Ben is spending his summer driving across the country. He is going to spend the first day
just driving straight west. The table below shows the distance traveled as a function of time.
Graph this relationship on a coordinate plane
The graph of the data presented is shown in the attached image to this solution.
It shows that the relationship between distance travelled in miles and the time take in hours is D = 55t
The distance travelled with the corresponding time taken are presented in the table
Note: D - Distance travelled (miles)
t - Time (hours)
D | t
55 | 1
110 | 2
165 | 3
220 | 4
275 | 5
330 | 6
We are then told to plot these distance travelled on a graph with the time taken.
The distance travelled is plotted on the y-axis and the time in hours is plotted on the x-axis.
The image of the graph of this function will be attached to this answer
It is evident that the graph shows the relationship between the distance travelled and time taken to be D = 55t
Hope this Helps!!!
"We interrupt your regular programming to bring you a special report. This is Carl Sterns, news anchor for Channel 1. Thirty minutes ago, the notorious crime syndicate Acute Perps struck again at the world-famous Wright Bank. Street reporter Stuart Olsen is live on the scene in Geo City. Let's go to Stuart now to find out more about these breaking developments. Stuart, what can you tell us?" "Well, Carl, at approximately 8:30 this morning, a trio of masked men overwhelmed security forces here at the Wright Bank in Geo City and robbed the bank of all its cash. This is the third robbery in as many days orchestrated by Acute Perps. According to police sources, the gang robs three locations in three days and then goes unseen for weeks before they strike again. Because this is their third robbery, officials expect the robbers will go underground for the next few weeks. However, the police need the help of Geo City citizens in the meantime." "This gang traditionally hits the three locations during each crime spree using the same pattern. Police are asking citizens to predict the next three locations Acute Perps will attack. They will use the information to stake out these locations in the coming weeks and bring Acute Perps to justice. Back to you, Carl." "Thanks, Stuart. It looks like the city has some important work to do!"
First, construct a triangle as indicated by your choice in step 1 on a coordinate plane. For example, if you chose to use an obtuse scalene triangle translation to prove SSS Congruence, then you will construct an obtuse scalene triangle. Make sure to measure your triangle's angles and sides. You can use the concept of distance and slope to ensure your triangle satisfies the criteria indicated by your choice. Write down the original coordinates of this triangle. Next, identify and label three points on the coordinate plane that are the transformation of your original triangle. Make sure you use the transformation indicated within the scenario you selected. For example, if you chose to use an obtuse scalene triangle translation to prove SSS Congruence, then you complete a translation of your triangle. Remember, you only need to complete one transformation on your triangle. Write down these new coordinates for this second triangle. • If you chose Obtuse Scalene Triangle Translation to prove SSS Congruence, use the coordinates of your transformation along with the distance formula to show that the two triangles are congruent by the SSS postulate. You must show all work with the distance formula and each corresponding pair of sides to receive full credit. • If you chose Isosceles Right Triangle Reflection to prove ASA Congruence, use the coordinates of your reflection to show that the two triangles are congruent by the ASA postulate. You can use the distance formula to show congruency for the sides. To show an angle is congruent to a corresponding angle, you can use slope or your compass and straightedge. (Hint: Remember when you learned how to copy an angle?) You must show all work with the distance formula for the corresponding pair of sides, and your work for the corresponding angles to receive full credit. If you chose Equilateral Equiangular Triangle Rotation to prove SAS Congruence, use the coordinates of your rotation to show that the two triangles are congruent by the SAS postulate. You can use the distance formula to show congruency for the sides. To show an angle is congruent to a corresponding angle, you can use slope or your compass and straightedge. (Hint: Remember when you learned how to copy an angle?) You must show all work with the distance formula for the corresponding pair of sides, and your work for the corresponding angles, to receive full credit.
Provide an answer to the questions that match your selected scenario. Because you only completed one scenario, only one group of questions should be answered in complete sentences and submitted with your work. Obtuse Scalene Triangle Translation to prove SSS Congruence 1. Describe the translation you performed on the original triangle. Use details and coordinates to explain how the figure was transformed, including the translation rule you applied to your triangle. 2.
A) Find the sketch in attachment.
In the sketch, we have plotted:
- The length of the arena on the x-axis (90 feet)
- The width of the arena on the y-axis (95 feet)
- The position of the robot at t = 2 sec (10,30) and its position at t = 8 sec (40,75)
The origin (0,0) is the southweast corner of the arena. The system of inequalities to descibe the region of the arena is:
Since the speed of the robot is constant, it covers equal distances (both in the x- and y- axis) in the same time.
Let's look at the x-axis: the robot has covered 10 ft in 2 s and 40 ft in 8 s. There is a direct proportionality between the two variables, x and t:
So, this means that at t = 0, the value of x is zero as well.
Also, we notice that the value of y increases by (7.5 feet every second), so the initial value of y at t = 0 is:
So, the initial position of the robot was (0,15) (15 feet above the southwest corner)
The speed of the robot is given by
where d is the distance covered in the time interval t.
The distance covered is the one between the two points (10,30) and (40,75), so it is
While the time elapsed is
Therefore the speed is
The equation for the line of the robot is:
where m is the slope and q is the y-intercept.
The slope of the line is given by:
Which means that we can write an equation for the line as
where q is the y-intercept. Substituting the point (10,30), we find the value of q:
So, the equation of the line is
By prolonging the line above (40,75), we see that the line will hit the north wall. The point at which this happens is the intersection between the lines
and the north wall, which has equation
By equating the two lines, we find:
So the coordinates of impact are (53.3, 95).
The distance covered between the time of impact and the initial moment is the distance between the two points, so:
From part B), we said that the y-coordinate of the robot increases by 15 feet/second.
We also know that the y-position at t = 0 is 15 feet.
This means that the y-position at time t is given by equation:
The time of impact is the time t for which
y = 95 ft
Substituting into the equation and solving for t, we find:
The path followed by the robot is sketched in the second graph.
As the robot hits the north wall (at the point (53.3,95), as calculated previously), then it continues perpendicular to the wall, this means along a direction parallel to the y-axis until it hits the south wall.
As we can see from the sketch, the x-coordinate has not changed (53,3), while the y-coordinate is now zero: so, the robot hits the south wall at the point
The perimeter of the triangle is given by the sum of the length of the three sides.
- The length of 1st side was calculated in part F:
- The length of the 2nd side is equal to the width of the arena:
- The length of the 3rd side is the distance between the points (0,15) and (53.3,0):
So the perimeter is
The area of the triangle is given by:
is the base (the distance between the origin (0,0) and the point (53.3,0)
is the height (the length of the 2nd side)
Therefore, the area is:
The percentage of balls lying within the area of the triangle traced by the robot is proportional to the fraction of the area of the triangle with respect to the total area of the arena, so it is given by:
is the area of the triangle
is the total area of the arena
Therefore substituting, we find:
B. (3, -1)
Step-by-step explanation: I got a 100 on the test
The rule for a reflection across line y = -x: (x, y) → (-y, -x)
F(1, -3) → F'(3, -1)
Im selfish, an idiot, and a bÄstard im sorry.
Step-by-step explanation:a horizontal line goes straight left to right across.
i wish i could u
i wish i could u