Answer:
18
Step-by-step explanation:
Number of pieces = Length of ribbon/Length of each piece
= (13½) ÷ (¾)
Convert the mixed number to an improper fraction
No. = (²⁷/₂) ÷ (¾)
Invert the proper fraction and change division to multiplication
No. = ²⁷/₂ × ⁴/₃
Cancel the 2s
No. = 27 × ⅔
Cancel the 3s
No. = 9 × 2
No. = 18
Sam can cut 18 pieces of ribbon.
Let the length be x and the width be y:
Area=x*y=600
thus
x=600/y
Perimeter=2(L+W)
100=2(x+y)
substituting the value of x we obtain:
100=2(600/y+y)
solving for y we shall have:
50=600/y+y
50y=600+y^2
thus
y^2-50y+600=0
solving the quadratic we obtain:
y=20 or y=30
thus the length=30 ft and the width=20 ft
Answer:
72 degrees.
Step-by-step explanation:
As it is a right angled triangle and if the smaller acute angle = x degrees then:
x + 4x + 90 = 180.
5x = 90
x = 18 degrees.
The larger acute angle = 4x = 4*18
= 72 degrees.
Step 1. Simplify
7x^2 - 8x - 4 - 2x^2 + 3x + 5 + 5x^2 - 10x - 8
Step 2. Collect like terms
(7x^2 - 2x^2 + 5x^2) + (-8x + 3x - 10x) + (-4 + 5 - 8)
Step 3. Simplify
10x^2 - 15x - 7
