Answer:
- x(27 +24) or 3x(9 +8)
- 0.5(n +5) or 2.5(n/5 +1)
Step-by-step explanation:
The distributive property of multiplication over addition tells us that the product of a value and a sum will be the same as the sum of products of the value and the sum's addends. This property can be used to add or remove parentheses from an arithmetic expression.
a(b +c) = ab +ac . . . . expression of the distributive property
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When applying the distributive property to a sum, the first step is to look for a factor common to the terms of the sum. That factor need not be the greatest common factor, though it is often useful if it is.
Below, we have written each expression using two different common factors.
<h3>a)</h3>
27x +24x = x(27 +24) = 3x(9 +8)
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<h3>b)</h3>
0.5n +2.5 = 0.5(n +5) = 2.5(n/5 +1)
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<em>Additional comment</em>
Finding a common factor can make use of knowledge of multiplication tables, rules of exponents, and identities involving various functions used in algebraic expressions. It is sometimes useful to list the prime factors of each of the terms as an aid to finding a common one. Where fractions are involved, it is sometimes helpful to express them all using a common denominator.
The Euclidean Algorithm can also be useful for finding common factors.
Answer:
- ribbon: $0.45
- markers: $0.08
Step-by-step explanation:
Each purchase will be the sum of products of item price and number of items. The two purchases give rise to two equations.
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<h3>equations</h3>
The variables are defined in the problem statement. The two purchases are ...
11r +16m = 6.23
13r +7m = 6.41
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<h3>solution</h3>
A calculator offers a simple way to find the solutions to these equations. The attachments show the solution to be ...
The cost of ribbon is $0.45; the cost of a marker is $0.08.
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The "cross-multiplication" method of solving these equations seems particularly useful when the coefficients are mutually prime. It starts with a rewrite to general form:
- 11r +16m -6.23 = 0
- 13r +7m -6.41 = 0
Then we define three "cross products":
Δ1 = (11)(7) -(13)(16) = -131
Δ2 = (16)(-6.41) -(7)(-623) = -58.95
Δ3 = (-6.23)(13) -(-6.41)(11) = -10.48
The solutions are ...
r = Δ2/Δ1 = -58.95/-131 = 0.45
m = Δ3/Δ1 = -10.48/-131 = 0.08
The cost of ribbon is $0.45; the cost of a marker is $0.08.
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For more about the cross-multiplication method you can read ...
brainly.com/question/26397343
Answer:
The slope is 1/2
Step-by-step explanation:
To find the slope you use the formula rise/run
The rise is the second y coordinate minus the first y coordinate
The run is the second x coordinate minus the first y coordinate
Step one:
Take 2 points: I used (2,1) and (4,2)
Step two:
Use the formula
2-1/4-2
The answer is the slope of the line
The slope is 1/2
Answer:
8
Step-by-step explanation:
