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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Related Questions
Can someone please take the time out of they’re day and help me and with this question
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 100) and (x₂, y₂ ) = (2, 200) ← 2 points on the line
m = [tex]\frac{200-100}{2-0}[/tex] = [tex]\frac{100}{2}[/tex] = 50
The line crosses the y- axis at (0, 100 ) ⇒ c = 100
y = 50x + 100 ← equation of line
where y is monthly savings and x the time in months
(b)
Slope is the monthly deposit , that is $50 per month
The y- intercept indicates the original amount in her account , that is $100
(I need this asap with explanation and work)
Answers
Answer:
Half of 24 is 12, and if all 12 have been red, then the other 12 are all black.
y=2x squared +4x-1 . help me
Answers
Answer:
y = 9/8 for part one of solving y in this equation .
Step-by-step explanation:
Answer:
x= (√2y+6/2)-1
Step-by-step explanation:
Swap sides so that all variable terms are on the left hand side.
2x^2+4x−1=y
Subtract y from both sides.
2x^2 +4x−1−y=0
Using quadratics formula:
x=-4±√4²-4*2(y-1)/2*2
x= −4±2√ 2y+6/4
Next solve the equation by using either ± = subtraction or addition
I am using ± = addition. This means I add -4 to 2. From there I simplify equation.
x= (√2y+6/2)-1
Not sure if this means to find x, but I think this is what it would be.
Solve.
(-2/3)(-1/4)
A. -2/7
B. -2/12
C. 2/12
D. 2/7
Answers
Answer:
C. 2/12
Step-by-step explanation:
multiplication and when two negatives are multiplied together they always equal a positive i hope this helps have a great day :)
Can you help this is a lot. I don't really get it
Answers
Answer:
country is 15 30 45 60 75 90 105 120 135 150 pop is 5.75 11.5 17.25 23 28.75 34.5 40.25 46 51.75 57.5
why you take my profile picture hello.....
please help me, please and thank youuu! :D
Answers
Answer:
f = - [tex]\frac{19}{7}[/tex]
Step-by-step explanation:
Given f varies directly with m then the equation relating them is
f = km ← k is the constant of variation
To find k use the condition f = - 19 when m = 14
- 19 = 14k ( divide both sides by 14 )
- [tex]\frac{19}{14}[/tex] = k
f = - [tex]\frac{19}{14}[/tex] m ← equation of variation
When m = 2 , then
f = - [tex]\frac{19}{14}[/tex] × 2 = - [tex]\frac{19}{7}[/tex]
the sum of all but one interior angle of a heptagon is 776°. what is the measure of the final interior angle?
Answers
Answer:
The final interior angle = 124°
Step-by-step explanation:
A heptagon has 7 sides. The sum of the interior angles formula:
The sum of the interior angles = (n - 2)180 where n = number of sides.
The sum of the interior angles= (7 - 2)180° = 900°
Six interior angles = 776°.
The final interior angle + six interior angle = 900°
The final interior angle + 776° = 900°
The final interior angle = 900° - 776°
The final interior angle = 124°
Answer:
124
Step-by-step explanation:
Right on Edge 2022
The world population is about 7.8 billion people now and the population grows at an annual rate of 1.1%. What will the population be in 2031?
Answers
Answer:
8.58 billion people
Step-by-step explanation:
7.8
1.1
78
78
858 place the decimal where it should be to get 8.58
Help me out plesseee!!
Answers
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)
because the slope of a line is the ratio "y coordinate change / x coordinate change".
Step-by-step explanation: HOPE IT HELPS YOU .THANKS .
which is an equation of the line that goes through the points (-4,7) and (-4,11)
Answers
Answer:
it's a answer!!
Step-by-step explanation:
ITS AN ANSWER BECAUSE IT CAN BE! THATS WHY! BLAH BLAH BLAH! I do not say blah blah blah
What is the value of the digit in the hundred thousands place?
61,889,248
A. 60,000,000
B. 800,000
c. 100,000
D. 80,000
Answers
Answer:
C
Step-by-step explanation:
Describe how modern entertainment has begun to reflect the changing makeup of families in America.
Answers
It should be noted that modern entertainment has played a vital role in shaping African culture and homes.
Through modern entertainment, Africans views on marriages have changed. Most African men now marry one wife which was quite different in the olden days when it was believed that an increase in the number of wives one had was used to show superiority.
Also, entertainment has been impactful in the issue of child-bearing. Women now give birth to lesser children at an average of 3 per home.
Lastly, modern entertainment has also influenced the kind of movies and music that are listened to.
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Evaluate –32 + (2 – 6)(10).
Answers
Answer:
-49
Step-by-step explanation:
You want to evaluate the expression -3² +(2 -6)(10).
Order of operationsThe Order of Operations tells you the expression in parentheses is evaluated first, followed by the term containing the exponent.
-3² +(2 -6)(10) = -3² +(-4)(10)
= -9 +(-4)(10)
= -9 -40
= -49
The value of the expression is -49.
