An expression is defined as a set of numbers, variables, and mathematical operations. The given statement can be modeled as (3m+7)/27 < n.
<h3>What is an Expression?</h3>
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given statement "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression as shown below.
(3m+7)/27 < n
Hence, the given statement can be modeled as (3m+7)/27 < n.
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Answer :
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Answer:
x=2/5
or
x=-22/5
Step-by-step explanation:
If Ciro's expression is equal to Gunther's expression x is equal to 2/5.
If Gerard's expression is equal to Gunther's expression x is equal to -22/5.
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Answer:
A)
B) Angle relationship used to find was alternate interior angles of a traversal between two parallel lines
Step-by-step explanation:
Given :
To find measure of .
Part A
From the figure we can say:
[Alternate interior angles are congruent]
∴ [By substitution ∵ ]
For Δ PQR
[Sum of two interior angles of a triangle is equal to the opposite exterior angle]
[By subtraction property of equality]
[By substitution ∵
Part B:
We used the angle relationship of alternate interior angles of traversal between two parallel lines to find measure one angle of the Δ PQR which in turn helped us to find the measure of other angle of triangle which is as the two angles found are opposite to the exterior angle that is =120°
Relation used:
[Alternate interior angles are congruent]
[By substitution ∵ ]
Answer:
Consider lining up all the blue marbles and placing one red marble in between them. Let that arrangement be fixed. The remaining red marbles will be 5 red marbles. Note that the arrangement will be:
x BR x BR x BR x BR x BR x BR x BR x B x
Note that this is the same even if our arrangement is
x B x RB x RB x RB x RB x RB x RB x RB x
Note that there are 9 spots, denoted by x, where we can put the 5 remaining red marbles. To find the number of ways of putting the remaining 5 red marbles to x, it is similar in finding the number of non-negative solution for the equation
which is given by
= 1287
Hence, there are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.