Answer:
c
Step-by-step explanation:
The expression equivalent to ∛162 is ∛6 × ∛27
<h3>What is the cube root of a number?</h3>
The cube root of a number is a number a such that when another number, b multiplies itself 3 times, we get a.
So,
- a = b × b × b = b³and
- b = ∛a
<h3>What is a perfect cube?</h3>
A perfect cube is a number such that its cube root which is an integer or whole number.
<h3>How to find ∛162.</h3>
Since we have ∛162.
Since 162 is not a perfect cube, to find its cube root, we have
∛162 = ∛(54 × 3)
= ∛(18 × 3 × 3)
= ∛(2 × 9 × 3 × 3)
= ∛(2 × 3 × 3 × 3 × 3)
= ∛(6 × 27)
= ∛6 × ∛27
So, the expression equivalent to ∛162 is ∛6 × ∛27
Learn more about perfect cube here:
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Answer:
The width of the door is 36 inches
Step-by-step explanation:
The given parameters are;
The given area of the door = 3024 in.²
The length of the door = 48 + The width of the door
Let W represent the width of the door
Therefore, we have;
The length of the door = 48 + W
The area of the door = The length of the door × The width of the door
∴ By substitution, the area of the door = 3024 = W × (48 + W)
3024 = W × (48 + W) = 48·W + W²
48·W + W² = 3024
∴ 48·W + W² - 3024 = 0
Rearranging, we get;
W² + 48·W - 3024 = 0
By trial and error, we have;
(W + 84)×(W - 36) = 0
Therefore, given that the width of the door is a natural number, we have;
The width of the door, W = 36 inches
Answer:
144?
Step-by-step explanation:
Answer:
The larger number is 37. This makes the smaller number 56 - 37, which is 19.
Step-by-step explanation:
The first step is to pick variables for the two numbers. Lets call the smaller number x and the larger number y.
Since the sum of the two numbers is 56, this means that x + y = 56. Let's call this equation 1 and save it for later.
The next sentence says:
The smaller number is 18 less than the larger number. So, 18 less than the larger number would be y - 18. So, the smaller number must be equal to this, so
x = y - 18
Replace the x in equation 1 with y - 18
x + y = 56
(y-18) + y = 56 (replace x with y-18)
2y - 18 = 56 (add the y's)
2y = 74 (add 18 to both sides)
y = 37 (divide both sides by 2)
So, the larger number is 37. This makes the smaller number 56 - 37, which is 19.
Hope this helps!! :)
