Answer:
(-∞, -4] ∪ [5, ∞)
Step-by-step explanation:
Hi!
Alright, so greater (or less) than or equal to is denoted with a bracket.
If x is less than or equal to -4, then the bracket is on the left side.
(___, -4]
Because x is <em>any</em> number under or equal to -4, x can range from negative infinity. However, we use a parentheses for infinity because infinity can never truly be reached.
So, x 
-4 = (-∞, -4]
X
5
Equal to = bracket
X is any number above 5, so
[5, ∞)
Because we want both of these, we use the union sign (∪)
so,
= (-∞, -4] ∪ [5, ∞)
Answer:
PR = 5 because LP + PR = LR according to the Segment Addition Postulate, and 7 + 5 = 12 using substitution
Step-by-step explanation:
The naming of the segments suggests that point P is between L and R, so that ...
LP + PR = LR
This corresponds to the last choice.
_____
<em>Comments on the alternate interpretation</em>
On the other hand, if point L is between P and R, then the segments are PL and LR. The Segment Addition Postulate would tell you that ...
PL + LR = PR
The Reflexive Property of Congruence would tell you that PL = LP. The Substitution Property would tell you LP can be substituted into this equation, making it ...
LP + LR = PR
and by the commutative property, ...
LR + LP = PR.
Multiple properties of addition and congruence are involved with this interpretation, which more or less matches the third choice. That is, the simple explanation of answer choice 3, by itself, is insufficient to explain why the length of PR should be considered to be 19, not 5.
The ratio of the volumes is equal to the scale factor cubed.
![\frac{V_1}{V_2}=k^3 \\ \\ \frac{320 \ cm^3}{1080 \ cm^3}=k^3 \\ \frac{8}{27}=k^3 \\ k=\sqrt[3]{\frac{8}{27}} \\ \boxed{k=\frac{2}{3}} \Leftarrow \hbox{answer B}](https://tex.z-dn.net/?f=%5Cfrac%7BV_1%7D%7BV_2%7D%3Dk%5E3%20%5C%5C%20%5C%5C%0A%5Cfrac%7B320%20%5C%20cm%5E3%7D%7B1080%20%5C%20cm%5E3%7D%3Dk%5E3%20%5C%5C%0A%5Cfrac%7B8%7D%7B27%7D%3Dk%5E3%20%5C%5C%0Ak%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B8%7D%7B27%7D%7D%20%5C%5C%0A%5Cboxed%7Bk%3D%5Cfrac%7B2%7D%7B3%7D%7D%20%5CLeftarrow%20%5Chbox%7Banswer%20B%7D)
