Enter an algebraic expression for the word expression. The quotient of −8 and y
1 answer:
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Answer:
Bouquets of roses = 20
Bouquets of carnations = 08
Step-by-step explanation:
Let,
x be the bouquets of roses sold
y be the bouquets of carnations sold
According to given statement;
x + y = 28 Eqn 1
16x + 10y = 400 Eqn 2
Multiplying Eqn 1 by 16
16(x+y=28)
16x + 16y = 448 Eqn 3
Subtracting Eqn 2 from Eqn 3
(16x+16y)-(16x+10y) = 448 - 400
16x + 16y - 16x - 10y = 48
6y = 48
Dividing both sides by 6
Putting y=8 in Eqn 1
x + 8 = 28
x = 28 - 8
x= 20
Hence,
Bouquets of roses = 20
Bouquets of carnations = 08
Length of segment of the hypotenuse adjacent to the shorter leg is 5 inches and the length of the altitude is 3 inches.
Step-by-step explanation:
Step 1: Let the triangle be ΔABC with right angle at B. The altitude drawn from B intersects the hypotenuse AC at D. So 2 new right angled triangles are formed, ΔADB and ΔCDB.
Step 2: According to a theorem in similarity of triangles, when an altitude is drawn from any angle to the hypotenuse of a right triangle, the 2 newly formed triangles are similar to each other as well as to the bigger right triangle. So ΔABC ~ ΔADB ~ ΔCDB.
Step 3: Identify the corresponding sides and form an equation based on proportion. Let the length of the altitude be x. Considering ΔABC and ΔADB, AB/DB = AC/AB
⇒ 6/x = 12/6
⇒ 6/x = 2
⇒ x = 3 inches
Step 4: To find length of the hypotenuse adjacent to the shorter leg (side AB of 6 inches), consider ΔADB.
⇒
⇒
⇒
⇒
⇒
⇒AD = 5 inches