Answer:
false
Step-by-step explanation:
-7=(-5)-(-12)
-7=-5+12
-7=7 is not true
I believe it would be 1% of change
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First, set up a proportion.
Then, cross multiply and solve.
Answer:
The drum capacity is 180 liters.
Step-by-step explanation:
Let the capacity of the drum be c. Then the contents of the drum at the beginning are (3/4)c, and
if 30 liters are drawn out, then the contents are (3/4)c - 30 liters = (7/12)c.
Here the LCD is 12, and so we have (9/12)c - (7/12)c = 30 liters, or
(2/12)c = 30 liters, or c = (12/2)(30 liters) = 180 liters
The drum capacity is 180 liters.
Options:
a) If corresponding pairs of sides and corresponding pairs of angles of two triangles are congruent, then the triangles can be matched up exactly using rigid motions.
b) If two triangles can be matched up exactly using rigid motions, then the corresponding pairs of sides and corresponding pairs of angles of the triangles are congruent.
c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
d) If corresponding pairs of sides and corresponding pairs of angles of two triangles are not congruent, then the triangles are not congruent.
Answer:
c) Two triangles can be matched up exactly using rigid motions if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Step-by-step explanation:
For both pairs of triangles, what you proved is how to use rigid motions (i.e. rigid transformations) to make congruent shapes.
When rigid transformation is applied to a shape, the image (i.e. result) of the transformation produces an exact shape (i.e. equal corresponding angles and corresponding sides), meaning that the side lengths and the angles of the preimage (before transformation) and the image (after transformation) is unaltered.
<em>Option (c) is true</em>
