Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
2 answers:
9514 1404 393
Answer:
p(x) = -x^2 +2x +24
Step-by-step explanation:
When the polynomial has a zero at x=q, it has a factor of (x -q). The zeros of -4 and 6 tell you the factors are (x -(-4)) and (x -6). The end behavior tells you the leading coefficient is negative.
p(x) = -(x +4)(x -6)
p(x) = -x^2 +2x +24
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Apply division by 10 when one tenth of a number is required and apply multiplication by 10 when 10 times of a number is required.
<u>Solution:</u>
Need to determine what operation is required to get one-tenth of a number and 10 times of a number
To get one tenth of a number, divide the number by 10.
For example to get one – tenth of 100, divide it by 10, we get 10 as a result.
To get ten times of a number, multiply the number by 10
For example 10 times of 10 = 10 x 10 = 100
Hence apply division by 10 when one tenth of a number is required and apply multiplication by 10 when 10 times of a number is required.
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.
