Answer:
640 m
Step-by-step explanation:
We can consider 4 seconds to be 1 time unit. Then 8 more seconds is 2 more time units, for a total of 3 time units.
The distance is proportional to the square of the number of time units. After 1 time unit, the distance is 1² × 80 m. Then after 3 time units, the distance will be 3² × 80 m = 720 m.
In the additional 2 time units (8 seconds), the ball dropped an additional
... (720 -80) m = 640 m
_____
<em>Alternate solution</em>
You can write the equation for the proportionality and find the constant that goes into it. If we use seconds (not 4-second intervals) as the time unit, then we can say ...
... d = kt²
Filling in the information related to the first 4 seconds, we have ...
... 80 = k(4)²
... 80/16 = k = 5
Then the distance equation becomes ...
... d = 5t²
After 12 seconds (the first 4 plus the next 8), the distance will be ...
... d = 5×12² = 5×144 = 720 . . . meters
That is, the ball dropped an additional 720 -80 = 640 meters in the 12 -4 = 8 seconds after the first data point.
Answer:
x=-2 x=1
Step-by-step explanation:
16x2 + 10x – 27 = -6x + 5
Add 6x to each side
16x^2+6x + 10x – 27 = -6x+6x + 5
16x^2 +16x -27 = 5
Subtract 5 from each side
16x^2 + 16x – 27-5 = 5 - 5
16x^2 +16x -32 = 0
Factor out 16
16 (x^2 +x-2)=0
Factor
16 (x+2) (x-1) =0
Using the zero product property
(x+2) =0 x-1=0
x=-2 x=1
Answer:
22 meters
Step-by-step explanation:
Area of yellow rectangle: 6x4=24
Area of gray rectangle: 8x=24
x=3
Thus, the perimeter is 3+3+8+8, which is 22.
Answer:
an=1*2.5^(n-1)
=2.5^(n-1)
Step-by-step explanation:
Complete question below:
What value, written as a decimal, should Lena use as the common ratio? Lena is asked to write an explicit formula for the graphed geometric sequence. On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 2.5), (3, 6.25).
Solution
Point (1, 1), (2, 2.5), (3, 6.25).
a=1
ar=2.5
ar^2=6.25
From ar and ar^2
r=6.25/2.5
=2.5
r=2.5
an=ar^(n-1)
Therefore, the explicit formula is
an=1*2.5^(n-1)
=2.5^(n-1)
Answer:
C
Step-by-step explanation:
