Answer: The correct answer is option (C); 25 feet
Step-by-step explanation: The standard of conversion between feet and yards is given as;
3 feet = 1 yard.
In other words, in every yard you will find times 3 feet. So in a spool of twine that contains four and two-thirds (4 2/3) yards of twine, conversion to feet would be given as;
X feet = (4 2/3) x 3
X feet = (14/3) x 3
X feet = 14
For the second spool the measurement is 11 feet of twine, so the total measurement would be derived as,
Spool 1 + Spool 2 = Total
14 + 11 = Total
25 = Total
Hence, the total measurement of twine would be 25 ft.
Answer:
x = 8.69
Step-by-step explanation:
we know that the perimeter of the dodecagon is 54, so each edge will be 54/12
54/12 = 4.5 cm
if we draw the lines to remove 6 vertices and form a hexagon, 6 triangles with 2 sides of 4.5 cm are formed.
we know that the angle of each vertex is 150 ° because it is a dodecagon
if we apply the law of cosines we can take the other side of the triangle, since we only need 2 side and the opposite angle to the side we want to know
a would be our x
b = 4.5
c = 4.5
A = 150°
a^2 = b^2 + c^2 - 2bc * cos (A)
x^2 = 4.5^2 + 4.5^2 - 2 * 4.5 * 4.5 * cos (150)
x^2 = 20.25 + 20.25 - 40.50 * -0.866
x^2 = 40.50 + 35.07
x = √ 75.57
x = 8.69
Answer:
D
Step-by-step explanation:
Expand factors using FOIL
A
(x + 1)² - x² = x² + 2x + 1 - x² = 2x + 1 ≠ 1 ← False
B
(5x - 2)² + 4 = 25x² - 20x + 4 + 4 = 25x² - 20x + 8 ≠ 25x² - 20x ← False
C
(x + 2y)(x - 2y) = x² - 4y² ≠ x² + 4xy - 4y² ← False
D
(2x + y)(- y - 2x) = - 2xy - 4x² - y² - 2xy = - 4x² - y² - 4xy ← True
