Answer:
8530
Step-by-step explanation:
The remainder is 5⁵ + 2(5)⁴ + 9(5)³ - 6(5)² + 3(5) + 3165 = 8530
Slope = 6 , through = (4,13)
1 answer:
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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.
Answer:
29% of the drive
Step-by-step explanation:
The plot of the problem is:
Transmitter at origin (0,0)
City to the north at (0,70)
City to the east at (74,0)
The path from city to city is a line with slope:
m = (-70)/74 = -35/37
and y-intercept at y = 70, so the equation is y = (-35/37)*x + 70.
The transmitter reach the area enclosed by the next circle:
x^2 + y^2 = 53^2
See the picture attached
The intersection is gotten from the picture or solving:
x^2 + [(-35/37)*x + 70]^2 = 53^2
the points approximately are: (24.1, 47.2) and (45.8, 26.7)
From Pythagorean theorem the total distance of the trip is:
d1 = √(70^2 + 74^2) ≈ 101.9 miles
And the distance when the signal is picked up is:
d2 =√ [(45.8 - 24.1)^2 + (47.2 - 26.7)^2] ≈ 29.9 miles
You will pick up a signal from the transmitter in (d2/d1)*100 = 29% of the drive.
