It is Figures A,B, and C. Answer D is not a polygon.
Answer:
i. LM || NO (converse alternate interior angle theorem)
ii. <1 ≅ <2 (alternate interior angle theorem)
Step-by-step explanation:
Two or more lines are said to be parallel if they do not meet when extended, even till infinity.
Alternate angles are said to be equal in measure.
Given that;
<1 ≅ < 3,
Since <2 ≅ <3 (alternate interior angle theorem)
Then,
<1 ≅ <2 (transitive property)
Also,
<1 ≅ <2 (alternate interior angle theorem)
Therefore since <1 ≅ <2, thus;
LM || NO (converse alternate interior angle theorem)
Answer:
Step-by-step explanation:
Let the total number of votes to choose a color = x
Number of votes for blue = 
Remaining votes = x -
= 
= 
Votes for green = 
= 
= 
Finally remaining votes = 
= 
= 
= 
Since these votes are for red therefore,
= 48
x = 48×6
= 288
a) Votes for blue are 
Therefore, exact number for blue votes = 
= 5×36
= 180
b). Votes for green = 
= 
= 60
c). Since 25 students were absent on that day of the vote, number of students at Riverside Elementary School = 288 + 25
= 313
d). Since seven tenths of the votes for blue were made by the girls.
Therefore, number of girls voted for blue = 
= 7×18
= 126
Since total votes made = 288
Therefore, half of the votes made = 
= 144
Now it's clear that number of votes made by girls is less than half of all the votes.
e). 126 girls voted for blue.
Answer:
D) Abner can spend $60 per month on school clothes and $20 per month on gym clothes and stay within his budget.
Step-by-step explanation:
In the problem it states that Abner will spend 3 times more on (s)school clothes than (g) gym clothes.
So it would appear as s ≥ 3g.
If we plug in $60 as s (school clothes) and $20 as g (gym clothes), the statement is true.
60 ≥ 3(20)
60 ≥ 60. These numbers make the linear system true.
If you have trouble with this, an easy way to find this answer is simply creating the linear system that represents the problem, (he will buy 3 times more school clothes than gym clothes) s ≥ 3g and plug in each variable from the answer choices until you find the variables that make the linear system true.
Answer:
b. (1, 3, -2)
Step-by-step explanation:
A graphing calculator or scientific calculator can solve this system of equations for you, or you can use any of the usual methods: elimination, substitution, matrix methods, Cramer's rule.
It can also work well to try the offered choices in the given equations. Sometimes, it can work best to choose an equation other than the first one for this. The last equation here seems a good one for eliminating bad answers:
a: -1 -5(1) +2(-4) = -14 ≠ -18
b: 1 -5(3) +2(-2) = -18 . . . . potential choice
c: 3 -5(8) +2(1) = -35 ≠ -18
d: 2 -5(-3) +2(0) = 17 ≠ -18
This shows choice B as the only viable option. Further checking can be done to make sure that solution works in the other equations:
2(1) +(3) -3(-2) = 11 . . . . choice B works in equation 1
-(1) +2(3) +4(-2) = -3 . . . choice B works in equation 2