__
Additional comment
The leading minus sign applies to the result from the squaring operation. If the square of -3 is wanted, it is put in parentheses: (-3)² = 9.
<95141404393>
So the answer is all of that
Answers
Answer:
What's the question?
Step-by-step explanation:
Sean is drinking a slushy as fast as he can. The amount of slushy left in the cup (in milliliters) as a function of time (in seconds) is graphed. How long did it take Sean to finish the slushy?
______ seconds
Answers
Answer:
75 seconds
Step-by-step explanation:
The graph intersects the x axis at 75 seconds. That means y = 0, and y is the amount remaining (in ml).
After 75 seconds the amount of slushy left in the cup becomes zero the answer is 75 seconds.
What is a line graph?A line graph is a type of graph where the data points are connected by segments of straight lines.
We have a line graph shown in the picture.
Sean is drinking a slushy as fast as he can. The amount of slushy left in the cup (in milliliters) as a function of time (in seconds) is graphed.
As we can see the amount of slushy left in the cup is decreasing as the time increases.
At time = 75 seconds
The amount of slushy left in the cup = 0
Thus, after 75 seconds the amount of slushy left in the cup becomes zero the answer is 75 seconds.
Learn more about the line graph here:
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#SPJ2
Graph the image of the polygon after a reflection in the line y= −x.
Answers
Answer:
If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed).
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.
rationalize the denominator 4√2/4√5
Answers
Answer:
answer given in the phot
The formula that relates the length of a ladder, L, that leans against a wall with distance d from the base of the wall and the height h that the ladder reaches up the wall is L = StartRoot d squared h squared EndRoot. What height on the wall will a 15-foot ladder reach if it is placed 3. 5 feet from the base of a wall?.
Answers
The height on the wall a 15-foot ladder will reach if it is placed 3. 5 feet from the base of a wall is 14.6 feet.
Using Pythagoras theorem,
c² = a² + b²
where
c = hypotenuse
a and b are the other two legs
The ladder length represent the hypotenuse sides
The distance of the ladder to the base of the wall is one of the leg.
The height on the wall the 15 ft ladder reach is the other leg
Therefore,
a² = 15² - 3.5²
a² = 225 - 12.25
a = √212.75
a = 14.5859521458
a ≈ 14.6 feet
learn more on Pythagoras theorem: https://brainly.com/question/13734303?referrer=searchResults
Answer:
C
Step-by-step explanation:
just took the test trust cuties
For homework Tina is asked to write down the opposite value for each number listed which comparison did Tina write incorrectly
Answers
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.
The comparison labelled X is incorrect because -(-9) = 9. Opposite of 9 is -9.
Therefore, in writing down the opposite value of each number, the comparison Tina wrote incorrectly is: Comparison X
Learn more about opposite value of a number on:
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Please help me with this
Answers
Answer:
A and F
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.
b=−30.50-0.20x
What is the remaining balance on the card if Jenny bought 30 prints?
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
Total cost of the prints = cost per print x number of prints bought
0.20 x 30 = $6
Balance = $30.50 - $6 = $24.50
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f(x)=1/2(x-2)(x+3)^3
Answers
Answer:y=
1
2
x4+
7
2
x3+
9
2
x2+
−27
2
x−27
Step-by-step explanation:
PLEASE NO LINKS AND NO NEGATIVITY
Answers
A=L*W
L=8x-2
W=4
A=(8x-2)(4)
A=32x-8
if m angle 2 =70, find m angle 6
Answers
m angle 6= 210
I'm not sure about this question
Can no one really help me? I've posted a question worth 50 points and people who are just in it for the points keep responding...I need help this is literally very important to my grade and no one is helping me please help
Answers
Answer:
repost so i can see
Step-by-step explanation:
repost so i can seee
Answer:
wheres the answer???
Step-by-step explanation:
cant find the answer thats all
Solve the following compound inequality: 4 less-than-or-equal-to x + 4 less-than-or-equal-to 12.
Answers
Answer:
Step-by-step explanation:
A. x mayor que 5
I want a picture of magnitic force and electric force
Answers
Answer:
Step-by-step explanation:
123
1.
In a proportional relationship between the variables x and y, which of the following
expressions would be constant?
(1) x + y
(3) xy
(2) y-x
(4)Y/x
Yes
Answers
Answer:
y/x
Step-by-step explanation:
If x is proportional to y, then:
y = kx, where k is a constant
This can be rearranged to give:
k = y/x
As mentioned, k is a constant, therefore, the answer is y/x
A typical tip at a restaurant is 18% of the total bill. If the bill is $60, what would the typical tip be?
The typical tip would be $_________.
Answers
What is equivalent to -2/5x=-4
A. -20
B. 1
C. -10
D. -8
E. X= -8/5
Answers
Answer:
10
Step-by-step explanation:
Multiply each side by the reciprocal, -5/2
x = -4 * -5/2
x = 20/2
x = 10