Given that △XYZ is mapped to △X'Y'Z' using the rules (x, y)→(x+5, y−3) followed by (x, y)→(−x, −y) .
We know that (x,y) => (x+h,y+k) type operation represents translation so rule (x, y)→(x+5, y−3) will cause translation.
We know that (x,y) => (-x,-y) type operation represents rotation about origin so rule (x, y)→(−x, −y) will cause rotation.
So combining both results and comparing with given choices. we find that only 1st choice "△XYZ is congruent to △X'Y'Z' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions."
is correct.
Answer:
3/9
Step-by-step explanation:
3/9 = 0.33333333
0.333333
is a reeating decimal
Answer - Width 23
Length - 26
W = Width
L + 3 = Length
Perimeter = 2L = 2W
98 = 2(W + 3) + 2W
98 = 2W + 6 + 2W
98 = 4W + 6
92 = 4W
W = 92/4
W = 23
Width is 23 inches
Length is 3 more -- 23 + 3 = 26
We can double check our work:
26 + 26 + 23 + 23 = 98 Inches
Best of luck,
The Artemis Wolf
Solution :
Given data :
The mean length of the steel rod = 29 centimeter (cm)
The standard deviation of a normally distributed lengths of rods = 0.07 centimeter (cm)
a). We are required to find the proportion of rod that have a length of less than 28.9 centimeter (cm).
Therefore, P(x < 28.9) = P(z < (28.9-29) / 0.07)
= P(z < -1.42)
= 0.0778
b). Any rods which is shorter than 
cm or longer than 
cm that re discarded.
Therefore,
P (x < 24.84 or 25.16 < x) = P( -59.42 < z or -54.85)
= 1.052
