The answers are 1) D. 43 items and 2) B. 58 seconds.
Step-by-step explanation:
Step 1; An experienced cashier takes a time of 2 seconds per item and another 40 seconds for processing the customer's payment. So if it took 2 minutes 6 seconds which equals ( 2× 60 ) + 6 = 126 seconds for a customer. Out of these 126 seconds, the last 40 seconds were to process the customer's payment so 126 seconds - 40 seconds = 86 seconds. So it took 86 seconds to scan the items and as it takes 2 seconds per item we divide 86 by 2 to get the number of items. So 86 / 2 = 43 items which is option D.
Step 2; Anna brought 31 items and due to some glitch, the total time took 2 minutes. So for 31 items, it took the cashier 31 × 2 = 62 seconds, 1 minute 2 seconds. So out of the 2 minutes, 1 minute 2 seconds were used to scan the items. So the remaining time was 2 minutes (120 seconds) - 1 minute 2 seconds (62 seconds) = 58 seconds which was the processing time. So option B is the answer.
The coordinates of point R of the given line segment are (-3.5, -7)
<h3>How to partition a line segment?</h3>
We are given the coordinates;
L (-8,-10) to M (4,-2)
We are told that they are partitioned in the ratio 3 to 5.
Thus;
The coordinates of R divide directed line segment from L (-8,-10) to M (4,-2) in ratio 3:5will be :
x = [3(4) + 5(-8)]/(3 + 5)
x = -3.5
y = [3(-2) + 5(-10)]/(3 + 5)
y = -7
Thus, the coordinates of point R are (-3.5, -7)
Read more about Line segment at; brainly.com/question/13293903
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(7) m∠A = 52°
(8) m∠B = 117°
Solution:
(7) Let us first define the supplementary and complementary angles.
Supplementary angles: Two angles are said to be supplementary angles if their sum is add up to 180°
Complementary angles: Two angles are said to be complementary angles if their sum is add up to 90°
Given supplement of 142° = 180° – 142°
= 38°
Complement of ∠A = Supplement of 142°
⇒ Complement of ∠A = 38°
Measure of ∠A = 90° – 38°
= 52°
Hence m∠A = 52°.
(8) Given complement of 27° = 90° – 27°
= 63°
Supplement of ∠B = Complement of 27°
⇒ Supplement of ∠B = 63°
Measure of ∠B = 180° – 63°
= 117°
Hence m∠B = 117°.
