Answer:
see below
Step-by-step explanation:
<em>Which of the equations from part A represent adding two rational numbers?</em>
Equations A, C, E
<em>What hypothesis can you make about the sum of two rational numbers?</em>
The sum of two rationals will always be rational
<em>Will the addition result in a rational or an irrational number?</em>
Our hypothesis is that the result is always rational. This can be justified by the fact that the sum of two rationals a/b + c/d, where a, b, c, d are integers and bd≠0, is (ad+bc)/(bd), a rational, based on closure of integers for multiplication and addition.
<em>Which equations represent the sum of a rational and an irrational number?</em>
Equations B, F
<em>What hypothesis can you make about the sum of an irrational and a rational number?</em>
The sum of a rational and irrational number is always irrational.
Answer:
C) (6,2)
Step-by-step explanation:
Rewrite equations:
y=x−4;x+2y=10
Step: Solve y=x−4for y:
y=x−4
Step: Substitute x − 4 for y in x+2y=10:
x+2y=10
x+2(x−4)=10
3x−8=10(Simplify both sides of the equation)
3x−8+8=10+8(Add 8 to both sides)
3x=18
3x
3
=
18
3
(Divide both sides by 3)
x=6
Step: Substitute6forxiny=x−4:
y=x−4
y=6−4
y=2(Simplify both sides of the equation)
Hope this helps!
:)
If sinα=cosß it means that ß=90-α. This also means that α+ß=90 so we can say:
4k-22+6k-13=90
10k-35=90
10k=125
k=12.5°
...
The above identity comes up a lot, and is one worth committing to memory for sure.
sinα=cos(90-α) or vice versa cosα=sin(90-α)
Find the Greatest Common Factor (GCF)
GCF = 4
Factor out the GCF. (Write the GCF first, then in parenthesis, divide each term by the GCF.)
4(8x/4 + 16y/4 + 44/4)
Simplify each term in parenthesis
<u>= 4(2x + 4y + 11) </u>
Answer: 2 lbs of cherries
Cherries = $5 per pound
Oranges = $2 per pound
Total Cost = $18
Total weight = 6 lb
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Define x and y
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Let x be the number of lb of cherries
Let y be the number of lb of oranges
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Construct equations
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x + y = 6 ---------------------------- (1)
5x + 2y = 18 ---------------------------- (2)
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Solve x and y
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From equation (1):
x + y = 6
x = 6 - y
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Substitute x = 6 - y into equation 2
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5x + 2y = 18
5 (6 - y) + 2y = 18
30 - 5y + 2y = 18
3y = 30 - 18
3y = 12
y = 4
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Substitute y = 4 into equation (1)
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x + y = 6
x + 4 = 6
x = 2
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Find the weight of cherries and oranges
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Cherry = x = 2 lb
Oranges = y = 4 lbs
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Answer: Alex bought 2 lb of cherries
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