Answer:
Step-by-step explanation:
Required
Determine the sets of natural number
Represent this set with letter N
From definition of natural numbers, they are integer numbers starting from 1;
In other words: 1,2,3,4,5, and so on.
To represent this as a set of N, we have
<em>The ..... means that the counting still continues</em>
The volume of the fourth box is of 410.1 cubic inches.
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The volume of a rectangular prism is given by the <u>base area multiplied by the height,</u> that is:
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- For the first three boxes, the height is constant at 9 inches.
- At the base, the <u>edge length is multiplied by 1.5</u> each time, as
, thus, for the fourth box, the edge length, in inches, will be of 
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- Square base, of<u> length 6.75 inches</u>, thus:
- Height of <u>9 inches</u>, thus
and:
The volume of the fourth gift box will be of 410.1 cubic inches.
A similar problem is given at brainly.com/question/23756783
Answer:
The force is 12 N
Step-by-step explanation:
* Lets explain how to solve the problem
- Direct variation is a relationship between two variables that can
be expressed by an equation in which one variable is equal to a
constant times the other
- If y ∝ x , then y = kx , where k is the constant of variation
* Lets solve the problem
- The force acting on the object varies directly with the object's
acceleration
∵ The force is F in newtons and a is the acceleration is m/s²
∴ F ∝ a
∴ F = ka
- To find k substitute F and a by the initial values of them
∵ A force of 10 N acts on a certain object, the acceleration of the
object is 5 m/s²
∵ F = 10 N when a = 5 m/s²
∵ F = ka
∴ 10 = k(5)
- Divide both sides by 5
∴ K = 2
- Substitute the value of k in the equation
∴ F = 2a
- Lets find the force when the acceleration is 6 m/s²
∵ a = 6 m/s²
∴ F = 2(6) = 12
* The force is 12 N
Answer:2.28571429 dollars. 4/1.75= 2.28571429, therefore showing how much one will cost.
Step-by-step explanation:
<span>Simplifying
25 + 10(12 + -1x) = 5(2x + -7)
25 + (12 * 10 + -1x * 10) = 5(2x + -7)
25 + (120 + -10x) = 5(2x + -7)
Combine like terms: 25 + 120 = 145
145 + -10x = 5(2x + -7)
Reorder the terms:
145 + -10x = 5(-7 + 2x)
145 + -10x = (-7 * 5 + 2x * 5)
145 + -10x = (-35 + 10x)
Solving
145 + -10x = -35 + 10x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-10x' to each side of the equation.
145 + -10x + -10x = -35 + 10x + -10x
Combine like terms: -10x + -10x = -20x
145 + -20x = -35 + 10x + -10x
Combine like terms: 10x + -10x = 0
145 + -20x = -35 + 0
145 + -20x = -35
Add '-145' to each side of the equation.
145 + -145 + -20x = -35 + -145
Combine like terms: 145 + -145 = 0
0 + -20x = -35 + -145
-20x = -35 + -145
Combine like terms: -35 + -145 = -180
-20x = -180
Divide each side by '-20'.
x = 9
Simplifying
x = 9.
Hope this helps you ! =')</span>
