Test 1 2021-22 19 of 9
The graph represents Samantha's walk in front of a motion detector. Identify two points marked on the graph that define the interval
where her average rate of change was 2/3 meters per second.
Motion Detector Walk
Answers
Given that the shape of the graph is curved, the rate of change can be
estimated by using the average value between specified points.
The points are;
[tex]\underline{(6, \, 6)}[/tex][tex]\underline {(9, \, 8)}[/tex]Reasons:
The coordinates of the points marked (distances and time) during the walk are;
[tex]\begin{tabular}{|c|c|}Time (seconds), x&Distance from motion detector (meters), y\\0&1\\3&2\\5&4\\6&6\\7&7\\9&8\end{array}\right][/tex]
Required: Identification of two points marked on the graph that define the
interval where Samantha's average rate of change was 2/3 meters per
second.
Solution:
The average rate of change between two points is given by the ratio of
difference in the distance from the motion detector to the difference in
time between the points.
[tex]\displaystyle Average \ rate \ of \ change = \frac{Change \ in \ distance}{Change \ in \ time} = \mathbf{ \frac{\Delta y}{\Delta x}}[/tex]
At the required points, the change in the y-values, will be 2 × a, while the
corresponding change in x-values will be 3 × a, where, a is rational number.
From the above table, at the points where the time is 6 seconds and 9
seconds, we have the following distance time ordered pair;
(6, 6), and (9, 8), from which we have;
[tex]\displaystyle Average \ rate \ of \ change =\frac{\Delta y}{\Delta x} = \mathbf{\frac{8 - 6}{9 - 6}} = \frac{2}{3}[/tex]
Therefore;
The points [tex]\underline{(6, \, 6)}[/tex], and [tex]\underline {(9, \, 8)}[/tex], are two points that represent an interval
where her average rate of change was 2/3 meters per second.
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In writing down the opposite value of each number, the comparison Tina wrote incorrectly is: Comparison X
Recall:
Opposite values of a number are numbers that are of the same distance from point zero on a number line.For example, if a is a number, the opposite of a is -a. Or if -3 is a number, the opposite of -3 is 3 because -3 and 3 are both 3 units away from point zero on a number line.Thus, Tina's comparison is given in the diagram attached below.
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
Swap sides so that all variable terms are on the left hand side.
2x^2+4x−1=y
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2x^2 +4x−1−y=0
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1.
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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We have a line graph shown in the picture.
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As we can see the amount of slushy left in the cup is decreasing as the time increases.
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Step-by-step explanation:
123
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
the rate of change is officially
(f(x2) - f(x1)) / (x2 - x1)
but for a line function (as we have here) this is totally easy : it is the slope of the line.
and that means it is the factor of x.
in our case this is -3/2.
because the slope of a line is the ratio "y coordinate change / x coordinate change". and that is exactly corresponding to the general rate of change definition above.
Answer: (f(x2) - f(x1)) / (x2 - x1)
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Step-by-step explanation: HOPE IT HELPS YOU .THANKS .
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Step-by-step explanation:
Given f varies directly with m then the equation relating them is
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Answers
Answer:
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Step-by-step explanation:
Since you didn't provide an image of the polygon I can't give you a direct answer but this is how you do it.
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Answers
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Step-by-step explanation:
Jenny received a $30.50 gift card for a photo center. She used it to buy prints that cost 20 cents each. The remaining balance, B (in dollars), on the card after buying x prints is given by the following.
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Answers
The remaining balance on the card is $24.50.
The balance on the card after buying the prints is the value of the gift card less the total cost of the prints
Balance = value of the gift card - total cost of the prints
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0.20 x 30 = $6
Balance = $30.50 - $6 = $24.50
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