Answer:
H(x) = 0.85x -2.00
Step-by-step explanation:
The original price of an item, x dollars, is discounted by 15%.
Let x be the original price of an item
15% =0.15 discount , so discounted amount is 0.15x
Now we subtract discounted amount from original amount
x - 0.15x = 0.85x
A coupon for $2.00 off is applied to the discounted price.
$2.00 is off, so we subtract 2
Function becomes H(x) = 0.85x -2.00
The equation would be y = 3/5x + 3
Answer:
Step-by-step explanation:
Urn U1: 3 red and 2 yellow marbles, in total 5 marbles.
The probability to select red marble is
Urn U2: 3 red and 7 yellow marbles, in total 10 marbles.
The probability to select red marble is
Urn U1: 1 red and 4 yellow marbles, in total 5 marbles.
The probability to select red marble is
The probability to choose each urn is the same and is equal to
Thus, the probability that the marble is red is
Diagram for part A and part C is attached herewith.
Solving for part B:-
Given is the circle O. We start with drawing two radii OA and OC, then we join two points A and C to make a chord AC of the circle. Now The radius of the circle intersects the chord AC at point B such that it bisects AC into two equal parts AB and BC. Now we have two triangles ΔOBA and ΔOBC. In these two triangles, we have OA=OC (radii of circle), OB=OB (reflexive property), and BA=BC (given in the question). Using SSS congruency of triangles we can say ΔOBA≡ΔOBC and using CPCTC, we can conclude ∡OBA=∡OBC (=90°). Hence OB⊥AC i.e. OB is perpendicular to AC.
Solving for part D:-
Given is the circle O. We start with drawing two radii OA and OC, then we join two points A and C to make a chord AC of the circle. Now The radius of the circle intersects the chord AC at point B such that AB is perpendicular to AC i.e. ∡B=90°. Now we have two Right triangles ΔOBA and ΔOBC. In these two triangles, we have OA=OC (radii of circle), OB=OB (reflexive property). Using HL congruency of right triangles we can say ΔOBA≡ΔOBC and using CPCTC, we can conclude BA=BC. Hence OB bisects AC into AB=BC.