the difference between two numbers is 9. the first number plus twice the other number is 27. find the two numbers
2 answers:
So,
Let's translate this into mathematical form.
x - y = 9
x + 2y = 27
Elimination by Addition
Divide both sides of the second equation by 2
Add the two equations together
Multiply both sides by
Substitute
15 - y = 9
Subtract 15 from both sides
-y = -6
y = 6
Substitute
15 - 6 = 9
9 = 9 This checks.
15 + 2(6) = 27
Distribute
15 + 12 = 27
27 = 27 This also checks.
S = {(15,6)}
Let's translate this into mathematical form.
x - y = 9
x + 2y = 27
Elimination by Addition
Divide both sides of the second equation by 2
Add the two equations together
Multiply both sides by
Substitute
15 - y = 9
Subtract 15 from both sides
-y = -6
y = 6
Substitute
15 - 6 = 9
9 = 9 This checks.
15 + 2(6) = 27
Distribute
15 + 12 = 27
27 = 27 This also checks.
S = {(15,6)}
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the Answer:
Notice that the "image" triangles are on the opposite side of the center of the dilation (vertices are on opposite side of O from the preimage). Also, notice that the triangles have been rotated 180º.
Step-by-step explanation:
A dilation is a transformation that produces an image that is the same shape as the original but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. The center of dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.
Note:
A dilation is NOT referred to as a rigid transformation (or isometry) because the image is NOT necessarily the same size as the pre-image (and rigid transformations preserve length).
What happens when scale factor k is a negative value?
If the value of scale factor k is negative, the dilation takes place in the opposite direction from the center of dilation on the same straight line containing the center and the pre-image point. (This "opposite" placement may be referred to as being a " directed segment" since it has the property of being located in a specific "direction" in relation to the center of dilation.)
Let's see how a negative dilation affects a triangle:
Notice that the "image" triangles are on the opposite side of the center of the dilation (vertices are on opposite side of O from the preimage). Also, notice that the triangles have been rotated 180º.
