Monday: Law of Detachment
Determine if Statement 3 is a valid conclusion using Law of Detachment. If it is, write
the conclusion. If not, write invalid.
1. (1) If an angle measures more than 90°, then it is not acute.
(2) MZABC = 120°
(3) ZABC is not acute.
2. (1) All 45° angles are congruent.
(2) ZAB
(3) ZA and ZB are 45°
3. (1) If you order the apple pie, then it will be served with ice cream.
(2) Matthew ordered the apple pie.
(3) Matthew was served ice cream.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

he has 140 chickens because he has 10 times more chickens than ducks and he has 14 ducks so 14*10=140