Answer:
Step-by-step explanation:
When , the variable
will be removed from the equation (
). Therefore, we are left with
. Thus, when
, the given equation has no solutions.
Is it possible for a figure to have 90° rotational symmetry but not 180° rotational symmetry.
1 answer:
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Answer:
Slices of chocolate cakes = 60, Slices of lemon cakes = 10
Step-by-step explanation:
Given:
Total number of cakes, Lisa sliced = 12
Number of slices of each chocolate cake had = 6
Number of slices of each lemon cake had = 5
Total number of slices = 70
Question asked:
How many of each type of cake did she slice ?
Solution:
Let number of chocolate cakes =
Then, number of lemon cakes =
Now, given that, each chocolate cake had 6 slices:
By using unitary method:
1 chocolate cake had = 6 slices
chocolates cake had =
Similarly, each lemon cake had 5 slices:
1 lemon cake had = 5 slices
lemon cake had =
Now, as it is given that Lisa made 70 slices in total:
Total number of slices of 12 cakes = Total number of slices of chocolate cakes + Total number of slices of lemon cakes
By subtracting both sides by 60,
Total number of chocolate cakes = 10
Total number of lemon cakes = 12- 10 = 2
Total number of slices of chocolate cakes = number of chocolate cakes number of slices of each chocolate cake
Total number of slices of chocolate cakes =
Total number of slices of lemon cakes = number of lemon cakes number of slices of each lemon cake
Total number of slices of lemon cakes =
Therefore, total number of slices of chocolate cakes and lemon cakes are 60 and 10.
The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.
To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.
Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...
A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1
translated, that's CD║BC and CD⊥BC - contradictory; second half right
B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1
CD ║ AB and CD ⊥ AB - only the parallelogram half is right
C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1
CD║AB and CD⊥BC - that's TRUE
D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1
CD║AC and CD⊥AB - nope
Answer: C
The way I'd get the proper expression is with the dot product.
A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.
Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have so one side is CD. The other side must be BC or AD; AD would give
terms which don't appear among the answer, so let's go with BC.
The direction vectors are
For perpendicularity we need a zero dot product:
That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.