2.
Distribute exponents:
2^3(y^2)^3
__________
8^2(y)^2
Numerator:
2 to the power of 3 equals (2 · 2 · 2) = 8
y to the power of 2 to the power of 3 equals, y to the power of 6 (this is because when exponents in parenthesis are held to the power of another number outside of the parenthesis, you multiply them)
Now let's simplify the denominator:
8 to the power of 2 equals (8 · 8) = 64
y to the power of 2 is just y to the power of 2, so our new expression is:
Let's cancel the terms further:
8/64 can be simplified to 1/8
And when you cancel exponents, you subtract the denominator's exponent from the numerator's exponent ( = )
Now put them together:
Which is,
=
y^4/8
3.
The common denominator for both fractions is 3t, so let's make -1/3's denominator 3t by multiplying t to both the numerator and the denominator:
-1 · t
_____ = -1(t)/3t = -t/3t
3 · t
Now let's solve for the numerator:
(t + 2) - t, the t's cancel out, t - t + 2 = 2
And the denominator stays the same, so it will still equal 3t
Finally, you'll get an answer of
=
2/3^2
Answer:
all work is shown/pictured