If A = {x | x is an even integer}, B = {5, 6, 7, 8}, list the elements of the set A U B
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ANSWER
B) A rectangle with a length of 15 cm and a width of 9 cm.
EXPLANATION
The given rectangle, A, has length, 10cm and its width is 6cm.
The rectangle that is similar to rectangle A, has the corresponding sides in the same proportion.
For option A, the triangle has length 9cm and width 6cm.
The ratio of the corresponding sides are:
Since the ratios are not equal, the two triangles are not similar.
For the triangle in option B, the length is 15cm and the width is 9cm.
The ratio of the corresponding sides are:
Since the sides of the triangle are in the same proportion, the two triangles are similar.
For option C, the proportions are not the same.
The proportions are not the same for the triangle in option D.
B) A rectangle with a length of 15 cm and a width of 9 cm.
EXPLANATION
The given rectangle, A, has length, 10cm and its width is 6cm.
The rectangle that is similar to rectangle A, has the corresponding sides in the same proportion.
For option A, the triangle has length 9cm and width 6cm.
The ratio of the corresponding sides are:
Since the ratios are not equal, the two triangles are not similar.
For the triangle in option B, the length is 15cm and the width is 9cm.
The ratio of the corresponding sides are:
Since the sides of the triangle are in the same proportion, the two triangles are similar.
For option C, the proportions are not the same.
The proportions are not the same for the triangle in option D.
Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line ⇒ 1st
Step-by-step explanation:
Parallel lines have:
- Same slopes
- Different y-intercepts
The formula of the slope of a line which passes through points and
is
∵ The given line passes through points (-12 , -2) and (0 , -4)
∴ = -12 ,
= 0
∴ = -2 ,
= -4
- Use the formula of the slope above to find the slope of the given line
∵
∴ The slope of the given line is
∵ The two lines are parallel
∴ Their slopes are equal
∴ The slope of the parallel line =
∵ The parallel line passes through point (0 , 6)
- The form of the linear equation is y = mx + b, where m is the slope
and b is the y-intercept (y when x = 0)
∵ m = and b = 6
∴ The equation of the parallel line is y = x + 6
Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line
Point (-12 , 8)
∵ x = -12 and y = 8
∵ y = (-12) + 6
∴ y = 2 + 6 = 8
- The value of y is equal the y-coordinate of the point
∴ Point (-12 , 8) is on the line
Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line
Learn more:
You can learn more about the equations of parallel lines in brainly.com/question/9527422
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