Step-by-step explanation:
h = height of rectangle (should be "length", but ok)
w = width of rectangle
w = h + 97
the diagonal of the rectangle is the Hypotenuse (baseline) of a right-angled triangle with the legs being one height and one width side of the rectangle.
so, we use Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle).
diagonal² = h² + (h + 97)² = h² + h² + 2×97h + 97²
113² = 12769 = 2h² + 194h + 9409
3360 = 2h² + 194h
1680 = h² + 97h = (h + 97/2)² - 9409/4
(completing the square)
6720/4 + 9409/4 = (h + 97/2)²
16129/4 = (h + 97/2)²
127/2 = h + 97/2
30/2 = h = 15
the height is 15.0 in
3 ways to express 3 to the 5th power as the product of powers
First expression
=> 3 x 3 x 3 x 3 x 3 - In this expression, we multiplied 3 5 times and the product is 243
Second expression
=> 3 ^ 5, in where ^ read as raised to the power, the product is also 243
Third expression
=> 3^2 x 3^3
=> (3 x 3) x (3 x 3 x 3)
=> 9 x 27, the product also equals to 243.
Answer:
Associative
Step-by-step explanation:
Associative property is the one that says that when 3 or more numbers are summed, the grouping of such numbers has no effect on the result of the sum. It is:
(a + b) + c = a + (b + c) for every a, b and c real numbers.
Answer:
True
Step-by-step explanation:
(6³ * 3³)² = 18⁶
Multiply inside the parenthesis.
(18³)² = 18⁶
When you put powers to powers, they multiply, eg:
(x³)⁴ = x³°⁴ = x¹²
18⁶ = 18⁶
True.
