10/9 x 7/4 in fraction in simplest form
1 answer:
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Answer:
the comparison must be reversed when multiplying by a negative
Step-by-step explanation:
The rules of equality apply to solving inequalities, with the exception that multiplication or division by a negative number reverses the sense of the comparison:
-x > 1
x < -1 . . . . . multiply both sides by -1
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Effectively, multiplication (or division) by a negative number is equivalent to reflection across the origin. Things that were ordered left/right (on the number line) are ordered right/left after such a reflection:
-2 < -1
1 < 2
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<em>Additional comment</em>
Application of any function requires that you pay attention to ordering. Some functions naturally reverse the order; others do so only on specific domains.
Consider f(x) = 1/x.
1 < 2
f(1) > f(2) . . . . because the slope of the f(x) function is negative everywhere.
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<em>In the first and second quadrants</em>, the cosine function also reverses order.
20° > 10°
cos(20°) < cos(10°)
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Probably the most commonly encountered function used with inequalities is the absolute value function.
|x-3| > 2
This function has one domain where the slope is negative, and another domain where the slope is positive.
For x < 3, the function negates its argument, so we have ...
-(x -3) > 2
-x +3 > 2
-x > -1
x < 1 . . . . . everywhere consistent with x < 3
For x ≥ 3, the function does nothing, so we have ...
x -3 > 2
x > 5
The solution to this absolute value inequality is (x < 1) ∪ (x > 5).
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You can also resolve negative coefficients by adding the opposite. Addition and subtraction never require any change to the comparison operator.
-x > 1
0 > x +1 . . . . x is added
-1 > x . . . . . . -1 is added
Answer:
Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile
Company (2) is $7.4 cheaper.
Step-by-step explanation:
From the tables given in the picture,
Let the equation representing the rental 'y' and distance traveled 'x' is represented by,
y = mx + b
For company (1),
Here m = per mile rental charges = Slope of the graph
b = Initial charges
Since slope of the line passing through two points and
is given by,
m =
Therefore, slope of the line passing through (30, 53.55) and (60, 87.15) will be,
m = = $1.12 per mile
So the equation will be,
y = 1.12x + b
Since this line passes through (30, 53.55),
53.55 = 1.12(30) + b
b = 53.55 - 33.6
b = 19.95
So the expression representing charges for the company (1) will be,
y = 1.12x + 19.95
For company (2),
Per mile charges = slope of the line
m =
m = $0.85 per mile
Equation for the charges will be,
y = 0.85x + b
Since this line passes through (25, 56.75),
56.75 = 0.85(25) + b
b = 56.75 - 21.25
b = 35.5
Therefore, equation representing total charges for company (2) will be,
y = 0.85x + 35.5
By comparing per mile charges,
Company (1) charges $1.12 per mile and company (2) charges $0.85 per mile
Steven plans to drive 85 km in rental truck.
Charges for company (1),
y = 1.12x + 19.95
y = 1.12(85) + 19.95
y = $115.15
Charges for company (2),
y = 0.85x + 35.5
y = 0.85(85) + 35.5
y = $107.75
Difference in charges of both the companies = 115.15 - 107.75 = $7.4
Therefore, company (2) is $7.4 cheaper.