You are given rectangle ABCD on the grid shown and are told that the figure is to be dilated from the origin, but you are not to
ld by what factor. Which COULD be the new coordinates of point D?
A) (-8, -4)
B) (-2, -2)
C) (-2, -4)
D) (2, 4)
A) (-8, -4)
B) (-2, -2)
C) (-2, -4)
D) (2, 4)
1 answer:
Answer:
The new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)
Step-by-step explanation:
The rectangle ABCD on the grid shown is attached below.
From the grid, it is clear that the coordinates of point D are (-4, -4)
i.e. D(-4, -4)
As we are told that the figure is to be dilated from the origin.
A dilation tends to stretch or shrink the original figure, depending upon scale factor.
- If scale factor > 1, then the image gets enlarged
- If the scale factor < 1, the image gets reduction
When we dilate a figure from the origin by any scale factor, the new coordinates of the image can be obtained by multiplying the scale factor with the coordinates of the original object/figure.
As the the coordinates of point D are (-4, -4). If we dilate the figure by a scale factor of 1/2, the new new coordinates of point D would be:
P(x, y) → P'(1/2x, 1/2y)
D(-4, -4) → D'(-4/2, -4/2) or D'(-2, -2)
Therefore, the new coordinates of point D(-4, -4) after the dilation by a scale factor of 1/2 will be: D'(-2, -2)
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Answer:
Step-by-step explanation:
Given is a function in x as
We have to find the zeroes of the function
Since this is a cubic function this function has three zeroes.
Let us try to factorise this function by grouping two terms together.
=
Equate each factor to 0 to find zeroes as
Let
x--------> <span>the number of sandwich lunch specials sold
y-------> </span><span>the number of wrap lunch specials sold
we know that
2x+3y=1470
Part 1) </span><span>Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
we know that
</span>the equation to slope-intercept form is of the form
y=mx+b
so
2x+3y=1470------> solve for y
3y=1470-2x-----> divide by 3 both sides
y=(-2/3)x+1470/3
y=(-2/3)x+490
the slope m=-2/3
the y-intercept is 490
Part 2) <span>Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
</span><span>the slope is -2/3 and the y-intercept is 490
Plot the point (0,490)------> the y-intercept.
With the slope count 3 squares to the right and 2 squares down and plot that point, which is (0+3,490-2)--------> (3,488)
Draw a line through the two points
Part 3) </span><span>Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
In function notation, the equation is:
f(x)=(-2/3)x+490
The graph of this function represents how the value of the function varies as the value of x varies. Looking back at the question context, this graph specifically represents how many wraps could have been sold at each number of sandwich sales, in order to maintain the same profit of $1470.</span><span>
Part 4) </span>Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology
using a graph tool
see the attached figure
Part 5) Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different
we have that
2x+3y=1593
3y=1593-2x--------> y=(-2/3)x+531
slope=(-2/3)
y intercept=531
therefore
similarities : same slope
differences : y intercepts are different.
<span>This is basically telling me that the lines are parallel lines because they have the same slope.
</span>
6) Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations
Select two points on the line and write down their coordinates
Let
A( 0,300) B (450,0)
a) find the slope
m=(y2-y1)/(x2-x1)----> m=(0-300)/(450-0)----> m=-2/3
b) with the slope m=(-2/3) and the point A (0,300)
y-y1=m*(x-x1)-----> y-300=(-2/3)*(x-0)----> y=(-2/3)x+300
the answer Part 6) is
y=(-2/3)x+300
x--------> <span>the number of sandwich lunch specials sold
y-------> </span><span>the number of wrap lunch specials sold
we know that
2x+3y=1470
Part 1) </span><span>Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
we know that
</span>the equation to slope-intercept form is of the form
y=mx+b
so
2x+3y=1470------> solve for y
3y=1470-2x-----> divide by 3 both sides
y=(-2/3)x+1470/3
y=(-2/3)x+490
the slope m=-2/3
the y-intercept is 490
Part 2) <span>Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
</span><span>the slope is -2/3 and the y-intercept is 490
Plot the point (0,490)------> the y-intercept.
With the slope count 3 squares to the right and 2 squares down and plot that point, which is (0+3,490-2)--------> (3,488)
Draw a line through the two points
Part 3) </span><span>Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
In function notation, the equation is:
f(x)=(-2/3)x+490
The graph of this function represents how the value of the function varies as the value of x varies. Looking back at the question context, this graph specifically represents how many wraps could have been sold at each number of sandwich sales, in order to maintain the same profit of $1470.</span><span>
Part 4) </span>Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology
using a graph tool
see the attached figure
Part 5) Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different
we have that
2x+3y=1593
3y=1593-2x--------> y=(-2/3)x+531
slope=(-2/3)
y intercept=531
therefore
similarities : same slope
differences : y intercepts are different.
<span>This is basically telling me that the lines are parallel lines because they have the same slope.
</span>
6) Below is a graph that represents the total profits for a third month. Write the equation of the line that represents this graph. Show your work or explain how you determined the equations
Select two points on the line and write down their coordinates
Let
A( 0,300) B (450,0)
a) find the slope
m=(y2-y1)/(x2-x1)----> m=(0-300)/(450-0)----> m=-2/3
b) with the slope m=(-2/3) and the point A (0,300)
y-y1=m*(x-x1)-----> y-300=(-2/3)*(x-0)----> y=(-2/3)x+300
the answer Part 6) is
y=(-2/3)x+300
For this case we have the following equation:
The variables are:
t: time in hours
d (t): distance traveled in miles.
We evaluate the distance traveled after 4 hours.
So we have that for t = 4:
Answer:
d (4) = 68
This means that after 4 hours Joanna cycled for 68 miles total
The variables are:
t: time in hours
d (t): distance traveled in miles.
We evaluate the distance traveled after 4 hours.
So we have that for t = 4:
Answer:
d (4) = 68
This means that after 4 hours Joanna cycled for 68 miles total