the line y=2x-4 is dilated bt a scale factor of 3/2 and centered at the origin. Write an equation that represent that image of t
2 answers:
Answer:
Step-by-step explanation:
Since, If (x,y) represents the coordinates of a line, then after dilation about the origin by the scale factor k, the coordinates of the resultant line will get by the rule,
Here, The equation of the given line is,
y = 2x - 4
x-intercept and y-intercept of the line are (2,0) and (0,-4) respectively,
Hence, the line y = 2x - 4 will be passes through the points (2,0) and (0,-4),
By the above property,
The dilated line about the origin will be passes through the points (3,0) and (0,-6), ( Because (3/2× 2, 3/2×0) = (3,0) and (3/2×0, 3/2×-4) = (0,-6) )
Hence, the equation of transformed line after dilation,
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Question 1:
The generic equation of the line is given by:
Where,
m: slope of the line
b: cutting point with the y axis
Substituting values we have:
Answer:
an equation for the line with slope 2/3 and y-intercept is:
Question 2:
The standard equation of the line is given by:
Where,
m: slope of the line
(xo, yo): ordered pair that belongs to the line
The slope of the line is:
Substituting values:
We choose an ordered pair:
Substituting values:
Rewriting:
Answer:
An equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1) is:
Question 3:
For this case, since the variation is direct, then we have an equation of the form:
Where,
k: constant of variation.
We then have the following equation:
Rewriting we have:
Therefore, the constate of variation is given by:
Answer:
the constant of variation is:
Question 4:
For this case, since the variation is direct, then we have an equation of the form:
Where,
k: constant of variation.
We must find the constant k, for this we use the following data:
y = 24 when x = 8
Substituting values:
Clearing k we have:
Therefore, the equation is:
Thus, substituting x = 10 we have that the value of y is given by:
Answer:
the value of y when x = 10 is:
The generic equation of the line is given by:
Where,
m: slope of the line
b: cutting point with the y axis
Substituting values we have:
Answer:
an equation for the line with slope 2/3 and y-intercept is:
Question 2:
The standard equation of the line is given by:
Where,
m: slope of the line
(xo, yo): ordered pair that belongs to the line
The slope of the line is:
Substituting values:
We choose an ordered pair:
Substituting values:
Rewriting:
Answer:
An equation in slope-intercept form for the line that passes through the points (1, -3) and (3,1) is:
Question 3:
For this case, since the variation is direct, then we have an equation of the form:
k: constant of variation.
We then have the following equation:
Answer:
the constant of variation is:
Question 4:
For this case, since the variation is direct, then we have an equation of the form:
k: constant of variation.
We must find the constant k, for this we use the following data:
y = 24 when x = 8
Substituting values:
Therefore, the equation is:
the value of y when x = 10 is:
Answer:
2388.16 in³
Step-by-step explanation:
1) find volume of cylinder
formula: πr²h
given:
π = 3.14
r = 8/2 = 4 in
h = 9 in
2) find volume of cuboid
formula: length × width × height
given:
length = 16 in
width = 11 in
height = 11 in
total volume of figure
= volume of cylinder + volume of cuboid
= 452.16 in³ + 1936 in³
= 2388.16 in³